From fdf7616bb6e97c794ab2f7058e451ab932efde2c Mon Sep 17 00:00:00 2001 From: Rithik Rai Date: Sun, 16 Nov 2025 13:50:19 +0530 Subject: [PATCH 01/12] 16th nov, 1pm ist --- .gitmodules | 3 + Data/Global_Datasets/Christofides/CMT01.xml | 376 +++++ Data/Global_Datasets/Christofides/CMT02.xml | 551 +++++++ Data/Global_Datasets/Christofides/CMT03.xml | 726 +++++++++ Data/Global_Datasets/Christofides/CMT04.xml | 1076 +++++++++++++ Data/Global_Datasets/Christofides/CMT05.xml | 1419 +++++++++++++++++ Data/Global_Datasets/Christofides/CMT06.xml | 376 +++++ Data/Global_Datasets/Christofides/CMT07.xml | 551 +++++++ Data/Global_Datasets/Christofides/CMT08.xml | 726 +++++++++ Data/Global_Datasets/Christofides/CMT09.xml | 1076 +++++++++++++ Data/Global_Datasets/Christofides/CMT10.xml | 1419 +++++++++++++++++ Data/Global_Datasets/Christofides/CMT11.xml | 866 ++++++++++ Data/Global_Datasets/Christofides/CMT12.xml | 726 +++++++++ Data/Global_Datasets/Christofides/CMT13.xml | 866 ++++++++++ Data/Global_Datasets/Christofides/CMT14.xml | 726 +++++++++ Data/Global_Datasets/Christofides/readme.txt | 8 + Notebooks/Graph_Coarsening_Experiment.ipynb | 1309 +++++++++++++++ Src/QuantumLogistics/Graph.py | 19 + .../LogisticsRoute/GraphCoarsening.py | 434 +++++ .../LogisticsRoute/LogisticsGraph.py | 86 + .../LogisticsRoute/LogisticsRoute.py | 246 +++ .../LogisticsRoute/VrpRepGraph.py | 73 + .../LogisticsRoute/__init__.py | 0 .../GraphCoarsening.cpython-312.pyc | Bin 0 -> 14315 bytes .../LogisticsGraph.cpython-312.pyc | Bin 0 -> 4518 bytes .../LogisticsRoute.cpython-312.pyc | Bin 0 -> 9655 bytes .../__pycache__/VrpRepGraph.cpython-312.pyc | Bin 0 -> 4019 bytes .../__pycache__/__init__.cpython-312.pyc | Bin 0 -> 208 bytes .../__pycache__/vrprep_utils.cpython-312.pyc | Bin 0 -> 7023 bytes .../LogisticsRoute/vrprep_utils.py | 119 ++ .../RouteSolver/Encoders/ILPEncoder.py | 278 ++++ .../RouteSolver/Encoders/StandardEncoder.py | 63 + .../Encoders/StandardQUBOEncoders.py | 1 + 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Src/QuantumLogistics/interfaces.py | 276 ++++ Src/external/VRP-explorations | 1 + Src/setup.py | 62 + 54 files changed, 14843 insertions(+) create mode 100644 .gitmodules create mode 100644 Data/Global_Datasets/Christofides/CMT01.xml create mode 100644 Data/Global_Datasets/Christofides/CMT02.xml create mode 100644 Data/Global_Datasets/Christofides/CMT03.xml create mode 100644 Data/Global_Datasets/Christofides/CMT04.xml create mode 100644 Data/Global_Datasets/Christofides/CMT05.xml create mode 100644 Data/Global_Datasets/Christofides/CMT06.xml create mode 100644 Data/Global_Datasets/Christofides/CMT07.xml create mode 100644 Data/Global_Datasets/Christofides/CMT08.xml create mode 100644 Data/Global_Datasets/Christofides/CMT09.xml create mode 100644 Data/Global_Datasets/Christofides/CMT10.xml create mode 100644 Data/Global_Datasets/Christofides/CMT11.xml create mode 100644 Data/Global_Datasets/Christofides/CMT12.xml create mode 100644 Data/Global_Datasets/Christofides/CMT13.xml create mode 100644 Data/Global_Datasets/Christofides/CMT14.xml create mode 100644 Data/Global_Datasets/Christofides/readme.txt create mode 100644 Notebooks/Graph_Coarsening_Experiment.ipynb create mode 100644 Src/QuantumLogistics/Graph.py create mode 100644 Src/QuantumLogistics/LogisticsRoute/GraphCoarsening.py create mode 100644 Src/QuantumLogistics/LogisticsRoute/LogisticsGraph.py create mode 100644 Src/QuantumLogistics/LogisticsRoute/LogisticsRoute.py create mode 100644 Src/QuantumLogistics/LogisticsRoute/VrpRepGraph.py create mode 100644 Src/QuantumLogistics/LogisticsRoute/__init__.py create mode 100644 Src/QuantumLogistics/LogisticsRoute/__pycache__/GraphCoarsening.cpython-312.pyc create mode 100644 Src/QuantumLogistics/LogisticsRoute/__pycache__/LogisticsGraph.cpython-312.pyc create mode 100644 Src/QuantumLogistics/LogisticsRoute/__pycache__/LogisticsRoute.cpython-312.pyc create mode 100644 Src/QuantumLogistics/LogisticsRoute/__pycache__/VrpRepGraph.cpython-312.pyc create mode 100644 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(1979). The vehicle routing problem. In: Christofides, N., Mingozzi, A., Toth, P., Sandi, C. (Eds.), Combinatorial Optimization. Wiley, Chichester, pp. 315– 338. +------------------------------------------------------------------------------------------ +Remarks: + - : attribute type=0 for the depot and 1 for customer nodes + - : Unfortunately there is no standard rounding rule for this dataset in the literature. Since the VRP-REP format (V.1.0.0) requires a rounding rule we suggest to round the distances to the closest integer value, following the TSPLIB standard. Be aware, however, that this is not necessarily the rounding rule used by the algorithms which delivered the best known solutions for the dataset registered in the VRP-REP platform. + + + \ No newline at end of file diff --git a/Notebooks/Graph_Coarsening_Experiment.ipynb b/Notebooks/Graph_Coarsening_Experiment.ipynb new file mode 100644 index 0000000..4d49bc4 --- /dev/null +++ b/Notebooks/Graph_Coarsening_Experiment.ipynb @@ -0,0 +1,1309 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Graph Coarsening" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Please use python version <=3.12 because \"cplex\" library is not compatible with higher versions" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# # Importing required packages from Src\n", + "# %pip install -e ../Src --q" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# %pip install qiskit-algorithms" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# Importing Libraries\n", + "\n", + "import numpy as np\n", + "from time import time\n", + "import csv, os\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from QuantumLogistics import logisticsGraph, Route, StandardRouteSolver, ILPPulpEncoder, GurobiSolver, CBCSolver, DeltaCoarseningEngine, CompositeRouteSolver, VRPExplorationsEncoder, VRPExplorationsSolver\n", + "from QuantumLogistics.LogisticsRoute.VrpRepGraph import vrpRepGraph" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[i] Loading graph file c:\\Users\\USER\\Documents\\GitHub\\Quantum-Vehicle-Routing-Problems\\Data\\Global_Datasets\\Christofides\\CMT01.xml...\n", + "Customer_id | Customer_coordinates | Demand\n", + "[i] Graph loaded successfully!\n" + ] + } + ], + "source": [ + "# Loading the data\n", + "\n", + "project_root = os.path.abspath(os.path.join(os.getcwd(), os.pardir))\n", + "data_dir = os.path.join(project_root, \"Data\", \"Global_Datasets\", \"Christofides\")\n", + "\n", + "cmt_file = 'CMT01.xml'\n", + "file_path = os.path.join(data_dir, cmt_file)\n", + "\n", + "print(f\"[i] Loading graph file {file_path}...\")\n", + "logistics_network = vrpRepGraph(file_path)\n", + "print(\"Customer_id | Customer_coordinates | Demand\")\n", + "logistics_network.generate_graph()\n", + "\n", + "print(\"[i] Graph loaded successfully!\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[i] Setting graph configurations for CMT01.xml...\n", + "[i] Number of nodes: 51\n", + "[i] Truck Capacity: 160.0\n", + "[i] Depot Node: 0\n" + ] + } + ], + "source": [ + "# Graph & Config\n", + "\n", + "print(f'[[i] Setting graph configurations for {cmt_file}...')\n", + "number_of_nodes = logistics_network.n\n", + "truck_capacity = max(logistics_network.nodeCapacities)\n", + "depot_node = logistics_network.nodelist.vehicle['arrival_node']\n", + "\n", + "print(f'[i] Number of nodes: {number_of_nodes}')\n", + "print(f'[i] Truck Capacity: {truck_capacity}')\n", + "print(f'[i] Depot Node: {depot_node}')\n", + "\n", + "# Define the route configuration\n", + "number_trucks = 5 # From CMTDetails dictionary for CMT01\n", + "route_config = {'vehicles': number_trucks, 'depot': depot_node, 'truckCapacity': truck_capacity}\n", + "\n", + "# Define the coarsening configuration\n", + "coarsening_rate = 0.7 # Let's try a rate of 0.7\n", + "coarsen_config = {'coarsenRate': coarsening_rate, 'radiusCoefficient': 0.2}\n", + "coarsening_engine = DeltaCoarseningEngine(**coarsen_config)\n", + "\n", + "# Create the Route object\n", + "route = Route(logistics_network, coarseningEngine=coarsening_engine, **route_config)\n", + "route.coarsen = (coarsening_rate < 1.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# # Solving\n", + "\n", + "# # Define the solver we want to use (ILP with CBC backend)\n", + "# encoder = ILPPulpEncoder()\n", + "# solver_alg = CBCSolver()\n", + "# solver = StandardRouteSolver(encoder, solver_alg)\n", + "\n", + "# solver_config = {\"timeLimit\": 300} # Time limit in seconds for pulp-based solvers\n", + "# solver_config = {\"solver\": \"neal\"} \n", + "\n", + "# print(\"[i] Solving the route...\")\n", + "# solved_route, solve_time, cost = solver.solve(route, config=solver_config)\n", + "\n", + "# print(f\"[i] Solved in {solve_time:.2f} seconds with a total cost of {cost:.2f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# Solving\n", + "\n", + "# Define the solver we want to use\n", + "encoder = VRPExplorationsEncoder()\n", + "solver_alg = VRPExplorationsSolver()\n", + "solver = StandardRouteSolver(encoder, solver_alg)\n", + "\n", + "solver_config = {\"timeLimit\": 300, \"solver\": \"neal\"} # Time limit in seconds\n", + "\n", + "# print(\"[i] Solving the route...\")\n", + "# solved_route, solve_time, cost = solver.solve(route, config=solver_config)\n", + "\n", + "# print(f\"[i] Solved in {solve_time:.2f} seconds with a total cost of {cost:.2f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Coarsening Graph now\n", + "Final coarse graph has 35 nodes\n", + "RAW SOLVER OUTPUT: [[[0. 1. 0. ... 0. 1. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [1. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[1. 1. 0. ... 1. 1. 1.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[0. 1. 1. ... 1. 0. 1.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[1. 1. 0. ... 1. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[0. 1. 1. ... 0. 1. 1.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]]\n", + "[[[0. 1. 0. ... 0. 1. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [1. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[1. 1. 0. ... 1. 1. 1.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[0. 1. 1. ... 1. 0. 1.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[1. 1. 0. ... 1. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]\n", + "\n", + " [[0. 1. 1. ... 0. 1. 1.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " ...\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]\n", + " [0. 0. 0. ... 0. 0. 0.]]]\n" + ] + } + ], + "source": [ + "print(solver.solve(route, config=solver_config))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[i] Visualizing the solution...\n", + "--- Debugging visualiseSolution ---\n", + "Number of routes: 5\n", + "Route solution: [[(np.int64(0), np.int64(32)), (np.int64(32), np.int64(1)), (np.int64(1), np.int64(27)), (np.int64(27), np.int64(23)), (np.int64(23), np.int64(7)), (np.int64(7), np.int64(43)), (np.int64(43), np.int64(41)), (np.int64(41), np.int64(38)), (np.int64(38), np.int64(11)), (np.int64(11), np.int64(6)), (np.int64(6), np.int64(0))], [(np.int64(0), np.int64(18)), (np.int64(18), np.int64(4)), (np.int64(4), np.int64(13)), (np.int64(13), np.int64(42)), (np.int64(42), np.int64(48)), (np.int64(48), np.int64(26)), (np.int64(26), np.int64(8)), (np.int64(8), np.int64(5)), (np.int64(5), np.int64(0))], [(np.int64(0), np.int64(22)), (np.int64(22), np.int64(2)), (np.int64(2), np.int64(49)), (np.int64(49), np.int64(10)), (np.int64(10), np.int64(30)), (np.int64(30), np.int64(21)), (np.int64(21), np.int64(34)), (np.int64(34), np.int64(50)), (np.int64(50), np.int64(9)), (np.int64(9), np.int64(16)), (np.int64(16), np.int64(29)), (np.int64(29), np.int64(0))], [(np.int64(0), np.int64(24)), (np.int64(24), np.int64(47)), (np.int64(47), np.int64(12)), (np.int64(12), np.int64(46)), (np.int64(46), np.int64(28)), (np.int64(28), np.int64(31)), (np.int64(31), np.int64(19)), (np.int64(19), np.int64(25)), (np.int64(25), np.int64(14)), (np.int64(14), np.int64(0))], [(np.int64(0), np.int64(33)), (np.int64(33), np.int64(39)), (np.int64(39), np.int64(45)), (np.int64(45), np.int64(44)), (np.int64(44), np.int64(15)), (np.int64(15), np.int64(20)), (np.int64(20), np.int64(3)), (np.int64(3), np.int64(35)), (np.int64(35), np.int64(36)), (np.int64(36), np.int64(40)), (np.int64(40), np.int64(17)), (np.int64(17), np.int64(37)), (np.int64(37), np.int64(0))]]\n", + "Graph has 51 nodes.\n", + "Graph has coordinates of shape: (51, 2)\n", + "Vehicle 0, tour: [(np.int64(0), np.int64(32)), (np.int64(32), np.int64(1)), (np.int64(1), np.int64(27)), (np.int64(27), np.int64(23)), (np.int64(23), np.int64(7)), (np.int64(7), np.int64(43)), (np.int64(43), np.int64(41)), (np.int64(41), np.int64(38)), (np.int64(38), np.int64(11)), (np.int64(11), np.int64(6)), (np.int64(6), np.int64(0))]\n", + "Hop: from 0 to 32\n", + "Hop: from 32 to 1\n", + "Hop: from 1 to 27\n", + "Hop: from 27 to 23\n", + "Hop: from 23 to 7\n", + "Hop: from 7 to 43\n", + "Hop: from 43 to 41\n", + "Hop: from 41 to 38\n", + "Hop: from 38 to 11\n", + "Hop: from 11 to 6\n", + "Hop: from 6 to 0\n", + "Vehicle 1, tour: [(np.int64(0), np.int64(18)), (np.int64(18), np.int64(4)), (np.int64(4), np.int64(13)), (np.int64(13), np.int64(42)), (np.int64(42), np.int64(48)), (np.int64(48), np.int64(26)), (np.int64(26), np.int64(8)), (np.int64(8), np.int64(5)), (np.int64(5), np.int64(0))]\n", + "Hop: from 0 to 18\n", + "Hop: from 18 to 4\n", + "Hop: from 4 to 13\n", + "Hop: from 13 to 42\n", + "Hop: from 42 to 48\n", + "Hop: from 48 to 26\n", + "Hop: from 26 to 8\n", + "Hop: from 8 to 5\n", + "Hop: from 5 to 0\n", + "Vehicle 2, tour: [(np.int64(0), np.int64(22)), (np.int64(22), np.int64(2)), (np.int64(2), np.int64(49)), (np.int64(49), np.int64(10)), (np.int64(10), np.int64(30)), (np.int64(30), np.int64(21)), (np.int64(21), np.int64(34)), (np.int64(34), np.int64(50)), (np.int64(50), np.int64(9)), (np.int64(9), np.int64(16)), (np.int64(16), np.int64(29)), (np.int64(29), np.int64(0))]\n", + "Hop: from 0 to 22\n", + "Hop: from 22 to 2\n", + "Hop: from 2 to 49\n", + "Hop: from 49 to 10\n", + "Hop: from 10 to 30\n", + "Hop: from 30 to 21\n", + "Hop: from 21 to 34\n", + "Hop: from 34 to 50\n", + "Hop: from 50 to 9\n", + "Hop: from 9 to 16\n", + "Hop: from 16 to 29\n", + "Hop: from 29 to 0\n", + "Vehicle 3, tour: [(np.int64(0), np.int64(24)), (np.int64(24), np.int64(47)), (np.int64(47), np.int64(12)), (np.int64(12), np.int64(46)), (np.int64(46), np.int64(28)), (np.int64(28), np.int64(31)), (np.int64(31), np.int64(19)), (np.int64(19), np.int64(25)), (np.int64(25), np.int64(14)), (np.int64(14), np.int64(0))]\n", + "Hop: from 0 to 24\n", + "Hop: from 24 to 47\n", + "Hop: from 47 to 12\n", + "Hop: from 12 to 46\n", + "Hop: from 46 to 28\n", + "Hop: from 28 to 31\n", + "Hop: from 31 to 19\n", + "Hop: from 19 to 25\n", + "Hop: from 25 to 14\n", + "Hop: from 14 to 0\n", + "Vehicle 4, tour: [(np.int64(0), np.int64(33)), (np.int64(33), np.int64(39)), (np.int64(39), np.int64(45)), (np.int64(45), np.int64(44)), (np.int64(44), np.int64(15)), (np.int64(15), np.int64(20)), (np.int64(20), np.int64(3)), (np.int64(3), np.int64(35)), (np.int64(35), np.int64(36)), (np.int64(36), np.int64(40)), (np.int64(40), np.int64(17)), (np.int64(17), np.int64(37)), (np.int64(37), np.int64(0))]\n", + "Hop: from 0 to 33\n", + "Hop: from 33 to 39\n", + "Hop: from 39 to 45\n", + "Hop: from 45 to 44\n", + "Hop: from 44 to 15\n", + "Hop: from 15 to 20\n", + "Hop: from 20 to 3\n", + "Hop: from 3 to 35\n", + "Hop: from 35 to 36\n", + "Hop: from 36 to 40\n", + "Hop: from 40 to 17\n", + "Hop: from 17 to 37\n", + "Hop: from 37 to 0\n" + ] + }, + { + "data": { + "image/png": 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", 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These solvers are based on a BQM formulation of the Vehicle Routing Problem.\n", + "\n", + "DBSCAN Solver The DBSCAN solver first clusters the nodes using the DBSCAN algorithm and then solves a TSP for each cluster.\n", + "\n", + "Solution Partitioning Solver (SPS) The SPS solver first solves the VRP as a single TSP, and then partitions the resulting tour into multiple routes for the vehicles." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--- Running DBSCAN Solver ---\n", + "[[1, 2, 3, 4, 5, 7, 8, 9, 10], [6]]\n", + "Optimized Cost: 226.44844340905547\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--- Running Solution Partitioning Solver (SPS) ---\n", + "Optimized Cost: 204.38511424156133\n" + ] + }, + { + "data": { + "image/png": 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", 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+ }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + } + ], + "source": [ + "# import sys\n", + "# import numpy as np\n", + "# import matplotlib.pyplot as plt\n", + "\n", + "# # Add the path to the AsishMandoi directory to the system path\n", + "# # IMPORTANT: Adjust this path to the correct location of the AsishMandoi directory\n", + "# asish_mandoi_path = 'c:\\\\Users\\\\USER\\\\Documents\\\\GitHub\\\\Quantum-Vehicle-Routing-Problems\\\\Delete this before uploading\\\\AsishMandoi VRP-explorations main VRP-quantum_BQM_based'\n", + "# if asish_mandoi_path not in sys.path:\n", + "# sys.path.append(asish_mandoi_path)\n", + "\n", + "# from utility import generate_vrp_instance\n", + "# from solution_partition_solver import SolutionPartitionSolver\n", + "# from dbscan_solver import DBSCANSolver\n", + "\n", + "# # Problem parameters\n", + "# n = 10 # Number of clients\n", + "# m = 3 # Number of vehicles\n", + "# seed = 1234\n", + "\n", + "# # Generate a VRP instance\n", + "# instance, xc, yc = generate_vrp_instance(n, seed)\n", + "\n", + "# # --- DBSCAN Solver ---\n", + "# print(\"--- Running DBSCAN Solver ---\")\n", + "# dbscan_solver = DBSCANSolver(n, m, instance)\n", + "# dbscan_solver.solve(solver='neal')\n", + "# print(f\"Optimized Cost: {dbscan_solver.evaluate_vrp_cost()}\")\n", + "# dbscan_solver.visualize(xc, yc)\n", + "\n", + "# # --- Solution Partitioning Solver (SPS) ---\n", + "# print(\"--- Running Solution Partitioning Solver (SPS) ---\")\n", + "# sps_solver = SolutionPartitionSolver(n, m, instance)\n", + "# sps_solver.solve(solver='neal')\n", + "# print(f\"Optimized Cost: {sps_solver.evaluate_vrp_cost()}\")\n", + "# sps_solver.visualize(xc, yc)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--- Running DBSCAN Solver on Coarsened Graph ---\n", + "[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50], [13, 19, 41, 42], [14, 25], [40], [43]]\n", + "Optimized Cost: 1630.1622467041016\n", + "--- Running Solution Partitioning Solver (SPS) on Coarsened Graph ---\n", + "Optimized Cost: 1699.1454664478365\n" + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + } + ], + "source": [ + "# # BQM Solver with Graph Coarsening\n", + "\n", + "# import sys\n", + "# asish_mandoi_path = 'c:\\\\Users\\\\USER\\\\Documents\\\\GitHub\\\\Quantum-Vehicle-Routing-Problems\\\\Delete this before uploading\\\\AsishMandoi VRP-explorations main VRP-quantum_BQM_based'\n", + "# if asish_mandoi_path not in sys.path:\n", + "# sys.path.append(asish_mandoi_path)\n", + "\n", + "# from solution_partition_solver import SolutionPartitionSolver\n", + "# from dbscan_solver import DBSCANSolver\n", + "# import networkx as nx\n", + "\n", + "# # After running the ILP solver, the route object contains the coarsened graph.\n", + "# # We can now use this coarsened graph with the BQM-based solvers.\n", + "# # Note: The ILP solver cell must be executed before this cell.\n", + "\n", + "# # Extract the necessary information from the route object\n", + "# coarsened_graph_pygsp = route.graph\n", + "# n_clients = coarsened_graph_pygsp.N - 1 # Number of clients (excluding depot)\n", + "# n_vehicles = route.vehicles\n", + "# cost_matrix = coarsened_graph_pygsp.W.toarray()\n", + "\n", + "# # The AsishMandoi solvers expect the number of clients, not nodes.\n", + "# # They also assume depot is at index 0.\n", + "\n", + "# # --- DBSCAN Solver on Coarsened Graph ---\n", + "# print(\"--- Running DBSCAN Solver on Coarsened Graph ---\")\n", + "# dbscan_solver_coarsened = DBSCANSolver(n_clients, n_vehicles, cost_matrix)\n", + "# dbscan_solver_coarsened.solve(solver='neal')\n", + "# print(f\"Optimized Cost: {dbscan_solver_coarsened.evaluate_vrp_cost()}\")\n", + "\n", + "# # --- Solution Partitioning Solver (SPS) on Coarsened Graph ---\n", + "# print(\"--- Running Solution Partitioning Solver (SPS) on Coarsened Graph ---\")\n", + "# sps_solver_coarsened = SolutionPartitionSolver(n_clients, n_vehicles, cost_matrix)\n", + "# sps_solver_coarsened.solve(solver='neal')\n", + "# print(f\"Optimized Cost: {sps_solver_coarsened.evaluate_vrp_cost()}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + } + ], + "source": [ + "# solved_route_bqm = sps_solver_coarsened.solve(solver='neal')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[i] Visualizing the solution...\n", + "--- Debugging visualiseSolution ---\n", + "--- ERROR in visualiseSolution ---\n", + "Exception type: \n", + "Exception message: object of type 'NoneType' has no len()\n", + "Traceback (most recent call last):\n", + " File \"C:\\Users\\USER\\Documents\\GitHub\\Quantum-Vehicle-Routing-Problems\\Src\\QuantumLogistics\\LogisticsRoute\\LogisticsRoute.py\", line 49, in visualiseSolution\n", + " print(f\"Number of routes: {len(routes)}\")\n", + " ^^^^^^^^^^^\n", + "TypeError: object of type 'NoneType' has no len()\n", + "\n" + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mnotebook controller is DISPOSED. \n", + "\u001b[1;31mView Jupyter log for further details." + ] + } + ], + "source": [ + "# # Visualizating\n", + "\n", + "# print(\"[i] Visualizing the solution...\")\n", + "# # Set the plot to be displayed inline in the notebook\n", + "# %matplotlib inline\n", + "# route.visualiseSolution(solved_route_bqm)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.12 (qintern_py312)", + "language": "python", + "name": "qintern_py312" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/Src/QuantumLogistics/Graph.py b/Src/QuantumLogistics/Graph.py new file mode 100644 index 0000000..957a71a --- /dev/null +++ b/Src/QuantumLogistics/Graph.py @@ -0,0 +1,19 @@ +from pygsp import graphs +import pygsp +import networkx as nx +import numpy as np + +from typing import Tuple, List + +class Graph: + """Generate the coordinates of 'n' instances (nodes)""" + + def set_seed(self, seed=None): + np.random.seed(seed if seed else self.seed ) + + + def generate_graph(self) -> graphs.Graph: + raise NotImplementedError() + + def plotGraph(self): + raise NotImplementedError() diff --git a/Src/QuantumLogistics/LogisticsRoute/GraphCoarsening.py b/Src/QuantumLogistics/LogisticsRoute/GraphCoarsening.py new file mode 100644 index 0000000..1d1bbd1 --- /dev/null +++ b/Src/QuantumLogistics/LogisticsRoute/GraphCoarsening.py @@ -0,0 +1,434 @@ +from abc import ABC, abstractclassmethod +import math +import networkx as nx +import pygsp +import matplotlib.pyplot as plt +import numpy as np + +from graph_coarsening import coarsening_utils +from graph_coarsening.coarsening_utils import * + +import graph_coarsening.graph_utils + + +class CoarseningEngine(ABC): + + def __init__(self): + """ + General coarsening Engine Class used to coarsen Logistics Graphs in VRP problem + """ + # ratio of coarse nodes to fine nodes + self.rate = 1 + + return + + @abstractclassmethod + def coarsen(self): + + raise NotImplementedError + + + + +class BlankCoarseningEngine: + def __init__(self): + """ + General coarsening Engine Class used to coarsen Logistics Graphs in VRP problem + """ + + return + + + def coarsen(self): + print("Using blank coarsening engine, no coarsening algorithm defined") + return + + + + + + + + +class DeltaCoarseningEngine: + + def __init__(self, coarsenRate = 0.1, radiusCoefficient = 0.2): + """ + General coarsening Engine Class used to coarsen Logistics Graphs in VRP problem + + Args: + coarsening_ration (float, optional): The size of the graph we are interested in preserving. Defaults to 0.2. + kmax (float, optional): The size of the subspace we are interested in preserving. Defaults to 0.2. + method (str, optional): The method of coarsening. Defaults to 'nearest'. + + """ + + # self.edl.values + self.rate = coarsenRate + self.radiusCoefficient = radiusCoefficient + + return + + + + + + + + def coarsen(self, graph, depot, nodeWeights, maxCapacity): + """ + Accepts a LogisticsRoute object + Returns: + Coarse graph object + Fine to coarse node mapping + + # This currently only handles a single depot - needs to be modified to handle multiple + """ + self.graph = graph + self.graphWeights = nodeWeights + self.depot = [depot] + self.maxCapacity = maxCapacity + + #TODO: Is there any reason this is using networkx? Need to move towards a consistent graph package + # Better to remove depot node from network and go from adjacency matrix + self.G = nx.from_numpy_array(self.graph.W) + self.edgList = { e:self.G.get_edge_data(*e)['weight'] for e in self.G.edges} + tempEdgList = self.edgList.copy() + + # removing edges to 0: + for key in list(tempEdgList.keys()): + if 0 in key: + tempEdgList.pop(key) + + pairsToCoarsen = [] + bounds = 1 + whileCounter = 0 + + while len(pairsToCoarsen) == 0 and whileCounter < 10: + # get coarsening radius + coarseningRadius = self.generateCoarseningRadius(tempEdgList, bounds*self.radiusCoefficient) + + # print("\n\n\n") + # print("COARSENING NEW GRAPH") + # print("Coarsening Radius :", coarseningRadius) + + # identify node pairs that can be coarsened in graph + pairsToCoarsen = self.identifyCoarseningPairs(coarseningRadius) + + # adjusting bouds if no pairs found + bounds = 1.4 * bounds + + whileCounter += 1 + + + # Coarsen Graph - what is the point of this if everything gets overwritten anyway? + coarseningMatrix, coarseGraph = self.generateCoarseGraph(pairsToCoarsen) + + plotCoords = False + if plotCoords == True: + #print(coarseGraph.coords) + plt.scatter(coarseGraph.coords[:,0], coarseGraph.coords[:,1]) + plt.scatter(self.graph.coords[:,0], self.graph.coords[:,1]) + plt.show() + + return coarseGraph, coarseningMatrix + + + + + + + + def generateCoarseGraph(self, nodePairsToCoarsen): + """ + Generates a coarse graph for a SINGLE STEP of coarsening + C : np.array of size n x N + The coarsening matrix. Maps n coarse nodes to N fine nodes using formula in Loukas + Gc : pygsp Graph + The smaller graph. + """ + + G = self.graph #the original graph + GAdjacency = G.W + + # Creating coarsening matrix based on pairs of nodes to contract + C = get_coarsening_matrix(G, nodePairsToCoarsen) # level n to level n-1 coarsening Matrix + + #print(C) + + # Coarse Graph Coords: + coarseCoords = coarsen_vector(G.coords, C) + + # Coarse Adjacency + # Generating a Loukas coarse graph to get a binary adjacency for connectivity: + Wc = graph_utils.zero_diag(coarsen_matrix(GAdjacency, C)) # coarsen and remove self-loops + Wc = (Wc + Wc.T) / 2 # this is only needed to avoid pygsp complaining for tiny errors + + # constructing own W: + nodeNum = coarseCoords.shape[0] + adj = Wc + distanceAdja = np.zeros((nodeNum, nodeNum)) + for pointIdx1 in range(nodeNum): + for pointIdx2 in range(pointIdx1 + 1, nodeNum): + if adj[pointIdx1, pointIdx2] != 0: + dist = np.linalg.norm(coarseCoords[pointIdx1] - coarseCoords[pointIdx2]) + distanceAdja[pointIdx1, pointIdx2] = dist + distanceAdja[pointIdx2, pointIdx1] = dist + + + # Making new coarse graph + #Gc = gsp.graphs.Graph(Wc, coords=coarsen_vector(G.coords, iC)) # Some Variable + Gc = gsp.graphs.Graph(distanceAdja, coords=coarseCoords) # New euclidean coarse graph + + # Coarsening Matrix + # In multilevel coarsening must propogate coarsening matrix: + # C = sp.sparse.eye(G.N, format="csc") # Some Variable + # C = iC.dot(C) # full coarsening matrix + + return C, Gc + + + + def generateCoarseningRadius(self, edgList, partitionCoefficient): + """ + Returns the radius under which nodes are coarsened + Based on parition weights + """ + # TODO : FIXIT ? + ''' + (1,2): 2.1, + (2,1): 5.1, + ''' + partition = partitionCoefficient + + w = list(edgList.values()) + w = list(sorted(w)) + + size = self.G.number_of_nodes() # 20 + #size = self.G.N # 20 + part = math.floor(size * partition) # 4 + + coarseningRadius = (w[part] + w[part+1]) / 2 + + return coarseningRadius + + + + + def identifyCoarseningPairs(self, coarseningRadius): + """ + Used to identify subgraphs to contract during coarsening + """ + self.visited = [] + self.collapse = [] + + # order nodes based on weights (minimum weight first) + sortedIdxs = np.argsort(self.graphWeights) + + for n in sortedIdxs: + #for n in self.G.nodes: + if n not in self.visited: + self.check_collapsable(n, self.edgList, coarseningRadius) + + return self.collapse + + + + + def check_collapsable(self, curr, edgList, coarseningRadius, debug=False): + """ + curr - current node being checked + edgList - list of edge lengths + """ + # TODO : Avoid 2 neghbourin... colla.. + + # If the current node has been + if curr in self.visited: + return + + neighbours = self.getNeighbourData(curr, edgList) + + # Possible speed up? + for nodes, weight in neighbours.items(): + a,b = nodes + coarsenedNodeCapacity = self.graphWeights[a] + self.graphWeights[b] + # Checks the followiung: + # If edge is small enough to contract + # If a nd b not the depot (cannot contract the depot) + # A and B have not already been coarsened/attached to a coarsened node + # the combined capacity of a coarsened a+b node is less than the capacity of a given truck + + if weight < coarseningRadius and (a not in self.depot and b not in self.depot) and (a not in self.visited and b not in self.visited) and (coarsenedNodeCapacity < self.maxCapacity): + self.collapse += [ nodes ] + self.visited += [ *nodes ] + + # adding all neigbour nodes of a and b to visited + for node in nodes: + listOfNeigbours = [k for v,k in self.getNeighbourData(node, edgList).keys()] + self.visited += [ *listOfNeigbours ] + + if debug: + print( f"[+] curr : {curr}", neighbours ) + print(f"Adding Nodes: {nodes}") + print(f'updated visitedList: {self.visited}') + print("\n") + + return + + self.visited += [ curr ] + + if debug: + print( f"[ ] curr : {curr}", neighbours ) + print(f'updated visitedList: {self.visited}') + print("\n") + + for nodes in set([ i for n in list(neighbours.keys()) for i in n ]): + self.check_collapsable(nodes, edgList, coarseningRadius) + + return + + + + def getNeighbourData(self, node, edgList): + # Finds all neighbours who have not been visited + # Returns a dict of {(node, neighbourNode):edgeWeight} + + neighbour_data = {} + + size = self.graph.N + for ConNode in range(size): + if ConNode not in self.visited: + edgBase = (node, ConNode) + edg = edgBase + if ConNode < node: + edg = (ConNode, node) + + if edg in edgList: + neighbour_data[edgBase] = edgList[edg] + + # sorted on value + neighbours = dict(sorted(neighbour_data.items(), key=lambda item: item[1])) + + return neighbours + + + + + + def inflateSolution(self, solution, fineGraph, coarseningMatrix): + """ + coarseSolution - [[(0,1), (1,5), (5,0)], [(0,2), (2, 4), (4, 0)] sequence of edges in solution + fineGraph - the coarse graph object + coarseningMatrix - mapping from coarse to fine matrix + """ + + inflatedSolution = [] + weightedAdj = fineGraph.W # this needs to be one step ahead + + # Getting coarsening Map: + coarseningMap = self.coarseMatrixToMap(coarseningMatrix) + + # make sure it works for one vehicle + numVehicles = len(solution) + + for vehicleIdx in range(numVehicles): + coarseVehicleRoute = solution[vehicleIdx] + + inflatedRoute = self.inflateSingleRoute(coarseVehicleRoute, coarseningMap, weightedAdj) + inflatedSolution.append(inflatedRoute) + + return inflatedSolution + + + + + def coarseMatrixToMap(self, coarseningMatrix): + + # Child to Parent Mapping + c, r = np.where((coarseningMatrix.todense() > 0) ) + coarsenMap = { i: [] for i in range(coarseningMatrix.shape[0]) } + + for (_c, _r) in zip(c, r): + coarsenMap[_c] += [_r] + + return coarsenMap + + + + + + def inflateSingleRoute(self, route, coarsenMap, weightedAdj): + """ + Expands Single Vehicle Route + THIS ASSUMES A SINGLE BINARY DECISION AT EACH STEP + """ + + # reducing solution from [(a,b), (b,c), (c,d)] to [a,b,c,d] + route = self.routeEdgeToNode(route) + inflatedRoute = [coarsenMap[route[0]][0]] + + # Should assert first and last node belong in depot - requires knowledge of depots in coarse nodes + # assert route[0] in self.depot and route[0] + for routeStopIdx in range(1, len(route[1:]) + 1): + + #skipping first and last points (they are depots) + nodeIdx = route[routeStopIdx] + inflatedNode = coarsenMap[nodeIdx] + + if len(inflatedNode) > 1: + # choice in direction - which node to go to first + # Only works if no contraction neigboursa + + start = coarsenMap[route[routeStopIdx-1]] + end = coarsenMap[route[routeStopIdx+1]] + + assert len(start) == 1 and len(end) == 1 + + node1 = inflatedNode[0] + node2 = inflatedNode[1] + + # Collective travelled distance + distance1 = weightedAdj[start[0], node1] + weightedAdj[end[0],node2] + distance2 = weightedAdj[start[0], node2] + weightedAdj[end[0],node1] + + if distance2 <= distance1: + inflatedNode = [node2, node1] + + inflatedRoute.extend(inflatedNode) + + inflatedRoute = self.routeNodeToEdge(inflatedRoute) + + return inflatedRoute + + + + + def routeEdgeToNode(self, route): + """ + Changing route from [(a,b), (b,c), (c,d)] to [a,b,c,d] + """ + reducedRoute = [] + + # adding first vertex of each edge sequentially + for edge in route: + reducedRoute.append(edge[0]) + + # adding last element + reducedRoute.append(route[-1][1]) + + return reducedRoute + + + + + def routeNodeToEdge(self, route): + """ + Changing route from [a,b,c,d] to [(a,b), (b,c), (c,d)] + """ + + reducedRoute = [(route[0], route[1])] + + for nodeIdx in range(1, len(route) - 1): + reducedRoute.append((route[nodeIdx], route[nodeIdx+1])) + + return reducedRoute \ No newline at end of file diff --git a/Src/QuantumLogistics/LogisticsRoute/LogisticsGraph.py b/Src/QuantumLogistics/LogisticsRoute/LogisticsGraph.py new file mode 100644 index 0000000..bf82c43 --- /dev/null +++ b/Src/QuantumLogistics/LogisticsRoute/LogisticsGraph.py @@ -0,0 +1,86 @@ +from pygsp import graphs +import pygsp +import networkx as nx +import numpy as np + +from typing import Tuple, List + +from ..Graph import Graph + +class logisticsGraph(Graph): + """Generate the coordinates of 'n' instances (nodes)""" + + def __init__(self, nodeCapacityDefintion, seed = 1543, graph_type = "fully_connected"): + """ + Input: + nodeCapacityDefinition: A list of capacities for each node in the graph. + seed: used in the generation of a graph + graph_type: the type of graph being made + """ + self.nodeCapacities = nodeCapacityDefintion + self.n = len(nodeCapacityDefintion) + self.seed = seed + self.graph_type = graph_type + self.set_seed() + + def set_seed(self, seed=None): + np.random.seed(seed if seed else self.seed ) + + def generate_graph(self) -> graphs.Graph: + xc, yc, instance = self.generateGraphPoints() + + # Define a Graph + graph = graphs.Graph(instance) + + coords = np.array([c for c in zip(xc, yc)]) + graph.set_coordinates(coords) + + self.graph = graph + + return graph + + def generateGraphPoints(self) -> Tuple[List, List, np.array]: + xy = np.random.rand(2, self.n) + + np.ones((2, self.n)) #What is the ones offset for?? + xc = xy[0] + yc = xy[1] + xy = xy.T + + # Creating NetworkX Graph + graphCreationFunctions = {"fully_connected" : nx.complete_graph(self.n), + "random" : nx.fast_gnp_random_graph(self.n, 0.6), + "small_world" : nx.newman_watts_strogatz_graph(self.n, 3, 0.75)} + + G = graphCreationFunctions[self.graph_type] + + # Checking connected: + assert nx.is_connected(G) , "Graph must be fully connected, please use a different graph" + # print("IS THE GRAPH CONNECTED: ") + # print(nx.is_connected(G)) + # input("") + + # Populate NetworkX Graph with appropiate Weight + for (u, v) in G.edges(): + uc = xy[u] + vc = xy[v] + G.edges[u,v]['weight'] = np.linalg.norm( uc - vc ) + + # Fetch NewtorkX Graph Adjacency Matrix + W = nx.adjacency_matrix(G).todense() + + return xc, yc, W + + def plotGraph(self): + """ + Visualises the LogisticsGraph's graph object + + """ + pygsp.plotting.plot_graph(self.graph) + input("Press any to continue") + + return + + def loadGraphPointsFromFile(self): + raise NotImplementedError + + def loadGraphFromFile(self): + raise NotImplementedError \ No newline at end of file diff --git a/Src/QuantumLogistics/LogisticsRoute/LogisticsRoute.py b/Src/QuantumLogistics/LogisticsRoute/LogisticsRoute.py new file mode 100644 index 0000000..42cf16f --- /dev/null +++ b/Src/QuantumLogistics/LogisticsRoute/LogisticsRoute.py @@ -0,0 +1,246 @@ +import matplotlib.pyplot as plt +from QuantumLogistics.LogisticsRoute.GraphCoarsening import BlankCoarseningEngine +import numpy as np +import scipy as sp +import pygsp +import copy + +class Route(object): + def __init__(self, LogisticsGraph, coarseningEngine = None, **config): + + graph = LogisticsGraph.graph + self.nodeCapacities = LogisticsGraph.nodeCapacities + + # Keeping the raw data as well + self._context = { + 'graph': graph + } + + self.graph = graph # PyGSP graph object + self.n = LogisticsGraph.n # Number of nodes + self.depot = config["depot"] # ID of the depot (default 0) + self.cursor = config["depot"] # Current location of the cursor vehicle + self.vehicles = config["vehicles"] # Number of vehicle + self.truckCapacity = config["truckCapacity"] # value of maximum truck capacity + self.coords = getattr(graph, 'coords', []) # Coordinates of the nodes + self.routes = None # Calculated Routes + self.solution = None + + # Coarsening Parameters: + self.coarsen = False + + if coarseningEngine == None: + self.coarseningEngine = BlankCoarseningEngine() + else: + self.coarseningEngine = coarseningEngine + + self.coarsenRate = self.coarseningEngine.rate + + #Must ADD Capacities and Time Windows + + def __call__(self, ): + pass + + + def visualiseSolution(self, routeSolution, colormap = "hsv", saveImgFilepath = False): + try: + routes = routeSolution + [xc, yc] = self.graph.coords.T + plt.figure() + plt.scatter(xc, yc, s=200) + # for i in range(len(xc)): + # plt.annotate(i, (xc[i] + 0.15, yc[i]), size=16, color="r") + + i = 0 + for x, y in zip(xc, yc): + plt.annotate(i, (x + 0.075, y), size=16, color="r") + i += 1 + + plt.plot(xc[0], yc[0], "r*", ms=20) + plt.grid() + + vehicle_cmap = self.get_cmap(len(routes) + 1, name=colormap) + for vehicle in range(len(routes)): + tour = routes[vehicle] + color = vehicle_cmap(vehicle) + for hop in tour: + _from, _to = hop + + plt.arrow( + xc[_from], + yc[_from], + xc[_to] - xc[_from], + yc[_to] - yc[_from], + length_includes_head=True, + head_width=0.02, + color = color + ) + + if not saveImgFilepath: + #print("THIS IS SHOWING THE THING HERE") + plt.show() + else: + print("SAVING FIGURE") + plt.savefig(saveImgFilepath) + except: + print("error when visualising route") + return + + def visualiseGraph(self): + pygsp.plotting.plot_graph(self.graph) + input("Press any button to continue") + return + + def evalutateKPIS(self, solution): + cost = self.calculateCost(solution) + return + + + def get_cmap(self, n, name='hsv'): + '''Returns a function that maps each index in 0, 1, ..., n-1 to a distinct + RGB color; the keyword argument name must be a standard mpl colormap name.''' + return plt.cm.get_cmap(name, n) + + + def pygsp_graph(self): + """ + Returns the source graph PyGSP object + """ + return self._context['graph'] + + + def graphEdges2Dict(self, graph): + edge_list = graph.get_edge_list() + n1, n2, w = edge_list + assert len(n1) == len(n2) == len(w) + return { (n1[i], n2[i]):w[i] for i in range(len(n1)) } + + + + def calculateCost(self, solution): + """ + Needs to be checked fundamentally + """ + _graph = self.pygsp_graph() + edl = self.graphEdges2Dict(_graph) + cost = 0 + for route in solution: + for (_from, _to) in route: + cost += edl.get((_from, _to), edl.get((_to, _from), 0) ) + + return cost + + + + def recordMetaData(self): + """ + Add important details to self.metaData for later analysis + """ + raise NotImplementedError + + + def setSolution(self): + #Solution to be in form: + # [ [list vehicle1 nodes], + # [list vehicle2 nodes], + # [list vehicle3 nodes],] + + raise NotImplementedError + + + + def coarsenGraph(self): + """ + Coarsens the graph using the coarseningEngine defined in the route instantiation + """ + # General parameters + coarseningRate = self.coarseningEngine.rate + initialGraphSize = self.n + newGraphSize = initialGraphSize + fineNodeCapacities = self.nodeCapacities + + # History lists + self.originalGraph = copy.deepcopy(self.graph) #pygsp object + self.coarsenGraphHistory = [self.originalGraph] + self.coarsenMappingHistory = [sp.sparse.eye(self.originalGraph.N, format="csc")] + + # Setting graph variable + graphToCoarsen = self.graph + + # Coarsening graphs - probably need to do metrics here to compare the original to final + while newGraphSize > coarseningRate * initialGraphSize: + # Coarsening + coarsenedGraph, fineToCoarseMapping = self.coarseningEngine.coarsen(graphToCoarsen, self.depot, fineNodeCapacities, self.truckCapacity) + + # updating node capacities + coarseNodeCapacities = self.propogateNodeCapacities(fineNodeCapacities, fineToCoarseMapping) + + # Saving history and iterating + self.coarsenGraphHistory.append(coarsenedGraph) + self.coarsenMappingHistory.append(fineToCoarseMapping) + graphToCoarsen = coarsenedGraph + coarseGraphSize = coarsenedGraph.N + + if coarseGraphSize == newGraphSize: + print("Has not decreased in size, terminating now: ") + break + + newGraphSize = coarseGraphSize + fineNodeCapacities = coarseNodeCapacities + + plotCoords = False + if plotCoords == True: + plt.scatter(self.originalGraph.coords[:,0], self.originalGraph.coords[:,1]) + plt.scatter(coarsenedGraph.coords[:,0], coarsenedGraph.coords[:,1]) + plt.show() + + self.graph = graphToCoarsen + self.nodeCapacities = fineNodeCapacities + + print("Final coarse graph has {0} nodes".format(self.graph.N)) + + return + + + def propogateNodeCapacities(self, fineNodeCapacities, fineToCoarseMapping): + """ + Updating coarse node capacities + """ + rows,cols = fineToCoarseMapping.nonzero() # When working, it's 13 x 14 i.e. 14 nodes coarsened to 13 + coarseNodeQty = max(cols) # Thus, this is max of the 14 elements [0...13] ie 13 ]---. + coarseNodeCapacities = np.zeros(coarseNodeQty) # | TODO: In case of un-successful + # | coarsening, this fineToCoarseMapping + for row,col in zip(rows,cols): # | is a square matrix, raising problems + coarseNodeCapacities[row] += fineNodeCapacities[col] # < --' $ python3 src/sample.py + return coarseNodeCapacities + + + + + + def inflateGraph(self, solution): + """ + Inflates solution from solver to coarsen engine + """ + + # need to inflate through graphs: + coarseGraphSol = solution #- list of lists for each vehicle + + inflatedRoutes = coarseGraphSol + + # Stepping through history + for graphIdx in range(len(self.coarsenGraphHistory) - 1, 0, -1): + coarsenedGraph = self.coarsenGraphHistory[graphIdx-1] + coarseningMatrix = self.coarsenMappingHistory[graphIdx] + inflatedSolution = self.coarseningEngine.inflateSolution(coarseGraphSol, coarsenedGraph, coarseningMatrix) + inflatedRoutes.append(inflatedSolution) + + # Setting current inflated to new coarse: + coarseGraphSol = inflatedSolution + + return inflatedSolution + + + + + \ No newline at end of file diff --git a/Src/QuantumLogistics/LogisticsRoute/VrpRepGraph.py b/Src/QuantumLogistics/LogisticsRoute/VrpRepGraph.py new file mode 100644 index 0000000..49872ca --- /dev/null +++ b/Src/QuantumLogistics/LogisticsRoute/VrpRepGraph.py @@ -0,0 +1,73 @@ +from pygsp import graphs +import pygsp +import networkx as nx +import numpy as np + +import math + +from typing import Tuple, List + +from ..Graph import Graph +from .vrprep_utils import loaddataset + +class vrpRepGraph(Graph): + """Generate the coordinates of 'n' instances (nodes)""" + + def __init__(self, file, seed = 1543): + """ + Input: + file: the location of xml graph file + seed: used in the generation of a graph + """ + self.graphFile = file + self.nodelist = loaddataset(self.graphFile) + self.n = len(self.nodelist.get_nodes()) + 1 + self.seed = seed + self.set_seed() + + def set_seed(self, seed=None): + np.random.seed(seed if seed else self.seed ) + + def generate_graph(self) -> graphs.Graph: + instance = np.zeros((self.n, self.n)) + coords = np.array([node.get_pos() for node in self.nodelist.get_all_nodes()]) + + # Create the Weight Adjacency + for x, points_A in enumerate(coords): + for y, points_B in enumerate(coords): + instance[x, y] = np.linalg.norm(points_A - points_B) + + np.fill_diagonal(instance, 0) + + # Define a Graph + graph = graphs.Graph(instance) + graph.set_coordinates(coords) + + self.graph = graph + + # Capacities + self.nodeCapacities = [ node.get_dem() for node in self.nodelist.get_all_nodes() ] + + assert len(self.nodeCapacities) == len(coords) == self.n + + # Number of vehicles + num_vehicles = math.ceil(sum(self.nodeCapacities) / self.nodelist._capacity) + + return graph + + + def plotGraph(self): + """ + Visualises the LogisticsGraph's graph object + + """ + pygsp.plotting.plot_graph(self.graph) + input("Press any to continue") + + return + + def loadGraphPointsFromFile(self): + raise NotImplementedError + + def loadGraphFromFile(self): + raise NotImplementedError \ No newline at end of file diff --git a/Src/QuantumLogistics/LogisticsRoute/__init__.py b/Src/QuantumLogistics/LogisticsRoute/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/Src/QuantumLogistics/LogisticsRoute/__pycache__/GraphCoarsening.cpython-312.pyc b/Src/QuantumLogistics/LogisticsRoute/__pycache__/GraphCoarsening.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..a22495b8df17c999e61157d0593a16df72de0c8c GIT binary patch literal 14315 zcmb_@Yj7Lcb!Io-02>7O00}bNd01!i=3tZjs%$?>+Z@?m6E%_u{`hoel~@=xcRB-vNsH4Ss0BtVUjb2O=vJ zM{#tBnxn_*Im5Vt#&1K&IBq0w)3}+uE#nsQw$9nc?JA99ybRKeA!g1w?j&iZQ2F0! zHMqtZ19g((%R z<1|N&8#wwMYTU@1IKw;CLzRBqykzv5WcQ$6=}>q&80G_XQH59^4(MeiJYWjxI5nYX zL&uH(!aLZaaFP%6fcoxB70Ks&(DZ#FwB18 z;(2ynh)jm~IlbTJ@46U)*$Yp1omUzWuZ#)-jY#j%6+MRJ{1wu_ z!d!LFFUhuviC{PwotTK#6*83Jc57K~=%H8+kFQZ14$4!LG~KqZ+sa=;3bkpbaVTV_ zk$8oQA^{0sr+qYzylNy8Jv}!MvjSt|xgkM_2!azxlvxm55S6X!#K*j^^hnLA!xFe> zzD9j&pQupCdjC4k+xO<0mF$$Hc^3gj)<@oSB$dSoDXK903O;nD9{zj|UVf zOd1z#n2HY^g4h6$cc>R8tJ$?tNm=SXF&NCPFO6DEDTmaX7+7PzmtM%(%D~9J<0itk zo;O4O@U^Xj+%%(5fik1m+ZAew_89~m_=tdYZ=E_auvl}+YW3B`T_sxKK~~f5B7@k} zC@vvc#(IdrGHT<2t@BWg)6^1d^^w@ow?*JWb`l4oZ3s-@$u{g{!}>PCRDWnXA_Su| zb1cVC!8YZ9CCu|eFdThlB)BlKrqUx(xnLKNsBHPn=FF6jJhh$6+sai=Fbf{Y7i#cP zix0BsSgkU3$S=y0<0u7uw7|c}zyp@tU^cs6x(#M!dPw%BHP(gHp8$Q)8kd8ZqCp;$ zRpyMa)@IHGPYcS{aVzKIERb*GK&Fn{IU7739LQ3T&JK7oTp2u_90SktC8y6Vdyey= zsQ(on!R66{F5g&4S)t;a2BkQ11Ol3p~B@0byD^q<>*k>e2x- zOn?v!M#5~zR4C$)cCwLq{Pc%>huEJo{dbgQHW2YSY>bUtY6?kxJG$_7eRWU zoSla#FIB<>$?c* zMIg+KYyz{c@HuXPSaV5!(uKooKqKOw0pZ}KJS>X(d`oZA^wic2B43de8YTfU3Iz#~ z6$X${uP~pnnEB#{X=F`p=TLDIeCdoFwPSS{W(gWn;@UG#&1%u2_bg7xmhezzcBmWs zMgo+^3EC27aYD9)t0N(9nMHlHC1{k|xQ|m;K{X_-oFQ(#4tn*r4azlb zDFmN!t5$-hZr7WrX)0mkj0rnuNI0S}b|u7Z8Wm@_)&X*IH16O`*I*5W5f}|J*_IHu z#O;vNx+NJtW572WVoa0)&5l=T;$>QU&>M5yj%5;dXww)2nDDthv*eP zFqvRcHZnQO2cny3FY?hvA-qLnU`2}hQ}uvSklj=giB15ZD8O<+9vsik`RC_BHx#5O z5^e_t6BOCNq9B0q3@x#dFg#}bVJ^gDM-kD4cz`JLkto~6hIyVNI%N{-i*UiIpaTDu z0_+^9oFE`ty+5+$1|OWBi3%v_gfe)1i~?YKiiF?3abj%5=atPwsmTm^T_OcU*-YA$ z%RpBR`auf?qf4?Od{cH$36Z&p@Z#M3(u7|S{7W)@Nv2QAW}choMcFycM<*~k!TF

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qY91ozLsa}XRJBGQqU?`GC>Q0KKKuy5 pl.LpProblem: + """ + Uses pulp to return the definition of ILP problem + This is based on the Miller Tucker Zemlin formulation of the CVRP problem of an n node graph + Decision Vars: + dec_x - whether to travel on edge ij [size nxn] + dec_u - the 'integral' variable indicating the 'used truck capacity' of the truck at that node + """ + print("Starting problem encoding") + + # to remember the route characteristics + self.route = route + n = route.graph.N + K = route.vehicles + graphAdjMatr = route.graph.W.toarray() + + # Capacities: + nodeCapacities = route.nodeCapacities + Q = self.route.truckCapacity + + # Start the LP problem definition + prob = pl.LpProblem("VRP", pl.LpMinimize) + + # define the decision variable + dec_x = list(range(n ** 2)) + dec_u = list(range(dec_x[-1] + 1, dec_x[-1] + n)) + dec_total = dec_x + dec_u + + var_x = pl.LpVariable.dicts("x", dec_x, 0, 1, cat='Integer') + var_u = pl.LpVariable.dicts("u", dec_u, min(nodeCapacities), Q, cat="Continuous") + + # merge both dictionaries + l = [var_x, var_u] + dec_vars = {**l[0], **l[1]} + + # create the dictonary for the weights: + my_obj = list(graphAdjMatr.reshape(1, n ** 2)[0]) + [0.0 for x in range(0, n - 1)] + weight_opt = dict(zip(dec_vars, my_obj)) + + # Define the Objective function + prob += pl.lpSum([weight_opt[i]*dec_vars[i] for i in dec_total]) + + # create the array with all the right hand size contrainst values + # This is the order in which constraints are made + # first line - sum of xijk for each node (depot is idx 0 ) must be either # vehicles or 1. Multipled by 2 for entry and exit + # second line - ui values are less than truck capacity + # third line - paths from node to node i (self paths) must not be selected + + # subject to the node-visiting and the depot-visiting constraints: + # MASS CONSERVATION CONSTRAINTS: + entryExitConstraints = [K] + [1 for x in range(0, n - 1)] + for ii in range(0, n): + # Summing by row - all exits must equal 1 (or # of vehicles for depot) + col = [x for x in range(0 + n * ii, n + n * ii)] + constraint = entryExitConstraints[ii] + prob += pl.lpSum([dec_vars[k] for k in col]) == constraint + + for ii in range(0, n): + # Summing by row - all entries must equal 1 (or # of vehicles for depot) + col = [x for x in range(0 + ii, n ** 2, n)] + constraint = entryExitConstraints[ii] + prob += pl.lpSum([dec_vars[k] for k in col]) == constraint + + # Sub-tour elimination constraints through capacities: + for ii in range(0, n): + for jj in range(0, n): + # NOTE : Sub-Tour Elimination + if (ii != jj) and (ii * jj > 0): # if i or j not 0 + col = [ii + (jj * n), n ** 2 + ii - 1, n ** 2 + jj - 1] + coef = [Q, 1, -1] + capDeltaConstraint = Q - nodeCapacities[jj] + prob += pl.lpSum([co*dec_vars[k] for co, k in zip(coef,col)]) <= capDeltaConstraint + + # setting decision variable associated with 0 elements in adjacency to 0: + zeroEdges = np.argwhere(graphAdjMatr == 0) + for entry in zeroEdges: + prob += pl.lpSum([dec_vars[entry[0] + (entry[1] * n)]]) == 0 + + # # This also includes - set the diagonal elements to zero , i=j + # for ii in range(0, n): + # col = [(ii) * (n + 1)] + # prob += pl.lpSum([dec_vars[k] for k in col]) == 0 + + return prob + + + def addCapacityConstraints(self): + raise NotImplementedError + + def addTWConstraints(self): + raise NotImplementedError + + + def extract(self, solution, verbose = True): + """ + Returns the route lists from the PULP ILP in the correct format + Format is: + + """ + # convert to route solution format + #route information + n = self.route.graph.N + _k = n*n + depotIdx = self.route.depot + vehicleNumber = self.route.vehicles + + # After solving the Linear Program, it is needed to extract the routes from the solution + routes = [] + _chain = [] + + travel_metrices = solution[0:_k].reshape((n, n)) + + for ix in range(0, n): + for iy in range(0, n): + if travel_metrices[ix][iy] > 0: + if (ix, iy) not in _chain and ix != iy: + _chain += [(ix, iy)] + + + #self.route.visualiseSolution([_chain]) + + for vehicle in range(vehicleNumber): + cur = depotIdx + route = [] + travel = True + if verbose: print(f"{cur}", end=' ') + counter = 0 + while travel: + counter+= 1 + + element = [(_from, _to) for (_from, _to) in _chain if _from == cur] + (_from, _to) = element[vehicle] if len(element) > 1 else element[0] + cur = _to + if (_from, _to) in route: + print("There is a repeating cycle") + print((_from, _to)) + self.route.visualiseSolution([route]) + print(ThisWillErrorThingsOut) + break + route += [(_from, _to)] + if verbose: print(f"-> {_to}", end=' ') + + if cur == depotIdx: + travel = False + #print(route) + routes += [route] + if verbose: print() + + # Check if all vehicles are accounted for, while calcultaing the routes + assert len(routes) == vehicleNumber + + return routes + + + + + + + + + + + + +class ILPCPLEXEncoder(ILPPulpEncoder): + """ + Converts the route into an ILP problem + Inherits the extract() method from the ILPPulpEncoder Class (they have equivalent answers) + THIS NEEDS TO BE UPDATED + """ + + def encode(self,route) -> cplex.Cplex: + # to remember the route characteristics + self.route = route + n = route.n + K = route.vehicles + graphAdjMatr = route.graph.W.toarray() + + Q = 10 + + my_obj = list(graphAdjMatr.reshape(1, n ** 2)[0]) + [0.0 for x in range(0, n - 1)] + my_ub = [1 for x in range(0, n ** 2 + n - 1)] + my_lb = [0 for x in range(0, n ** 2)] + [0.1 for x in range(0, n - 1)] + my_ctype = "".join(["I" for x in range(0, n ** 2)]) + "".join( + ["C" for x in range(0, n - 1)] + ) + + my_rhs = ( + 2 * ([K] + [1 for x in range(0, n - 1)]) + + [Q - 0.1 for x in range(0, (n - 1) ** 2 - (n - 1))] + + [0 for x in range(0, n)] + ) + my_sense = ( + "".join(["E" for x in range(0, 2 * n)]) + + "".join(["L" for x in range(0, (n - 1) ** 2 - (n - 1))]) + + "".join(["E" for x in range(0, n)]) + ) + + try: + my_prob = cplex.Cplex() + self.populatebyrow(my_prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs) + except cplex.CplexError as exc: + print(exc) + return + + return my_prob + + + def populatebyrow(self, prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs): + + Q = 10 #THIS NEEDS TO BE PROVED AND INTEGRATED BETTER + + n = self.route.n + + prob.objective.set_sense(prob.objective.sense.minimize) + prob.variables.add(obj=my_obj, lb=my_lb, ub=my_ub, types=my_ctype) + + prob.set_log_stream(None) + prob.set_error_stream(None) + prob.set_warning_stream(None) + prob.set_results_stream(None) + + rows = [] + for ii in range(0, n): + col = [x for x in range(0 + n * ii, n + n * ii)] + coef = [1 for x in range(0, n)] + rows.append([col, coef]) + + for ii in range(0, n): + col = [x for x in range(0 + ii, n ** 2, n)] + coef = [1 for x in range(0, n)] + + rows.append([col, coef]) + + # Sub-tour elimination constraints: + for ii in range(0, n): + for jj in range(0, n): + if (ii != jj) and (ii * jj > 0): + + col = [ii + (jj * n), n ** 2 + ii - 1, n ** 2 + jj - 1] + coef = [Q, 1, -1] + + rows.append([col, coef]) + + for ii in range(0, n): + col = [(ii) * (n + 1)] + coef = [1] + rows.append([col, coef]) + + prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs) + + + + + + + diff --git a/Src/QuantumLogistics/RouteSolver/Encoders/StandardEncoder.py b/Src/QuantumLogistics/RouteSolver/Encoders/StandardEncoder.py new file mode 100644 index 0000000..315af6a --- /dev/null +++ b/Src/QuantumLogistics/RouteSolver/Encoders/StandardEncoder.py @@ -0,0 +1,63 @@ +from abc import ABC, abstractclassmethod, abstractmethod +from QuantumLogistics import Route # solver #, Encoder, solver + + + +class Encoder(ABC): + + def __init__(self): + """ + The encoder serves as the interface between the route and solver backend objects. + + The encoder converts the CVRP problem in the route object to a mathematical representation for solving byt the solver backend + After solving, the encoder then extracts the information from the solver output and converts it to a route solution list + """ + + return + + @abstractmethod + def encode(self,route: Route): + """ + This encodes the cvrp problem in the route object into a problem be solved by a solver API + + Input: + route - route object + + Output: + solver api dependant + + """ + + # to remember the route characteristics + self.route = route + + # Must be output to a standard problem format + raise NotImplementedError + + @abstractmethod + def extract(self,solution) -> list: + + """ + This extracts the route solution from the solution given by the solver backend + + Input: + problemSolution - solver dependant + + Output: + Standard solution List - a list of vehicle routes where each route is a list of edges the vehicle travels (eadges in tuple format) + + i.e routeSol = [[(idxDepot, idx1), (idx1, idx4), (idx4, idx5), (idx5, idxDepot)], # Vehicle 1 route + [(idxDepot, idx2), (idx2, idx3), (idx3, idxDepot)], # vehicle 2 route + [(idxDepot, idx9), (idx9, idx8), (idx8, idx7), (idx7, idx6), (idx6, idxDepot)]] # vehicle 3 route + """ + + raise NotImplementedError + + + def addTWConstraints(self): + + """ + Not yet implemented - maybe coming soon + """ + + raise NotImplementedError diff --git a/Src/QuantumLogistics/RouteSolver/Encoders/StandardQUBOEncoders.py b/Src/QuantumLogistics/RouteSolver/Encoders/StandardQUBOEncoders.py new file mode 100644 index 0000000..5491481 --- /dev/null +++ b/Src/QuantumLogistics/RouteSolver/Encoders/StandardQUBOEncoders.py @@ -0,0 +1 @@ +from abc import ABC, abstractclassmethod diff --git a/Src/QuantumLogistics/RouteSolver/Encoders/VRPExplorationsEncoder.py b/Src/QuantumLogistics/RouteSolver/Encoders/VRPExplorationsEncoder.py new file mode 100644 index 0000000..28b267f --- /dev/null +++ b/Src/QuantumLogistics/RouteSolver/Encoders/VRPExplorationsEncoder.py @@ -0,0 +1,49 @@ +from dataclasses import dataclass + +import numpy as np +from QuantumLogistics import Route +from .StandardEncoder import Encoder + + +@dataclass +class VRPInstance: + clients_num: int + vehicles_num: int + cost_matrix: np.ndarray + capacity: list + demands: list + xc: np.ndarray + yc: np.ndarray + + +class VRPExplorationsEncoder(Encoder): + def encode(self, route: Route): + # to remember the route characteristics + self.route = route + + coords = list(zip(*route.coords)) + self.vrp_instance = VRPInstance( + clients_num=route.graph.N, + vehicles_num=route.vehicles, + cost_matrix=route.graph.W.toarray(), + capacity=route.truckCapacity, + demands=route.nodeCapacities, + xc=np.array(coords[0]), + yc=np.array(coords[1]), + ) + + return self.vrp_instance + + def extract(self, solution, verbose=False) -> list: + solution, variables = solution + + routeSol = [] + for i in range(solution.shape[0]): + var_list = np.transpose(variables[i]).reshape(-1) + sol_list = np.transpose(solution[i]).reshape(-1) + active_vars = [var_list[k] for k in range(len(var_list)) if sol_list[k] == 1] + route = [int(var.split('.')[2]) for var in active_vars] + edgelist = [(0, route[0])] + [(route[j], route[j + 1]) for j in range(len(route) - 1)] + [(route[-1], 0)] + routeSol.append(edgelist) + + return routeSol diff --git a/Src/QuantumLogistics/RouteSolver/Encoders/__init__.py b/Src/QuantumLogistics/RouteSolver/Encoders/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/Src/QuantumLogistics/RouteSolver/Encoders/__pycache__/ILPEncoder.cpython-312.pyc b/Src/QuantumLogistics/RouteSolver/Encoders/__pycache__/ILPEncoder.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..775ba902365e71670c6e41e4b2d2fba422e954f3 GIT binary 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Only overwrite solveAlgorithm() and extractSolution() + """ + + def __init__(self): + raise NotImplementedError + + + def solve(self,route:Route, config = None): + """ + DO NOT OVERWRITE METHOD + """ + self.config = config + startTime = time() + + # check if graph must be coarsened + if route.coarsen: + print("Coarsening Graph now") + route.coarsenGraph() + + #TODO: Sometimes the solver may not find a feasible solution in the timelimit + # Need to develop an exception handling method for this + problemSol = self.solveAlgorithm(route) + print("RAW SOLVER OUTPUT:", problemSol) # <--- ADD THIS + return problemSol + # routeSol = self.extractSolution(problemSol) + + # #route.visualiseSolution(routeSol) + + # if route.coarsen: + # routeSol = route.inflateGraph(routeSol) + # route.graph = route.originalGraph + + # #route.visualiseSolution(routeSol) + + # # Standard solver details + # solveTime = time() - startTime + # costValue = route.calculateCost(routeSol) + + # return routeSol, solveTime, costValue + + + @abstractclassmethod + def solveAlgorithm(self, route: Route): + """ + Returns raw output from solver in terms of decision variables. + This should only include logic to SOLVE the problem (it should NOT DECODE the solution - this happens in extractSolution) + + Input: + route: Route object + + Output: + problem solution: solver dependant + The output from the solver API/interface (not converted to route form) + + """ + + raise NotImplementedError + + @abstractclassmethod + def extractSolution(self, problemSol): + """ + Decodes the solution from solver output to a standard route list for plotting and analysis. + + Input: + problem solution: solver dependant + + Output: + Standard solution List - a list of vehicle routes where each route is a list of edges the vehicle travels (eadges in tuple format) + + i.e routeSol = [[(idxDepot, idx1), (idx1, idx4), (idx4, idx5), (idx5, idxDepot)], # Vehicle 1 route + [(idxDepot, idx2), (idx2, idx3), (idx3, idxDepot)], # vehicle 2 route + [(idxDepot, idx9), (idx9, idx8), (idx8, idx7), (idx7, idx6), (idx6, idxDepot)]] # vehicle 3 route + + """ + raise NotImplementedError + + + + + + + + + + +class StandardRouteSolver(CompositeRouteSolver): + + def __init__(self, encoder, solver): + self.encoder = encoder + self.solver = solver + return + + def solveAlgorithm(self, route:Route): + #Encode problem + problem = self.encoder.encode(route) + + #solving problem + problemSol = self.solver.solve(problem, config = self.config) + + return problemSol + + + def extractSolution(self,solverSolution): + # must return standard solution + return self.encoder.extract(solverSolution, verbose=False) + + + + + + diff --git a/Src/QuantumLogistics/RouteSolver/SolverAlgorithmModules/__init__.py b/Src/QuantumLogistics/RouteSolver/SolverAlgorithmModules/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py b/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py new file mode 100644 index 0000000..fc3b12c --- /dev/null +++ b/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py @@ -0,0 +1,198 @@ +from abc import ABC, abstractclassmethod +import pulp as pl +import numpy as np +import cplex +import pandas as pd +import os +import sys + +# # dirty hack, I am aware +# sys.path.insert(0, "/home/knalecz/Pulpit/PhD/aktualne_projekty/QReaserch/VRP-explorations") + +# Path to the 'Src' directory. +# This goes up three levels from the current file's directory +# (SolverBackends -> RouteSolver -> QuantumLogistics -> Src) +src_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), '..', '..', '..')) + +# Path to the VRP-explorations submodule inside 'Src/external/' +vrp_explorations_path = os.path.join(src_dir, 'external', 'VRP-explorations') + +# Add the submodule to the Python path +if vrp_explorations_path not in sys.path: + sys.path.insert(0, vrp_explorations_path) + +from VRP.quantum.BQM_based.full_qubo_solver import CapcFullQuboSolver as CFQS + + +class Solver(ABC): + def __init__(self): + + return + + @abstractclassmethod + def solve(self, problemFormat, config): + """ + This accepts a standardised problemFormat datatype (dependant on encoder) and runs the problem using a specified solver backend. + + This format should be as general as possible to cater to a wide range of solvers. + + For example: + ILP problems accepts a PULP problem which encodes the ILP problem + Standard qubo problems will likely accept a standard 'QUBO' format that can be readily converted into DWAVE, QISKIT etc solver format. + + """ + + raise NotImplementedError + + +class PulpSolver(Solver): + def __init__(self): + return + + def defineSolver(self): + """ + """ + raise NotImplementedError("Use either Gurobi or CBC solvers") + + def solve(self, problem: pl.LpProblem, config=None): + # Define the solver - defaults if no config specified + if config: + gap_rel = config["gapRel"] + timeLimit = config["timeLimit"] + else: + gap_rel = 0.01 + timeLimit = 300 + print( + f"No config specified, defaulting to gap_rel = {gap_rel} and timeLimit {timeLimit}" + ) + + self.solver = self.defineSolver(gap_rel=gap_rel, time_lim=timeLimit) + + prob = problem + solver = self.solver + prob.solve(solver) + + print(f'"Status:", {pl.LpStatus[prob.status]}') + + if prob.status == 0: + print( + f"Not possible to find a solution with the tolerance {gap_rel} in {timeLimit}s" + ) + return + + elif prob.status == 1: + obj = pl.value(prob.objective) + print(f"The Objective function Value is: {round(obj,3)}") + + solution = [] + solution_name = [] + + for v in prob.variables(): + value = round(v.varValue, 4) + if v.isInteger(): + value = round(v.varValue) + solution.append(value) + solution_name.append(v.name) + + # map the pulp solution format to matchs with CPLEX + temp = [ + (ii, jj, int(jj.split("_")[1])) + for ii, jj in zip(solution, solution_name) + ] + df = pd.DataFrame(temp, columns=["Value", "Name", "position"]) + df = df.sort_values(by="position") + x = df.Value.values + solution_name = df.Name.values + return x + + else: + print("Problem is infeasible") + return + + def verifyConstraints(self, prob): + + soln_dict = {i.name: round(i.varValue, 1) for i in prob.variables()} + + for c in prob.constraints.values(): + c_dict = c.toDict() + # print(c_dict) + satisfied = False + + LHS = sum( + [soln_dict[i["name"]] * i["value"] for i in c_dict["coefficients"]] + ) + LHS = LHS + c_dict["constant"] + + if c_dict["sense"] == 0: + satisfied = LHS == 0 + + if c_dict["sense"] == -1: + satisfied = LHS <= 0 + + if c_dict["sense"] == 1: + satisfied = LHS >= 0 + + if not satisfied: + # print('LHS: ', LHS) + print(c) + print("not satisfied") + + return + + +class GurobiSolver(PulpSolver): + def defineSolver(self, gap_rel, time_lim): + return pl.GUROBI_CMD(msg=1, gapRel=gap_rel, timeLimit=time_lim) + + +class GurobiSolver2(PulpSolver): + def defineSolver(self, gap_rel, time_lim): + return pl.GUROBI(msg=1, gapRel=gap_rel, timeLimit=time_lim) + + +class CBCSolver(PulpSolver): + def defineSolver(self, gap_rel, time_lim): + return pl.PULP_CBC_CMD(msg=1, gapRel=gap_rel, timeLimit=time_lim) + + +class CPLEXSolver(PulpSolver): + def defineSolver(self, gap_rel, time_lim): + return pl.CPLEX_PY(msg=1, gapRel=gap_rel, timeLimit=time_lim) + + +class CPLEXNativeSolver(Solver): + def __init__(self): + + return + + def solve(self, my_prob: cplex.Cplex): + + try: + my_prob.solve() + except cplex.CplexError as exc: + print(exc) + return + + x = my_prob.solution.get_values() + x = np.array(x) + cost = my_prob.solution.get_objective_value() + + # needs a consistent return - + return x + + +class VRPExplorationsSolver(Solver): + + def solve(self, problemFormat, config): + # przykład wykorzystania CapcSolutionPartitionSolver → https://github.com/AsishMandoi/VRP-explorations/blob/main/VRP/quantum/BQM_based/Vehicle%20Routing%20Problem.ipynb + self.vrp_explorations_solver = CFQS( + problemFormat.clients_num - 1, + problemFormat.vehicles_num, + problemFormat.cost_matrix, + [problemFormat.capacity]*problemFormat.vehicles_num, + problemFormat.demands + ) + self.vrp_explorations_solver.solve(solver=config['solver']) + + # self.vrp_explorations_solver.solution → efekt wywołania metody VehicleRouter#extract_solution + return self.vrp_explorations_solver.solution diff --git a/Src/QuantumLogistics/RouteSolver/SolverBackends/__init__.py b/Src/QuantumLogistics/RouteSolver/SolverBackends/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/Src/QuantumLogistics/RouteSolver/SolverBackends/__pycache__/SolverBackends.cpython-312.pyc b/Src/QuantumLogistics/RouteSolver/SolverBackends/__pycache__/SolverBackends.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..73eaccbde56d73fc0bfbc4fd705bce110d892b43 GIT binary patch literal 9064 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0000000000000000000000000000000000000000..c1d41d3f184fc8a807f47cb9a89b4d1f6706a64b GIT binary patch literal 1103 zcmb7@&uiN-6vrheahxAc+9v5?>>tP>*(mf<${0ya){%`Yp*;vg>e`~wDp^6c$9muY zu)krq{U7@e3}uI%b{k}+u+t>RZn6xzPTnRDIoZ-u zvG^dxN8kYuQotaBP-%^7EQfN5&e1$8paRp8p7?oMWCk)=36&DRK+CLxDv8!eq9$vh76e!2cICUeQX9rK$}dO|5;qtKXFijW z!k9-PZfkL?M;-sN&m9q9pZFJ+e?fd4w~jCkoz1X3-WLt5==OKheh1%b2jGz z3GrG~R?(OHQWY)VcjNAx$nnF74YLk(?^JTvm7BCi$f<(=fRY>{ub?OYs+1I1wNw-& zC3J|sC@RQM(80aXvI9NGy~Ms3bpLckNhR37H$gfCiKYWj148`)@zaN~ za?}}CQP|f}9o1O* graphs.Graph: + self.graph = None + + raise NotImplementedError + + + def loadGraphFromFile(self): + + raise NotImplementedError + + + + + # required functions: + # Generate a graph instance (in networkx graph) (generate x,y points and put into graph) + # Set seed + # Coarsen graph for easier representation + # Uncoarsen graph + + + + + +class VRPRoute: + """ + Should include capacity and demand + """ + def __init__(self, graph, config): + + self.status = {'solved':False} + + return + + + + def visualiseRoute(self, VRPSolution): + + raise NotImplementedError + + + + def evaluateKPIs(self): + + + raise NotImplementedError + + + def recordMetaData(self): + """ + Add important details to self.metaData for later analysis + """ + raise NotImplementedError + + + def coarsenGraph(self, coarsenConfig, coarsenAlg = None): + """ + Coarsen a provided graph to generate a compressed representation + """ + coarseGraph = None + coarsenConfig = coarsenConfig + + raise NotImplementedError + + + + def inflateGraph(self, coarseGraph): + """ + Is this needed? + """ + raise NotImplementedError + + + + + +class VRPSolver(ABC): + + "ABC with both a solver and model converter" + + + # required functions: + # Solve the route problem + # Convert problem to a sufficient model + # Solve the problem using either quantum or classical (or both) methods + # Validate feasibility + # Extract data from solution + + + def __init__(self, RouteEncoder): + + return + + + @abstractclassmethod + def solveVRP(self, VRPRoute: VRPRoute) -> list: + """ + Needs the route instance + """ + # converts to required format + # solves + # extracts data + # validates feasibility + # returns a k-long list of routes (one route for each vehicle) + #[[1,2,5,6,1], [8,9,10,8]] + + + + return + + + @abstractclassmethod + def validateFeasibility(self): + + return + + + @abstractclassmethod + def extractData(self): + + return + + + + + + + + + +class VRPVQESolver(VRPSolver): + + def __init__(self, RouteEncoder, ): + + return + + + + + + +class VRPQASolver(VRPSolver): + + def __init__(self, RouteEncoder, ): + + return + + + + + + +class VRPQAOASolver(VRPSolver): + + def __init__(self, RouteEncoder, ): + + return + + + + + + +class VRPClassicalSolver(VRPSolver): + + def __init__(self, RouteEncoder): + + return + + + + + + +class RouteEncoder(ABC): + """ Converts to either a QUBO, ILP etc for solving""" + + def __init__(self, ): + + return + + @abstractclassmethod + def encodeRoute(): + + return + + + +class QUBOEncoder(RouteEncoder): + def __init__(self, ): + + return + + + + +class ILPEncoder(RouteEncoder): + def __init__(self, ): + + return + + + + + +class solver_backend(): + """Collection of solver functions for all interfaces - i.e gurobi, qiskit, dwave""" + + + + + +# Definitions +# VRP Graph - collection of (x,y) points representing locations. Assumes all locations are fully connected +# Route - a sequence (or combination of sequences) travelled by a vehicle to reach all (x,y) points in route +# VRPSolver - an object which + +if __name__ == "__main__": + + # example of comparing multiple types of solvers + + # 1. generate graph object - loading in from a saved file + graphFileName = 'experimentalGraph.csv' + VRPnetwork = VRPGraph(loadFromeFile = True, filename = graphFileName) + + # 2. Define configuration for route: + config = { 'vehicles' : 7, + 'depot' : 0, + 'capacity': -1, + 'demand': -1 } + + # 3. Define solvers to compare: (including all variations etc) + solverList = [VRPClassicalSolver, VRPQAOASolver, VRPVQESolver, VRPQASolver] + solutionList = [] + + # 4. Iterate through solver list and solve for each tested + for solver in solverList: + # define route + route = VRPRoute(VRPnetwork, config) + + #route.coarsenGraph() + + # solve route + solvedRoute = solver.solve(route, solverConfig) + + # add solved route to list for post-processing + solutionList.append(solvedRoute) + + # 5. Post Process - can also do it while solving stuff + for solvedRoute in solutionList: + results = solvedRoute.evaluateKPIs() + + + diff --git a/Src/external/VRP-explorations b/Src/external/VRP-explorations new file mode 160000 index 0000000..191564e --- /dev/null +++ b/Src/external/VRP-explorations @@ -0,0 +1 @@ +Subproject commit 191564ed4e9084d89ed4969ff1bd5084ee63b8b5 diff --git a/Src/setup.py b/Src/setup.py new file mode 100644 index 0000000..1316ee2 --- /dev/null +++ b/Src/setup.py @@ -0,0 +1,62 @@ +from setuptools import find_packages, setup + +long_description = ''' + QIntern 2021 +Implementation of space-efficient variational algorithms +for the Graph Coloring or Traveling Salesperson problems +in Qiskit +''' + +setup( + name="QuantumLogistics", + version="0.0.1", + description="A quantum optimisation toolkit for the Vehicle routing problem", + long_description=long_description, + long_description_content_type="text/markdown", + url="https://gitlab.com/qworld/qresearch/qintern2021/21_solving-vehicle-routing-problem-and-its-variants-using-quantum-computing_b", + project_urls={ + "HomePage": "https://qworld.net/", + }, + keywords='quantum logistics', + packages=find_packages(), + install_requires=[ + "matplotlib==3.5.1", + "cplex", + "pygsp", + "networkx", + "qiskit", + "qiskit_optimization", + "dwave-ocean-sdk", + "pulp", + "pytest", + "pandas", + "graph_coarsening @ git+https://github.com/loukasa/graph-coarsening", + ], + classifiers=[ + # Project Maturity + "Development Status :: 1 - Planning", + + # Topic + "Topic :: Communications", + "Topic :: Scientific/Engineering :: Physics", + + # Intended Audience + "Intended Audience :: Science/Research", + + # Compatibility + "Operating System :: Microsoft :: Windows", + "Operating System :: MacOS", + "Operating System :: POSIX :: Linux", + + # Python Version + "Programming Language :: Python :: 3", + "Programming Language :: Python :: 3.4", + "Programming Language :: Python :: 3.5", + "Programming Language :: Python :: 3.6", + "Programming Language :: Python :: 3.7", + "Programming Language :: Python :: 3.8", + "Programming Language :: Python :: 3.9", + "Programming Language :: Python :: 3.10", + "Programming Language :: Python :: 3.11" + ], +) \ No newline at end of file From 563014777dad2f817d5be97557d70aeee4c510d7 Mon Sep 17 00:00:00 2001 From: Rithik Rai Date: Sun, 16 Nov 2025 14:00:43 +0530 Subject: [PATCH 02/12] Remove VRP-explorations submodule --- .gitmodules | 3 --- Src/external/VRP-explorations | 1 - 2 files changed, 4 deletions(-) delete mode 160000 Src/external/VRP-explorations diff --git a/.gitmodules b/.gitmodules index 64378bb..e69de29 100644 --- a/.gitmodules +++ b/.gitmodules @@ -1,3 +0,0 @@ -[submodule "Src/external/VRP-explorations"] - path = Src/external/VRP-explorations - url = https://github.com/AsishMandoi/VRP-explorations diff --git a/Src/external/VRP-explorations b/Src/external/VRP-explorations deleted file mode 160000 index 191564e..0000000 --- a/Src/external/VRP-explorations +++ /dev/null @@ -1 +0,0 @@ -Subproject commit 191564ed4e9084d89ed4969ff1bd5084ee63b8b5 From 01cebbfd6d6e9a8805f0dd303206171fa367c029 Mon Sep 17 00:00:00 2001 From: Rithik Rai Date: Sun, 16 Nov 2025 14:07:04 +0530 Subject: [PATCH 03/12] Add VRP-explorations as normal folder --- .../RouteSolver/SolverBackends/SolverBackends.py | 1 + 1 file changed, 1 insertion(+) diff --git a/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py b/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py index fc3b12c..b144312 100644 --- a/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py +++ b/Src/QuantumLogistics/RouteSolver/SolverBackends/SolverBackends.py @@ -9,6 +9,7 @@ # # dirty hack, I am aware # sys.path.insert(0, "/home/knalecz/Pulpit/PhD/aktualne_projekty/QReaserch/VRP-explorations") + # Path to the 'Src' directory. # This goes up three levels from the current file's directory # (SolverBackends -> RouteSolver -> QuantumLogistics -> Src) From 8bf258ce503812df2cef0564205ef3bd0bea2ad9 Mon Sep 17 00:00:00 2001 From: Rithik Rai Date: Sun, 16 Nov 2025 14:08:16 +0530 Subject: [PATCH 04/12] Add VRP-explorations as normal folder --- Src/external/VRP-explorations | 1 + 1 file changed, 1 insertion(+) create mode 160000 Src/external/VRP-explorations diff --git a/Src/external/VRP-explorations b/Src/external/VRP-explorations new file mode 160000 index 0000000..191564e --- /dev/null +++ b/Src/external/VRP-explorations @@ -0,0 +1 @@ +Subproject commit 191564ed4e9084d89ed4969ff1bd5084ee63b8b5 From 1c0e3f13435955c3c42bd8b89309b8b72a89f584 Mon Sep 17 00:00:00 2001 From: Rithik Rai Date: Sun, 16 Nov 2025 14:18:17 +0530 Subject: [PATCH 05/12] Delete VRP-explorations --- Src/external/VRP-explorations | 1 - 1 file changed, 1 deletion(-) delete mode 160000 Src/external/VRP-explorations diff --git a/Src/external/VRP-explorations b/Src/external/VRP-explorations deleted file mode 160000 index 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b/Src/external/VRP-explorations/LICENCE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2023 Asish Kumar Mandoi + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Src/external/VRP-explorations/README.md b/Src/external/VRP-explorations/README.md new file mode 100644 index 0000000..9afa3e0 --- /dev/null +++ b/Src/external/VRP-explorations/README.md @@ -0,0 +1,147 @@ +# **Solving the Vehicle Routing Problem** +*Exploring various quantum annealing-based approaches to solve the vehicle routing problem.* + +This project was part of the **QOSF Quantum Computing Mentorship Program 2021 Cohort 4**, mentored by [**Dr. Vesselin G. Gueorguiev**](https://www.linkedin.com/in/vgg-consulting/)
+Mentees: *The Qubit Players* + - **Asish Kumar Mandoi**
+ *Junior Undergraduate at Indian Institute of Technology Kanpur, Department of Electrical Engineering*
+ [`Website`](https://asishmandoi.github.io/) ~ [`LinkedIn`](https://www.linkedin.com/in/asish-mandoi-4178581b4/) ~ [`GitHub`](https://github.com/AsishMandoi) + - **Arya Bhatta**
+ *Junior Undergraduate at Indian Institute of Technology Kanpur, Department of Electrical Engineering*
+ [`LinkedIn`](https://www.linkedin.com/in/arya-bhatta-26a877200/) + +This is now under development as part of a research group at QWorld. + +**Any usage of this code is free but do cite this code's authors and the organizations if you use it for research or commercial purposes. Please contact the authors for more information.** + +## Introduction +Vehicle routing is a challenging logistics management problem. More precisely, it is an **NP-hard** combinatorial optimization problem. +- Problem statement: ***What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?*** +- Generalises **The Travelling Salesman Problem (TSP)**. + +## Overview +The primary focus of the project has been on improving the applicability of quantum annealing-based solvers for the Vehicle Routing Problem (VRP) for large numbers of customers and vehicles by using a minimal number of qubits. It includes implementations of three solvers: + - Route Activation Solver + - GPS Solver (Guillermo, Parfait, Saúl) ~ [[4](https://github.com/AsishMandoi/VRP-explorations#references)] + - DBSCAN Solver ~ [[7](https://github.com/AsishMandoi/VRP-explorations#references)] + +The first two are non-clustering solvers that give exact solutions for the simplest variant of the VRP for small datasets and the third one is a clustering-based solver that gives approximate solutions for large datasets. The project also demonstrates the usage of the [Binary Quadratic Model](https://docs.ocean.dwavesys.com/en/stable/concepts/bqm.html) and [Constrained Quadratic Model](https://docs.ocean.dwavesys.com/en/stable/concepts/cqm.html) provided by D-Wave to formulate various other solvers including the above. The accuracy and runtimes of these solvers, calculated against the exact solutions obtained by classical implementations using [Google's OR-Tools](https://developers.google.com/optimization), are compared with each other. +
+ +*The project was inspired from [this video](https://youtu.be/GK8IT0C9Upk) and [this paper](https://link.springer.com/chapter/10.1007/978-3-030-50433-5_42) by [**Paweł Gora**](https://www.mimuw.edu.pl/~pawelg/) and others. A lot of initial ideas were borrowed from [a project on the same topic](https://github.com/VGGatGitHub/QOSF-cohort3) by **Shantom Borah** and others.* + +## Get started +You may start with the `solve_vrp.ipynb` notebook where you can choose to run any solver on any model and get the solutions to the Vehicle Routing Problem for any number of clients and vehicles. You can play with the `time_limit` parameter to see how the solver performs on different datasets, but make sure not to set it too high as you may exhaust your limited monthly resources on your D-Wave Leap account. + +The `quantum` subfolder in the VRP folder further contains two more subfolders `CQM_based` and `BQM_based`. The first one contains the implementations of the solvers using the Constrained Quadratic Model (CQM) and the second one contains the implementations of the solvers using the Binary Quadratic Model (BQM).: +- Constrained Quadratic Model is a new model recently released by D-Wave Systems that is capable of encoding Quadratically Constrained Quadratic Programs (QCQPs) +- Binary Quadratic Model is a model that encodes Ising or QUBO problems. + +### **Directory Structure** +

+ (click to expand) + + ```bash + VRP-explorations + ├── _venv_ # (virtual python environment) + ├── presentations + │ ├── notebook_1.ipynb + │ ├── . + │ ├── . + │ └── notebook_9.ipynb + ├── datasets + │ ├── generate_dataset_for_vrp.ipynb + │ └── dataset.csv + ├── results + │ ├── sol2.log + │ ├── . + │ ├── . + │ ├── sol11.log + │ ├── sol2.csv + │ ├── . + │ ├── . + │ ├── sol11.csv + │ └── results.png + ├── TSP + │ ├── classical + │ │ └── gps.py + │ └── quantum + │ ├── fqs.py + │ └── gps.py + ├── VRP + │ ├── classical + │ │ ├── ras.py + │ │ └── sps.py + │ └── quantum + │ ├── BQM_based + │ │ ├── full_qubo_solver.py + │ │ ├── route_activation_solver.py + │ │ ├── solution_partition_solver.py + │ │ ├── dbscan_solver.py + │ │ └── ... + │ └── CQM_based + │ ├── fqs.py + │ ├── gps.py + │ └── ras.py + ├── utils.py + ├── solve_tsp.py + ├── solve_vrp.py + ├── vrp_comparision_results.py + ├── post_processing_results.py + ├── requirements.txt + ├── setup.sh + ├── .gitignore + └── README.md + ``` +
+ +## Results +The following is a concise comparision of results obtained by running (non-clustering) solvers for [this dataset](https://gitlab.com/qworld/qresearch/qintern2021/21_solving-vehicle-routing-problem-and-its-variants-using-quantum-computing_b/-/tree/master/Datasets%20for%20VRP) (`generate_dataset_for_vrp.ipynb`) using the `ConstrainedQuadraticModel` and `LeapHybridCQMSampler` provided by D-Wave. + +![results.png](https://github.com/AsishMandoi/VRP-explorations/blob/main/results/results.png) + + +The results for more instances can be found in the [results](https://github.com/AsishMandoi/VRP-explorations/tree/main/results) folder. + +It can be seen that these solvers give exact solutions for upto 7 nodes (6 clients and 1 depot) and are as good as classical ones in terms of accuracy and runtimes, and acceptable solutions till upto 15 nodes. + +## Run this repo + +### Locally +Requirements: +- A bash terminal +- Python version >= 3.9 +- D-Wave Leap account + +```bash +# Clone this repo +git clone https://github.com/AsishMandoi/VRP-explorations.git + +# Go into the project's main directory and setup the environment to run all codes +cd VRP-explorations && bash setup.sh + +### The `setup.sh` script consists of the following steps: +# 1. Create a virtual environment (named '_venv_') if it doesn't exist +# 2. Install the required packages in the virtual environment +# 3. Run `dwave setup` to get access to the D-Wave backend solvers +``` +*The above process will also run the `dwave setup` command. This will require your authentication token from your account on D-Wave Leap. Learn more about how to [set up your environment](https://docs.ocean.dwavesys.com/en/latest/overview/install.html#set-up-your-environment) for using `dwave-ocean-sdk`.* + +### On D-Wave Leap platform +*Coming soon* + +## Future work +- [ ] Incorporate solutions for other more general variants of the problem (especially for the CVRPTW) +- [ ] Make a circuit based algorithm from scratch (that does not use any application modules from any libraries) to solve VRP +- [ ] Find potential real life applications for VRP (for e.g. Supply Chain, Traffic Flow Optimization) + +## References +1. Borowski, Michal, Gora, Pawel, *"New Hybrid Quantum Annealing Algorithms for Solving Vehicle Routing Problem"* (2020) +2. Feld, Sebastian, et al. *"A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer"* (2019) +3. Fisher, Marshall L., Jaikumar, Ramchandran, *"A generalized assignment heuristic for vehicle routing"* (1981) +4. Gonzalez-Bermejo, Saul, et al. *"GPS: Improvement in the formulation of the TSP for its generalizations type QUBO"* +5. The [QOSF cohort - 3 project](https://github.com/VGGatGitHub/QOSF-cohort3) by Shantom, Aniket and Avneesh based on this topic +6. [Vehicle routing problem - Wikipedia](https://en.wikipedia.org/wiki/Vehicle_routing_problem) +7. [DBSCAN - Wikipedia](https://en.wikipedia.org/wiki/DBSCAN) +8. D-Wave's documentations on [Binary Quadratic Model](https://docs.ocean.dwavesys.com/en/stable/concepts/bqm.html) and [Constrained Quadratic Model](https://docs.ocean.dwavesys.com/en/stable/concepts/cqm.html) +11. [Google's OR-Tools](https://developers.google.com/optimization/routing/vrp) diff --git a/Src/external/VRP-explorations/TSP/classical/gps.py b/Src/external/VRP-explorations/TSP/classical/gps.py new file mode 100644 index 0000000..bf449bc --- /dev/null +++ b/Src/external/VRP-explorations/TSP/classical/gps.py @@ -0,0 +1,151 @@ +from ortools.sat.python import cp_model +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import time + + +''' +Solving a custom formulation (GPS) of TSP using Google's OR-Tools +''' + + +class GPS(): + '''Guillermo Alonso-Linaje, Parfait Atchade-Adelomou, and Saúl Gonzalez-Bermejo''' + + def __init__(self, n, cost, xc, yc): + self.n = n + self.cost = cost + self.xc = xc + self.yc = yc + self.sol = None + self.model = cp_model.CpModel() + self.formulate_and_solve() + self.visualize() + + + def formulate_and_solve(self): + '''Formulate and solve the problem''' + + ##### Declare Variables ##### + x = [[[None] * 3 for _ in range(self.n+1)] for __ in range(self.n+1)] + w = [[[[None] * 3 for _ in range(self.n+1)] for __ in range(self.n+1)] for ___ in range(self.n+1)] + + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + for r in range(3): + x[i][j][r] = self.model.NewBoolVar(f'x.{i}.{j}.{r}') + + for i in range(self.n+1): + for j in range(self.n+1): + for k in range(self.n+1): + if i != j and i != k and j != k: + for r in range(1, 3): + w[i][j][k][r] = self.model.NewBoolVar(f'w.{i}.{j}.{k}.{r}') + + + ##### CONSTRAINTS ##### + # Constraint 1: For each i, j one and only one of the possibilities must be met for r. + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + self.model.Add(sum(x[i][j][r] for r in range(3)) == 1) + + # Constraint 2a: Each city (including depot) must be reached only once. + for j in range(self.n+1): + self.model.Add(sum(x[i][j][1] for i in range(self.n+1) if i != j) == 1) + + # Constraint 2b: Each city (including depot) must be exited only once. + for i in range(self.n+1): + self.model.Add(sum(x[i][j][1] for j in range(self.n+1) if i != j) == 1) + + # Constraint 3: A city i can either be reached earlier or later than a city j. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + self.model.Add(x[i][j][0] + x[j][i][0] == 1) + + # Constraint 4: If city i is reached before city j, and city j is reached before city k, then city i must be reached before city k. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + for k in range(1, self.n+1): + if i != j and j != k and k != i: + self.model.Add(x[i][j][0] + x[j][k][0] <= 2 * x[i][k][0] + w[i][j][k][1]) + self.model.Add(x[i][j][0] + x[j][k][0] >= 2 * x[i][k][0] - w[i][j][k][2]) + + + ##### OBJECTIVE ##### + self.model.Minimize(sum(self.cost[i][j] * x[i][j][1] for i in range(self.n+1) for j in range(self.n+1) if i != j)) + + + ##### SOLVE + # Call the solver + solver = cp_model.CpSolver() + t = time.time() + status = solver.Solve(self.model) + t = time.time() - t + + + # Display the solution + if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE: + print(f'\nMinimum cost: {solver.ObjectiveValue()}') + self.sol = [[None for _ in range(self.n+1)] for __ in range(self.n+1)] + for i in range(self.n+1): + for j in range(self.n+1): + if j != i: + self.sol[i][j] = solver.Value(x[i][j][1]) + else: + print('No solution found.') + + print(f'\nTime taken to solve: {t*1000:.3f} ms') + + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Travelling Salesman Problem - {self.n} Clients') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color='C1', node_shape='s') + + edgelist = [] + nodelist = [] + for i in range(self.n + 1): + for j in range(self.n + 1): + if i != j and self.sol[i][j] == 1: + if i: + nodelist.append(i) + edgelist.append((i, j)) + + # Plot other nodes and edges + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist, ax=ax, alpha=0.75, node_size=300, node_color='C0') + + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=1.5, edge_color='C2') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/TSP/quantum/fqs.py b/Src/external/VRP-explorations/TSP/quantum/fqs.py new file mode 100644 index 0000000..b4afc72 --- /dev/null +++ b/Src/external/VRP-explorations/TSP/quantum/fqs.py @@ -0,0 +1,142 @@ +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import dimod +from neal import SimulatedAnnealingSampler +from dwave.system import LeapHybridCQMSampler + +''' +Solving a custom formulation (FQS) of TSP using LeapHybridCQMSampler +''' + +class FQS(): + '''Full Qubo Solver''' + + def __init__(self, n, cost, xc, yc): + self.n = n + self.cost = cost + self.xc = xc + self.yc = yc + self.sol = None + self.model = dimod.ConstrainedQuadraticModel() + self.formulate() + # self.solve() + # self.visualize() + + + def formulate(self): + '''Formulate the problem''' + + x = [[None] * (self.n+1) for _ in range(self.n+1)] + + + ##### Declare variables ##### + for i in range(self.n+1): + for t in range(1, self.n+1): + x[i][t] = dimod.Binary(label=f'x.{i}.{t}') + + + ##### OBJECTIVE ##### + self.model.set_objective( + sum(self.cost[0][i] * x[i][1] for i in range(1, self.n+1)) + + sum(self.cost[i][0] * x[i][self.n] for i in range(1, self.n+1)) + + sum(self.cost[i][j] * x[i][t] * x[j][t+1] for i in range(1, self.n+1) for j in range(1, self.n+1) if i != j for t in range(1, self.n)) + ) + + + ##### CONSTRAINTS ##### + # Exactly one client node is visited at every time step. + for t in range(1, self.n+1): + self.model.add_constraint(sum(x[i][t] for i in range(1, self.n+1)) == 1) + + # Each client node is visited once throughout all the time steps. + for i in range(1, self.n+1): + self.model.add_constraint(sum(x[i][t] for t in range(1, self.n+1)) == 1) + + + def solve(self): + '''Solve the problem''' + + sampler = LeapHybridCQMSampler() + sampleset = sampler.sample_cqm(self.model, label=f'Travelling Salesman Problem ({self.n} Clients) - FQS') + feasible_sampleset = sampleset.filter(lambda row: row.is_feasible) + + if len(feasible_sampleset): + self.sol = feasible_sampleset.first + print("{} feasible solutions of {}.".format(len(feasible_sampleset), len(sampleset))) + print(f'Minimum total cost: {self.sol.energy}') + + ### DONE ABOVE ### + # # Evaluate cost of the solution + # x = [[None] * (self.n+1) for _ in range(self.n+1)] + # varList = [var for var in self.sol.sample] + # for var in varList: + # i=int(var.split('.')[1]) + # t=int(var.split('.')[2]) + # x[i][t] = self.sol.sample[var] + # tot_cost = sum(self.cost[0][i] * x[i][1] for i in range(1, self.n+1)) + sum(self.cost[i][0] * x[i][self.n] for i in range(1, self.n+1)) + sum(self.cost[i][j] * x[i][t] * x[j][t+1] for i in range(1, self.n+1) for j in range(1, self.n+1) if i != j for t in range(1, self.n)) + # print(f'Minimum total cost: {tot_cost}') + + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + + return sampleset + + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + activeVarList = [] + for i in self.sol.sample: + if self.sol.sample[i] == 1: + activeVarList.append((int(i.split('.')[1]), int(i.split('.')[2]))) + + activeVarList = sorted(activeVarList, key=lambda x: x[1]) + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Travelling Salesman Problem - {self.n} Clients') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C1', node_shape='s') + + nodelist = [] + edgelist = [] + tmp = 0 + for var in activeVarList: + if var[0] != tmp: + if var[0]: + nodelist.append(var[0]) + edgelist.append((tmp, var[0])) + tmp = var[0] + edgelist.append((tmp, 0)) + + # Plot other nodes and edges + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist, ax=ax, alpha=0.75, node_size=300, node_color=f'C0') + + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=1.5, edge_color=f'C2') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/TSP/quantum/gps.py b/Src/external/VRP-explorations/TSP/quantum/gps.py new file mode 100644 index 0000000..37b937c --- /dev/null +++ b/Src/external/VRP-explorations/TSP/quantum/gps.py @@ -0,0 +1,155 @@ +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import dimod +from neal import SimulatedAnnealingSampler +from dwave.system import LeapHybridCQMSampler + +''' +Solving a custom formulation (GPS) of TSP using LeapHybridCQMSampler +''' + +class GPS(): + '''Guillermo Alonso-Linaje, Parfait Atchade-Adelomou, and Saúl Gonzalez-Bermejo''' + + def __init__(self, n, cost, xc, yc): + self.n = n + self.cost = cost + self.xc = xc + self.yc = yc + self.sol = None + self.model = dimod.ConstrainedQuadraticModel() + self.formulate() + # self.solve() + # self.visualize() + + + def formulate(self): + '''Formulate the problem''' + + ##### Declare Variables ##### + x = [[[None] * 3 for _ in range(self.n+1)] for __ in range(self.n+1)] + # a = [[None] * (self.n+1) for _ in range(self.n+1)] + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + # a[i][j] = dimod.Binary(f'a.{i}.{j}') + for r in range(3): + x[i][j][r] = dimod.Binary(f'x.{i}.{j}.{r}') + + + ##### OBJECTIVE ##### + self.model.set_objective(sum(self.cost[i][j] * x[i][j][1] for i in range(self.n+1) for j in range(self.n+1) if i != j) + + # Objective function for Constraint-4 + # + sum(x[i][j][0] * x[j][k][0] - x[i][j][0] * x[i][k][0] - x[j][k][0] * x[i][k][0] + x[i][k][0] for i in range(1, self.n+1) for j in range(1, self.n+1) for k in range(1, self.n+1) if i != j and j != k and k != i) + ) + + + ##### CONSTRAINTS ##### + # Constraint 1: For each i, j, one and only one of the possibilities must be met for r. + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + self.model.add_constraint(sum(x[i][j][r] for r in range(3)) == 1) + + # Constraint 2a: Each city (including depot) must be reached only once. + for j in range(self.n+1): + self.model.add_constraint(sum(x[i][j][1] for i in range(self.n+1) if i != j) == 1) + + # Constraint 2b: Each city (including depot) must be exited only once. + for i in range(self.n+1): + self.model.add_constraint(sum(x[i][j][1] for j in range(self.n+1) if i != j) == 1) + + # Constraint 3: A city i can either be reached earlier or later than a city j. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + self.model.add_constraint(x[i][j][2] + x[j][i][2] == 1) + + # Constraint 4: If city i is reached before city j, and city j is reached before city k, then city i must be reached before city k. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + for k in range(1, self.n+1): + if i != j and j != k and k != i: + self.model.add_constraint(x[j][i][2] * x[k][j][2] - x[j][i][2] * x[k][i][2] - x[k][j][2] * x[k][i][2] + x[k][i][2] == 0) + + + def solve(self): + '''Solve the problem''' + + sampler = LeapHybridCQMSampler() + sampleset = sampler.sample_cqm(self.model, label=f"Travelling Salesman Problem ({self.n} Clients) - GPS") + feasible_sampleset = sampleset.filter(lambda row: row.is_feasible) + + if len(feasible_sampleset): + print("{} feasible solutions of {}.".format(len(feasible_sampleset), len(sampleset))) + self.sol = feasible_sampleset.first + print(f'Minimum total cost: {self.sol.energy}') + + ### DONE ABOVE ### + # # Evaluate cost of the solution + # x = [[None] * (self.n+1) for _ in range(self.n+1)] + # varList = [var for var in self.sol.sample if var.split('.')[3] == '1'] + # for var in varList: + # i=int(var.split('.')[1]) + # j=int(var.split('.')[2]) + # x[i][j] = self.sol.sample[var] + # tot_cost = sum(self.cost[i][j] * x[i][j] for i in range(self.n+1) for j in range(self.n+1) if i != j) + # print(f'Minimum total cost: {tot_cost}') + + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + + return sampleset + + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + activeVarList = [i for i in self.sol.sample if self.sol.sample[i] == 1] + activeVarList = [(int(i.split('.')[1]), int(i.split('.')[2])) for i in activeVarList if i.split('.')[3] == '1'] + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Travelling Salesman Problem - {self.n} Clients') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C1', node_shape='s') + + edgelist = [] + nodelist = [] + for var in activeVarList: + if var[0]: + nodelist.append(var[0]) + edgelist.append((var[0], var[1])) + + # Plot other nodes and edges + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist, ax=ax, alpha=0.75, node_size=300, node_color=f'C0') + + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=1.5, edge_color=f'C2') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/VRP/classical/ras.py b/Src/external/VRP-explorations/VRP/classical/ras.py new file mode 100644 index 0000000..9121039 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/classical/ras.py @@ -0,0 +1,176 @@ +from ortools.sat.python import cp_model +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import time + +''' +Solving VRP using a CP-SAT solver +CP-SAT solver: A constraint programming solver that uses SAT (satisfiability) methods. +''' + +class RAS(): + '''Classical Implementation of Route Activation Solver (Method-1)''' + + def __init__(self, n, m, cost, xc, yc): + self.n = n + self.m = m + self.cost = cost + self.xc = xc + self.yc = yc + self.T_max = max(self.n-self.m+1, 1) + self.B = 2*self.n + self.sol = None + self.model = cp_model.CpModel() + # self.formulate_and_solve() + # self.visualize() + + def formulate_and_solve(self): + '''Formulate and solve the problem''' + + x = [[None] * (self.n+1) for _ in range(self.n+1)] + y = [[None] * (self.m+1) for _ in range(self.n+1)] + t = [[None] * (self.m+1) for _ in range(self.n+1)] + w = [[None] * (self.m+1) for _ in range(self.n+1)] + + + ##### Designate variable names + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + x[i][j] = self.model.NewBoolVar(f'x.{i}.{j}') + + for i in range(1, self.n+1): + for k in range(1, self.m+1): + y[i][k] = self.model.NewBoolVar(f'y.{i}.{k}') + t[i][k] = self.model.NewIntVar(1, self.T_max, f't.{i}.{k}') + w[i][k] = self.model.NewIntVar(0, self.T_max, f'w.{i}.{k}') + + + ##### CONSTRAINTS + for i in range(1, self.n+1): + + # Each client node must have exactly one edge directed away from it + self.model.Add(sum(x[i][j] for j in range(self.n+1) if j != i) == 1) + + # Each client node must have exactly one edge directed towards it + self.model.Add(sum(x[j][i] for j in range(self.n+1) if j != i) == 1) + + # Each client must be visited by exactly one vehicle + self.model.Add(sum(y[i][k] for k in range(1, self.m+1)) == 1) + + # m vehicles coming from depot + self.model.Add(sum(x[0][i] for i in range(1, self.n+1)) == self.m) + + # m vehicles going to depot + self.model.Add(sum(x[i][0] for i in range(1, self.n+1)) == self.m) + + # If there is an edge from node i to node j, then they must be visited by the same vehicle + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + for k in range(1, self.m+1): + self.model.Add(y[i][k] >= y[j][k] - (1 - x[i][j])) + self.model.Add(y[j][k] >= y[i][k] - (1 - x[i][j])) + + # Each vehicle must be used at least once + for k in range(1, self.m+1): + self.model.Add(sum(y[i][k] for i in range(1, self.n+1)) >= 1) + + # Eliminate subtours - MTZ constraint + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + for k in range(1, self.m+1): + self.model.Add(w[j][k] >= w[i][k] + y[i][k] - self.B*(1 - x[i][j])) + self.model.Add(w[i][k] >= y[i][k]) + self.model.Add(w[i][k] >= self.T_max*y[i][k] + t[i][k] - self.T_max) + self.model.Add(w[i][k] <= self.T_max*y[i][k]) + self.model.Add(w[i][k] <= t[i][k] + y[i][k] - 1) + + + ##### OBJECTIVE FUNCTION + self.model.Minimize(sum(self.cost[i][j]*x[i][j] for i in range(self.n+1) for j in range(self.n+1) if i != j)) + + + ##### SOLVE + # Call the solver + solver = cp_model.CpSolver() + t = time.time() + status = solver.Solve(self.model) + t = time.time() - t + + + # Display the solution + if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE: + sol = { + 'min_cost': solver.ObjectiveValue(), + 'runtime': t*1000 + } + + print('\nEXACT (CLASSICAL) SOLVER') + print(f'Minimum cost: {sol["min_cost"]}') + self.sol = [[[None] * (self.n+1) for _ in range(self.n+1)]] + [[[None] * (self.m+1) for _ in range(self.n+1)]] + for i in range(self.n+1): + for j in range(self.n+1): + if j != i: + self.sol[0][i][j] = solver.Value(x[i][j]) + for i in range(1, self.n+1): + for k in range(1, self.m+1): + self.sol[1][i][k] = solver.Value(y[i][k]) + print(f'Time taken to solve: {t*1000:.3f} ms') + return sol + else: + print('No solution found.') + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C0', node_shape='s') # shapes - 'so^>v' + route_distance += self.routing.GetArcCostForVehicle(nodelists[i][j], nodelists[i][j+1], 0) + plan_output += f' {nodelists[i][-1]}\n' + plan_output += f'Route distance: {route_distance}\n' + print(plan_output) + total_route_distance += route_distance + + print(f"Total Distance: {total_route_distance}") + + + # Create and register a transit callback. + def distance_callback(self, from_index, to_index): + """Returns the distance between the two nodes.""" + # Convert from routing variable Index to distance matrix NodeIndex. + from_node = self.manager.IndexToNode(from_index) + to_node = self.manager.IndexToNode(to_index) + return self.data['distance_matrix'][from_node][to_node] + + + def main(self): + transit_callback_index = self.routing.RegisterTransitCallback(self.distance_callback) + + # Define cost of each arc. + self.routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index) + + # Add Distance constraint. + dimension_name = 'Distance' + self.routing.AddDimension( + transit_callback_index, + 0, # no slack + 3000, # vehicle maximum travel distance + True, # start cumul to zero + dimension_name) + distance_dimension = self.routing.GetDimensionOrDie(dimension_name) + distance_dimension.SetGlobalSpanCostCoefficient(100) + + # Setting first solution heuristic. + search_parameters = pywrapcp.DefaultRoutingSearchParameters() + search_parameters.first_solution_strategy = ( + routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC) + + # Solve the problem. + self.sol = self.routing.SolveWithParameters(search_parameters) + + def partition(self): + depot = index = self.routing.Start(0) + indexList = [] + while not self.routing.IsEnd(index): + indexList.append(index) + index = self.sol.Value(self.routing.NextVar(index)) + + indexList.append(depot) + + partitionCost = [] + # Get the cost partitioning + for i, idx in enumerate(indexList): + prev_idx = idx + if i == self.n: + break + idx = indexList[i+1] + if prev_idx != depot and idx != depot: + cost = self.routing.GetArcCostForVehicle(prev_idx, depot, 0) + self.routing.GetArcCostForVehicle(depot, idx, 0) - self.routing.GetArcCostForVehicle(prev_idx, idx, 0) + partitionCost.append((prev_idx, idx, cost)) + partitionCost.sort(key=lambda x: x[2]) + + nodelists = [] + j, k = 0, 0 + for i in range(len(partitionCost)): + if j == self.m-1: + nodelists.append(indexList[k:]) + break + if partitionCost[i][0] != depot and partitionCost[i][1] != depot: + j += 1 + idx = indexList.index(partitionCost[i][0]) + indexList[idx:idx+1] = partitionCost[i][0], depot + nodelists.append(indexList[k:idx+2]) + k = idx+1 + + return nodelists + + def visualize(self, nodelists=None): + '''Visualize solution''' + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C0', node_shape='s') + + # Loop over cars and plot other nodes and edges + for vehicle_id in range(self.m): + nodelist = nodelists[vehicle_id] + edgelist = [] + for i in range(len(nodelist) - 1): + edgelist.append((nodelist[i], nodelist[i+1])) + + # Plot nodes + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist[1:][:-1], ax=ax, alpha=0.75, node_size=300, node_color=f'C{vehicle_id + 1}') + + # Plot edges + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=1.5, edge_color=f'C{vehicle_id + 1}') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() \ No newline at end of file diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/README.md b/Src/external/VRP-explorations/VRP/quantum/BQM_based/README.md new file mode 100644 index 0000000..06566bb --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/README.md @@ -0,0 +1,28 @@ +# Vehicle Routing Problem - Core Solvers +This directory contains the core solvers for solving the Vehicle Routing Problem. API usage instructions may be found in the code docstrings. Example usage is shown in the ***Vehicle Routing.ipynb*** notebook. + +## Core Solvers +Following core solvers have been implemented. + + - ***FQS*** - Full Qubo Solver + - ***APS*** - Average Partitioning Solver + - ***RAS*** - Route Activation Solver + - ***QNS*** - Qiskit Native Solver + - ***CTS*** - Clustered Tsp Solver + - ***SPS*** - Solution Partitioning Solver + +Descriptions of individual solvers may be found in the ***Vehicle Routing.ipynb*** notebook. + +## Solver Backends +Following backend solvers may be used. + + - D-Wave Sampler + - D-Wave Hybrid Sampler + - Leap Hybrid Sampler + - Qiskit QAOA Backend + +## Python Files +Each solver is implemented as a seperate python class in a seperate python file. The solver classes inherit from a base **VehicleRouter** class defined in **vehicle_routing.py**. There are three other files: + - **node_clustering.py:** This file implements a **NodeClustering** class for clustering in CTS via Leap's Hybrid DQM Sampler. + - **solver_backend.py:** This file contains the backend solvers listed above. + - **utility.py:** This file implements general utility functions such as generatinga random VRP instance. diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/Vehicle Routing Problem.ipynb b/Src/external/VRP-explorations/VRP/quantum/BQM_based/Vehicle Routing Problem.ipynb new file mode 100644 index 0000000..6125f19 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/Vehicle Routing Problem.ipynb @@ -0,0 +1,681 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "Gnwwha9_1yRa" + }, + "source": [ + "# Vehicle Routing Problem\n", + "\n", + " - **QOSF Mentorship Program - Spring 2021**\n", + " - **Mentor: Dr. Vesselin Gueorguiev**\n", + " - **Mentees: Aniket Sanjay Sinha, Avneesh Verma, Shantom Kumar Borah**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "This document explores various formulations and algorithms involved in solving the Vehicle Routing Problem (VRP) via Quadratic Unconstrained Binary Optimization (QUBO) on a quantum computer. For the solution of QUBOs on a quantum computer, currently available gate-based quantum computers are only able to solve the simplest versions of the problem, due to a very limited number of qubits. In this document, we use D-Wave's quantum computers based on Quantum Annealing to solve the Vehicle Routing Problem. D-Wave's quantum computers have access to a signifiantly larger number of qubits (more than 5000 for the newest Advantage Systems) and enable the solution of significantly larger versions of the VRP. The contents of this document are organized as follows:\n", + "\n", + " - *Problem Statement*\n", + " - *Core Solvers*\n", + " - *Qubit Complexity Comparison*\n", + " - *QUBO Cost and Execution Times*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem Statement\n", + "The Vehicle Routing Problem (VRP) may be thought of as a generalization of the Travelling Salesman Problem (TSP) with $M$ salesmen instead of one. Specifically, we have depot with a certain amount of goods that need to be delivered to a number of clients located at different places. The depot has access to $M$ delivery vehicles to make these deliveries. Let $N$ be the number of clients. Consider a fully connected graph of $N + 1$ nodes with the depot being the node $0$ and the variouis clients being nodes $\\{1, 2, \\dots N\\}$. Every edge $(i, j)$ of this fully connected graph represents the cost of moving from node $i$ to node $j$. This cost could be the time taken, the distance covered or anything at all that needs to be minimized. In our case, we have chosen it to be distance. The objective is to simply find the optimal route through this graph, for each vehicle, so that all deliveries are made with minimum cost. We use the following notation for the rest of this document:\n", + "\n", + " - *$N$: No. of clients, excluding the depot*\n", + " - *$M$: No. of vehicles*\n", + " - *$C_{ij}$: Cost of moving from node $i$ to node $j$*\n", + "\n", + "**Objective**: Find the optimal route for all $M$ vehicles covering all $N$ routes so that the total cost of this route is minimized." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Core Solvers\n", + "\n", + "In this project, we have investigated six different formulations of the VRP for solving via quantum annealing. Each of these have their own advantages and disadvantages. These six solvers are listed below:\n", + "\n", + " - *Full QUBO Solver*\n", + " - *Average Partitioning Solver*\n", + " - *Route Activation Solver*\n", + " - *Qiskit Native Solver*\n", + " - *Clustered TSP Solver*\n", + " - *Solution Partitioning Solver*\n", + "\n", + "In this section, we shall outline each of these solvers and demonstrate their solution using D-Wave's Leap Hybrid Solvers. For each solver, we outline how the problem is represented in QUBO form below, along with the objective function to be minimized and the various associated constraints, followed by an example usage of the code. We begin by importing the necessary files and creating a test VRP instance to demonstrate the working of each of these solvers." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import utility\n", + "\n", + "from full_qubo_solver import FullQuboSolver\n", + "from average_partition_solver import AveragePartitionSolver\n", + "from qiskit_native_solver import QiskitNativeSolver\n", + "from route_activation_solver import RouteActivationSolver\n", + "from clustered_tsp_solver import ClusteredTspSolver\n", + "from solution_partition_solver import SolutionPartitionSolver" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "04qampda2ZKn" + }, + "outputs": [], + "source": [ + "n = 5\n", + "m = 2\n", + "seed = 1543" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "instance, xc, yc = utility.generate_vrp_instance(n, seed)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Full Qubo Solver (FQS)\n", + "\n", + "***Representation***\n", + "\n", + "$x_{i,j,k} = 1$ if $i^{th}$ vehicle is in $j^{th}$ node at the $k^{th}$ timestep.\n", + "\n", + "$$i \\in \\{1, 2, \\dots M\\}; \\; j \\in \\{0, 1, \\dots N\\}; \\; k \\in \\{1, 2, \\dots N\\}$$\n", + "\n", + "***Objective Function***\n", + "\n", + "$$C = \\sum_{m=1}^M \\sum_{n=1}^N C_{0,n} x_{m,n,1} + \\sum_{m=1}^M \\sum_{n=1}^N C_{n,0} x_{m,n,N} + \\sum_{m=1}^M \\sum_{n=1}^{N-1} \\sum_{i=0}^{N} \\sum_{j=0}^{N} C_{i,j} x_{m,i,n} x_{m,j,n+1}$$\n", + "\n", + "Here, the first term represents the cost of moving from the depot to the first visited client for each vehicle, the second term represents the cost of moving from the last visited client to the depot for each vehicle, and the third term represents the costs at the intermediate nodes.\n", + "\n", + "***Constraints***\n", + "\n", + " - Every node (other than the depot) is served by exactly one vehicle at exactly one time instant.\n", + "\n", + "$$\\sum_{i=1}^M \\sum_{j=1}^N x_{i,k,j} = 1 \\;\\;\\forall k$$\n", + "\n", + " - A vehicle can be at only one place at any given timestep.\n", + "\n", + "$$\\sum_{k=0}^N x_{i,k,j} = 1 \\;\\;\\forall i, j$$\n", + "\n", + "***Qubit Complexity***\n", + "\n", + " - No. of Logical Variables: $MN(N+1)$\n", + " - Best Case: $N(N+1)$\n", + " - Worst Case: $N^2(N+1)$\n", + "\n", + "![](images/fqs_complexity.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fqs = FullQuboSolver(n, m, instance)\n", + "fqs.solve(solver='leap')\n", + "fqs.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Average Partitioning Solver (APS)\n", + "\n", + "***Representation***\n", + "\n", + "$x_{i,j,k} = 1$ if $i^{th}$ vehicle is in $j^{th}$ node at the $k^{th}$ timestep.\n", + "\n", + "$$i \\in \\{1, 2, \\dots M\\}; \\; j \\in \\{0, 1, \\dots N\\}; \\; k \\in \\{1, 2, \\dots T\\}$$\n", + "\n", + "The maximum timestep $T$ is evaluated as follows\n", + "\n", + "$$T = \\min\\{N, \\frac{N}{M} + L\\}$$\n", + "\n", + "Here, $L$ is a solver parameter called *Limit Radius* and naturally, we round up the above $T$ to the next integer.\n", + "\n", + "***Objective Function***\n", + "\n", + "$$C = \\sum_{m=1}^M \\sum_{n=1}^N C_{0,n} x_{m,n,1} + \\sum_{m=1}^M \\sum_{n=1}^N C_{n,0} x_{m,n,T} + \\sum_{m=1}^M \\sum_{n=1}^{T-1} \\sum_{i=0}^{N} \\sum_{j=0}^{N} C_{i,j} x_{m,i,n} x_{m,j,n+1}$$\n", + "\n", + "Here, the first term represents the cost of moving from the depot to the first visited client for each vehicle, the second term represents the cost of moving from the last visited client to the depot for each vehicle, and the third term represents the costs at the intermediate nodes.\n", + "\n", + "***Constraints***\n", + "\n", + " - Every node (other than the depot) is served by exactly one vehicle at exactly one time instant.\n", + "\n", + "$$\\sum_{i=1}^M \\sum_{j=1}^T x_{i,k,j} = 1 \\;\\;\\forall k$$\n", + "\n", + " - A vehicle can be at only one place at any given timestep.\n", + "\n", + "$$\\sum_{k=0}^N x_{i,k,j} = 1 \\;\\;\\forall i, j$$\n", + "\n", + "***Qubit Complexity***\n", + "\n", + " - No. of Logical Variables: $MT(N+1)$\n", + " - Best Case: $N(N+1)$\n", + " - Worst Case: $N^2(N+1)$\n", + "\n", + "![](images/aps_complexity.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "aps = AveragePartitionSolver(n, m, instance)\n", + "aps.solve(solver='leap')\n", + "aps.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Route Activation Solver (RAS)\n", + "\n", + "***Representation***\n", + "\n", + "$x_{i,j} = 1$ if the route from the $i^{th}$ node to the $j^{th}$ node is traversed by any vehicle at any time.\n", + "\n", + "$$i \\in \\{0, 1, \\dots N\\}; \\; j \\in \\{0, 1, \\dots N\\}; \\; i \\neq j$$\n", + "\n", + "***Objective Function***\n", + "\n", + "$$C = \\sum_{i=0}^N \\sum_{j=0}^N C_{i,j} x_{i,j}$$\n", + "\n", + "***Constraints***\n", + "\n", + " - Each node (other than the depot) has exactly $1$ outgoing active edge and exactly $1$ incoming active edge.\n", + "\n", + "$$\\sum_{j\\neq i,j=0}^N x_{i,j} = 1 \\;\\;\\forall i$$\n", + "$$\\sum_{i\\neq j,i=0}^N x_{i,j} = 1 \\;\\;\\forall j$$\n", + "\n", + " - The depot has exactly $M$ outgoing and $M$ incoming connections.\n", + "\n", + "$$\\sum_{j=1}^N x_{0,j} = M $$\n", + "$$\\sum_{j=1}^N x_{j,0} = M $$\n", + "\n", + "***Qubit Complexity***\n", + "\n", + " - No. of Logical Variables: $N(N+1)$\n", + " - Best Case: $N(N+1)$\n", + " - Worst Case: $N(N+1)$\n", + "\n", + "![](images/ras_complexity.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ras = RouteActivationSolver(n, m, instance)\n", + "ras.solve(solver='leap')\n", + "ras.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Qiskit Native Solver (QNS)\n", + "\n", + "***Representation***\n", + "\n", + "$x_{i,j} = 1$ if the route from the $i^{th}$ node to the $j^{th}$ node is traversed by any vehicle at any time.\n", + "\n", + "$$i \\in \\{0, 1, \\dots N\\}; \\; j \\in \\{0, 1, \\dots N\\}; \\; i \\neq j$$\n", + "\n", + "***Objective Function***\n", + "\n", + "$$C = \\sum_{i=0}^N \\sum_{j=0}^N C_{i,j} x_{i,j}$$\n", + "\n", + "***Constraints***\n", + "\n", + " - Each node (other than the depot) has exactly $1$ outgoing active edge and exactly $1$ incoming active edge.\n", + "\n", + "$$\\sum_{j\\neq i,j=0}^N x_{i,j} = 1 \\;\\;\\forall i$$\n", + "$$\\sum_{i\\neq j,i=0}^N x_{i,j} = 1 \\;\\;\\forall j$$\n", + "\n", + " - The depot has exactly $M$ outgoing and $M$ incoming connections.\n", + "\n", + "$$\\sum_{j=1}^N x_{0,j} = M $$\n", + "$$\\sum_{j=1}^N x_{j,0} = M $$\n", + "\n", + " - DFJ Constraints for subtour elimination. Basically consider every possible subtour loop and eliminate them individually. Very inefficient.\n", + "\n", + "$$\\sum_{i, j \\in S, i \\neq j} x_{i,j} \\leq |S| - 1 \\;\\;\\forall S$$\n", + "\n", + "Here, $S$ represents a set of nodes excluding the depot that can form a loop and $|S|$ is the number of nodes in the loop $S$. The above constraint needs to be enforced for all possible loops $S$, which is what makes it so inefficient.\n", + "\n", + "***Qubit Complexity***\n", + "\n", + " - No. of Logical Variables: $N(N+1)$\n", + " - Best Case: $N(N+1)$\n", + " - Worst Case: $N(N+1)$\n", + "\n", + "![](images/qns_complexity.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "qns = QiskitNativeSolver(n, m, instance)\n", + "qns.solve(solver='leap')\n", + "qns.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Clustered Tsp Solver (CTS)\n", + "\n", + "***Algorithm***\n", + "\n", + "Use a multilevel maxcut with $M$ partitions to cluster the nodes into $M$ clsuters. Assign each cluster to a different vehicle and solve Travelling Salesman for each. Clustering is done using D-Wave's Leap Hybrid DQM Solvers. Below we show the formulation for TSP with $P$ nodes. This TSP is to be repeated for each cluster.\n", + "\n", + "***Representation***\n", + "\n", + "$x_{i,j} = 1$ if the salesman is at the $i^{th}$ node at the $j^{th}$ timestep.\n", + "\n", + "$$i \\in \\{1, \\dots P\\}; \\; j \\in \\{1, \\dots P\\}$$\n", + "\n", + "***Objective Function***\n", + "\n", + "$$C = \\sum_{n=1}^P C_{0,n} x_{n,1} + \\sum_{n=1}^P C_{n,0} x_{n,P} + \\sum_{n=1}^{N-1} \\sum_{i=1}^{N} \\sum_{j=1}^{N} C_{i,j} x_{i,n} x_{j,n+1}$$\n", + "\n", + "Here, the first term represents the cost of moving from the depot to the first visited client for each vehicle, the second term represents the cost of moving from the last visited client to the depot for each vehicle, and the third term represents the costs at the intermediate nodes.\n", + "\n", + "***Constraints***\n", + "\n", + " - Every node is served at only one time.\n", + "\n", + "$$\\sum_{j=1}^P x_{i,j} = 1 \\;\\;\\forall i$$\n", + "\n", + " - The vehicle can be at only one place at a given time\n", + "\n", + "$$\\sum_{i=1}^P x_{i,j} = 1 \\;\\;\\forall j$$\n", + "\n", + "***Qubit Complexity***\n", + "\n", + " - No. of Logical Variables: $MN + \\frac{N^2}{M}$\n", + " - Best Case: $2N\\sqrt{N}$\n", + " - Worst Case: $N(N+1)$\n", + "\n", + "![](images/cts_complexity.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cts = ClusteredTspSolver(n, m, instance)\n", + "cts.solve(solver='leap')\n", + "cts.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solution Partitioning Solver (SPS)\n", + "\n", + "***Algorithm***\n", + "\n", + "Assume a single vehicle and solve the TSP for the problem. Then cut the TSP solution at $M-1$ points to generate $M$ routes for $M$ vehicles. While selecting the cuts, out of a total possible $N-1$ choices, choose the $M-1$ cuts that would minimize the extra cost incurred. Below, we outline the TSP formulation used.\n", + "\n", + "***Representation***\n", + "\n", + "$x_{i,j} = 1$ if the salesman is at the $i^{th}$ node at the $j^{th}$ timestep.\n", + "\n", + "$$i \\in \\{1, \\dots P\\}; \\; j \\in \\{1, \\dots P\\}$$\n", + "\n", + "***Objective Function***\n", + "\n", + "$$C = \\sum_{n=1}^P C_{0,n} x_{n,1} + \\sum_{n=1}^P C_{n,0} x_{n,P} + \\sum_{n=1}^{N-1} \\sum_{i=1}^{N} \\sum_{j=1}^{N} C_{i,j} x_{i,n} x_{j,n+1}$$\n", + "\n", + "Here, the first term represents the cost of moving from the depot to the first visited client for each vehicle, the second term represents the cost of moving from the last visited client to the depot for each vehicle, and the third term represents the costs at the intermediate nodes.\n", + "\n", + "***Constraints***\n", + "\n", + " - Every node is served at only one time.\n", + "\n", + "$$\\sum_{j=1}^P x_{i,j} = 1 \\;\\;\\forall i$$\n", + "\n", + " - The vehicle can be at only one place at a given time\n", + "\n", + "$$\\sum_{i=1}^P x_{i,j} = 1 \\;\\;\\forall j$$\n", + "\n", + "***Qubit Complexity***\n", + "\n", + " - No. of Logical Variables: $N^2$\n", + " - Best Case: $N^2$\n", + " - Worst Case: $N^2$\n", + "\n", + "![](images/sps_complexity.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sps = SolutionPartitionSolver(n, m, instance)\n", + "sps.solve(solver='leap')\n", + "sps.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Qubit Complexity\n", + "\n", + "By Qubit Complexity of a solver, we refer to the number of logical variables in the Quadratic Program for the associated solver. We have already specified the number of variables required for each Solver in the previous section. We tabulate this data below.\n", + "\n", + "| Solver | Best Case Complexity | Worst Case Complexity |\n", + "| :-: | :-: | :-: |\n", + "| ***FQS*** | $N(N + 1)$ | $N^2(N + 1)$ |\n", + "| ***APS*** | $N(N + 1)$ | $N^2(N + 1)$ |\n", + "| ***RAS*** | $N(N + 1)$ | $N(N + 1)$ |\n", + "| ***QNS*** | $N(N + 1)$ | $N(N + 1)$ |\n", + "| ***CTS*** | $2N\\sqrt{N}$ | $N(N + 1)$ |\n", + "| ***SPS*** | $N^2$ | $N^2$ |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For comparison, we plot the best and worst case qubit complexities for the solvers below:\n", + "![](images/qubit_complexity.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## QUBO Cost and Execution Times\n", + "In this section, we show how we may evaluate the performance of the various solvers by monitoring the exection times and optimized cost. A more detailed performance analysis may be found in the Jupyter Notebooks inside the **'QOSF-cohort3/vehicle_routing/Performance_Comparisons/\n", + "'** folder of the github repository.\n", + "\n", + "### Optimized Cost" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FQS - Optimized Cost: 45.994911845526076\n", + "APS - Optimized Cost: 45.994911845526076\n", + "RAS - Optimized Cost: 25.41893410233024\n", + "QNS - Optimized Cost: 45.97415357583668\n", + "CTS - Optimized Cost: 45.99419584261341\n", + "SPS - Optimized Cost: 45.99428951003456\n" + ] + } + ], + "source": [ + "vrp_list = [fqs, aps, ras, qns, cts, sps]\n", + "solver_types = ['FQS', 'APS', 'RAS', 'QNS', 'CTS', 'SPS']\n", + "for i, vrp in enumerate(vrp_list):\n", + " print(f'{solver_types[i]} - Optimized Cost: {vrp.evaluate_vrp_cost()}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### QUBO Build Times" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FQS - Classical QUBO Build Time: 223975.65841674805 us\n", + "APS - Classical QUBO Build Time: 343986.27281188965 us\n", + "RAS - Classical QUBO Build Time: 110995.76950073242 us\n", + "QNS - Classical QUBO Build Time: 461000.6809234619 us\n", + "CTS - Classical QUBO Build Time: 44999.122619628906 us\n", + "SPS - Classical QUBO Build Time: 139993.90602111816 us\n" + ] + } + ], + "source": [ + "qubo_time = [vrp.timing['qubo_build_time'] for vrp in vrp_list]\n", + "for i in range(len(vrp_list)):\n", + " print(f'{solver_types[i]} - Classical QUBO Build Time: {qubo_time[i]} us')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### D-Wave QPU Access Times" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FQS - QPU Access Time: 46680 us\n", + "APS - QPU Access Time: 70023 us\n", + "RAS - QPU Access Time: 94983 us\n", + "QNS - QPU Access Time: 73041 us\n", + "CTS - QPU Access Time: 227030 us\n", + "SPS - QPU Access Time: 109557 us\n" + ] + } + ], + "source": [ + "qpu_time = [vrp.timing['qpu_access_time'] for vrp in vrp_list]\n", + "qpu_time[4] += cts.timing['clustering_time']['qpu_access_time']\n", + "for i in range(len(vrp_list)):\n", + " print(f'{solver_types[i]} - QPU Access Time: {qpu_time[i]} us')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Capacitated Solvers\n", + "\n", + "The github repository also includes a set of solvers for solving the capacitated vehicle routing problem. An example of this, the Capacitated SPS, is shown below. All other solvers, other than QNS, also have their capacitated versions, which are accessed in a similar manner. It is to be noted that almost all all capacitated solvers are in general, quite poor-performing in comparison to the basic solvers, largely due to the additional constraints introduced. The Capacitated SPS, is basically the only algorithm that seems to provide a decent performance in this case." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from solution_partition_solver import CapcSolutionPartitionSolver\n", + "\n", + "cap = 10\n", + "dem = [1, 2, 3, 4, 5]\n", + "sps = CapcSolutionPartitionSolver(n, m, instance, cap, dem)\n", + "sps.solve(solver='leap')\n", + "sps.visualize(xc, yc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "In this document, we have explored the formulations of six different solvers for the Vehicle Routing Problem and have provided the example code for their usage. A more detailed performance analysis of each of these as well as comparisons against classical CPLEX solvers may be found in the **'QOSF-cohort3/vehicle_routing/Performance_Comparisons/\n", + "'** folder of the github repository." + ] + } + ], + "metadata": { + "colab": { + "collapsed_sections": [], + "name": "Vehicle Routing", + "provenance": [], + "toc_visible": true + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/average_partition_solver.py b/Src/external/VRP-explorations/VRP/quantum/BQM_based/average_partition_solver.py new file mode 100644 index 0000000..b58c3aa --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/average_partition_solver.py @@ -0,0 +1,137 @@ +import numpy as np +import networkx as nx +import matplotlib.pyplot as plt + +from collections import Counter +from matplotlib.colors import rgb2hex +from .vehicle_routing import VehicleRouter +from qiskit_optimization import QuadraticProgram + + +class AveragePartitionSolver(VehicleRouter): + + """APS Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, **params): + + """Initializes any required variables and calls init of super class.""" + + # Extract parameters + self.limit_radius = params.setdefault('limit_radius', 2) + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_quadratic_program(self): + + """Builds the required quadratic program and sets the names of variables in self.variables.""" + + # Initialization + self.qp = QuadraticProgram(name='Vehicle Routing Problem') + tn = min(self.n, int(np.ceil(self.n / self.m) + self.limit_radius)) + + # Designate variable names + self.variables = np.array([[['x.{}.{}.{}'.format(i, j, k) for k in range(1, tn + 1)] + for j in range(self.n + 1)] for i in range(1, self.m + 1)]) + + # Add variables to quadratic program + for var in self.variables.reshape(-1): + self.qp.binary_var(name=var) + + # Build objective function + obj_linear_a = {self.variables[m, n, 0]: self.cost[0, n] for m in range(self.m) for n in range(1, self.n + 1)} + obj_linear_b = {self.variables[m, n, -1]: self.cost[n, 0] for m in range(self.m) for n in range(1, self.n + 1)} + obj_quadratic = {(self.variables[m, i, n], self.variables[m, j, n + 1]): self.cost[i, j] for m in range(self.m) + for n in range(tn - 1) for i in range(self.n + 1) for j in range(self.n + 1)} + + # Add objective to quadratic program + self.qp.minimize(linear=dict(Counter(obj_linear_a) + Counter(obj_linear_b)), quadratic=obj_quadratic) + + # Add constraints - single delivery per client + for k in range(1, self.n + 1): + constraint_linear = {self.variables[i, k, j]: 1 for i in range(self.m) for j in range(tn)} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, name=f'single_delivery_{k}') + + # Add constraints - vehicle at one place at one time + for m in range(self.m): + for n in range(tn): + constraint_linear = {self.variables[m, k, n]: 1 for k in range(self.n + 1)} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, + name=f'single_location_{m + 1}_{n + 1}') + + def visualize(self, xc=None, yc=None): + + """Visualizes solution. + Args: + xc: x coordinates of nodes. Defaults to random values. + yc: y coordinates of nodes. Defaults to random values. + """ + + # Resolve coordinates + if xc is None: + xc = (np.random.rand(self.n + 1) - 0.5) * 10 + if yc is None: + yc = (np.random.rand(self.n + 1) - 0.5) * 10 + + # Initialize figure + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + cmap = plt.cm.get_cmap('Accent') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + # Plot nodes + pos = {i: (xc[i], yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + nx.draw_networkx_nodes(G, pos=pos, ax=ax, node_color='b', node_size=500, alpha=0.8) + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=16) + + # Loop over cars + for i in range(self.solution.shape[0]): + + # Get route + var_list = np.transpose(self.variables[i]).reshape(-1) + sol_list = np.transpose(self.solution[i]).reshape(-1) + active_vars = [var_list[k] for k in range(len(var_list)) if sol_list[k] == 1] + route = [int(var.split('.')[2]) for var in active_vars] + + # Plot edges + edgelist = [(0, route[0])] + [(route[j], route[j + 1]) for j in range(len(route) - 1)] + [(route[-1], 0)] + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=2, edge_color=rgb2hex(cmap(i))) + + # Show plot + plt.grid(True) + plt.show() + + +class CapcAveragePartitionSolver(AveragePartitionSolver): + + """Capacitated APS Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, capacity, demand, **params): + + """Initializes any required variables and calls init of super class.""" + + # Store capacity data + self.capacity = capacity + self.demand = demand + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_quadratic_program(self): + + """Builds the required quadratic program and sets the names of variables in self.variables.""" + + # Build quadratic program without capacity + super().build_quadratic_program() + tn = min(self.n, int(np.ceil(self.n / self.m) + self.limit_radius)) + + # Add capacity constraints + for i in range(self.m): + constraint = {self.variables[i, j + 1, k]: self.demand[j] for j in range(self.n) for k in range(tn)} + self.qp.linear_constraint(linear=constraint, sense='<=', rhs=self.capacity[i], name=f'capacity_{i}') diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/clustered_tsp_solver.py b/Src/external/VRP-explorations/VRP/quantum/BQM_based/clustered_tsp_solver.py new file mode 100644 index 0000000..779c5e0 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/clustered_tsp_solver.py @@ -0,0 +1,175 @@ +import time +import numpy as np +import networkx as nx +import matplotlib.pyplot as plt + +from itertools import product +from collections import Counter +from matplotlib.colors import rgb2hex +from .vehicle_routing import VehicleRouter +from node_clustering import NodeClustering +from node_clustering import CapcNodeClustering +from qiskit_optimization import QuadraticProgram + + +class ClusteredTspSolver(VehicleRouter): + + """CTS Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, **params): + + """Initializes any required variables and calls init of super class.""" + + # Initialize cluster data + self.cluster = None + self.cluster_dict = None + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_clusters(self): + + """Sets up clusters for tsp solver.""" + + # Cluster nodes and time execution + self.cluster = NodeClustering(self.n, self.m, self.cost[1:, 1:]) + self.cluster.solve() + self.cluster_dict = {i: [j + 1 for j in range(self.n) if self.cluster.solution[j] == i] for i in range(self.m)} + self.timing['clustering_time'] = self.cluster.result.info + + def build_quadratic_program(self): + + """Builds the required quadratic program and sets the names of variables in self.variables. Also runs + clustering prior to building quadratic program.""" + + # Build clusters and reinitialize clock + self.build_clusters() + self.clock = time.time() + + # Initialization + self.qp = QuadraticProgram(name='Vehicle Routing Problem') + + # Designate variable names + self.variables = [] + for i in range(self.m): + node_list = self.cluster_dict[i] + self.variables += [f'x.{i}.{j}.{k}' for k in range(1, len(node_list) + 1) for j in node_list] + self.variables = np.array(self.variables) + + # Add variables to quadratic program + for var in self.variables: + self.qp.binary_var(name=var) + + # Initialize objective function containers + obj_linear_a = {} + obj_linear_b = {} + obj_quadratic = {} + + # Build objective function + for i in range(self.m): + + # Extract cluster + node_list = self.cluster_dict[i] + edgelist = [(j, k) for j, k in product(node_list, repeat=2) if j != k] + + # Build quadratic terms + for j, k in edgelist: + for t in range(1, len(node_list)): + obj_quadratic[(f'x.{i}.{j}.{t}', f'x.{i}.{k}.{t + 1}')] = self.cost[j, k] + + # Build linear terms + for j in node_list: + obj_linear_a[f'x.{i}.{j}.{1}'] = self.cost[0, j] + obj_linear_b[f'x.{i}.{j}.{len(node_list)}'] = self.cost[j, 0] + + # Add objective to quadratic program + self.qp.minimize(linear=dict(Counter(obj_linear_a) + Counter(obj_linear_b)), quadratic=obj_quadratic) + + # Add constraints - single delivery per client + for i in range(self.m): + node_list = self.cluster_dict[i] + for j in node_list: + constraint_linear = {f'x.{i}.{j}.{k}': 1 for k in range(1, len(node_list) + 1)} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, name=f'single_delivery_{i}_{j}') + + # Add constraints - vehicle at one place at one time + for i in range(self.m): + node_list = self.cluster_dict[i] + for k in range(1, len(node_list) + 1): + constraint_linear = {f'x.{i}.{j}.{k}': 1 for j in node_list} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, name=f'single_location_{i}_{k}') + + def visualize(self, xc=None, yc=None): + + """Visualizes solution. + Args: + xc: x coordinates of nodes. Defaults to random values. + yc: y coordinates of nodes. Defaults to random values. + """ + + # Resolve coordinates + if xc is None: + xc = (np.random.rand(self.n + 1) - 0.5) * 10 + if yc is None: + yc = (np.random.rand(self.n + 1) - 0.5) * 10 + + # Initialize figure + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + cmap = plt.cm.get_cmap('Accent') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + node_colors = [rgb2hex(cmap(self.m))] + [rgb2hex(cmap(i)) for i in self.cluster.solution] + + # Plot nodes + pos = {i: (xc[i], yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + nx.draw_networkx_nodes(G, pos=pos, ax=ax, node_color=node_colors, node_size=500, alpha=0.8) + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=16) + + # Evaluate active variables + active_vars = [self.variables[k] for k in range(len(self.variables)) if self.solution[k] == 1] + + # Loop over cars + for i in range(self.m): + + # Get route + route = [int(var.split('.')[2]) for var in active_vars if int(var.split('.')[1]) == i] + + # Plot edges + edgelist = [(0, route[0])] + [(route[j], route[j + 1]) for j in range(len(route) - 1)] + [(route[-1], 0)] + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=2, edge_color=rgb2hex(cmap(i))) + + # Show plot + plt.grid(True) + plt.show() + + +class CapcClusteredTspSolver(ClusteredTspSolver): + + """Capacitated CTS Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, capacity, demand, **params): + + """Initializes any required variables and calls init of super class.""" + + # Store capacity data + self.capacity = capacity + self.demand = demand + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_clusters(self): + + """Sets up capacitated clusters for tsp solver.""" + + # Cluster nodes and time execution + self.cluster = CapcNodeClustering(self.n, self.m, self.cost[1:, 1:], self.capacity, self.demand) + self.cluster.solve() + self.cluster_dict = {i: [j + 1 for j in range(self.n) if self.cluster.solution[j] == i] for i in range(self.m)} + self.timing['clustering_time'] = self.cluster.result.info diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/dbscan.py b/Src/external/VRP-explorations/VRP/quantum/BQM_based/dbscan.py new file mode 100644 index 0000000..dd93d85 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/dbscan.py @@ -0,0 +1,162 @@ +from queue import Queue + +class DBSCAN: + + """Class for performing Density-Based Spatial Clustering of Applications with Noise (DBSCAN)""" + + def __init__(self, costs, max_size = 10, anti_noiser = True): + self.anti_noiser = anti_noiser + self.max_size = max_size + self.max_dist = 2 * max(map(max, costs)) + self.weights = None + + self.solution = None + + # Returns subset of dests with elements x that satisfies + # costs[source][x] + costs[x][source] <= 2 * radius + def range_query(self, dests, costs, source, radius): + result = list() + for dest in dests: + if (costs[source][dest] + costs[dest][source]) / 2 <= radius: + result.append(dest) + return result + + # Standard dbscan clustering dests. + # Returns list of clusters. + def dbscan(self, dests, costs, radius = 10, min_size = 1): + clusters_num = -1 + + states = dict() + # Undifined cluster. + for d in dests: + states[d] = -2 + + for d in dests: + neighbours = self.range_query(dests, costs, d, radius) + if len(neighbours) < min_size: + states[d] = -1 + + for dest in dests: + if states[dest] != -2: + continue + + clusters_num += 1 + q = Queue() + q.put(dest) + + while not q.empty(): + dest2 = q.get() + states[dest2] = clusters_num + neighbours = self.range_query(dests, costs, dest2, radius) + for v in neighbours: + if states[v] == -2: + q.put(v) + + for dest in dests: + if states[dest] == -1: + min_dist = self.max_dist + best_neighbour = -1 + for d in dests: + if states[d] != -1: + if costs[d][dest] < min_dist: + best_neighbour = d + min_dist = costs[d][dest] + if best_neighbour == -1: + clusters_num += 1 + states[dest] = clusters_num + else: + states[dest] = states[best_neighbour] + + clusters = list() + for i in range(clusters_num + 1): + clusters.append(list()) + for dest in dests: + cl = states[dest] + clusters[cl].append(dest) + + self.solution = clusters + return clusters + + # Recursive dbscan. Returns list of clusters. + # dests - set that need to be clustered. + # costs - array with costs between dests. + # min_radius, max_radius - lower and upper bound for radius parameter in dbscan. + # clusters_num - expected maximum number of clusters. It is not guaranteed that + # function won't return more clusters. + # max_size - maximum size of a cluster. It is guaranteed that every cluster will + # have at most max_size elements. + # max_weight - maximum sum of deliveries' weights of a cluster. It is guaranteed that every cluster will + # have at most max_weight sum of weights. + def recursive_dbscan(self, dests, costs, min_radius=5, max_radius=15, clusters_num=50, max_size=10, max_weight=100): + best_res = [[d] for d in dests] + + min_r = min_radius + max_r = max_radius + curr_r = max_r + + # Searching best radius with binary search. + while min_r + 1 < max_r: + curr_r = (min_r + max_r) / 2 + + clusters = self.dbscan(dests, costs, curr_r, 1) + + if len(clusters) < clusters_num: + max_r = curr_r + else: + min_r = curr_r + if len(clusters) < len(best_res): + best_res = clusters + print("Radius:", curr_r) + + # Recursive dbscan on clusters with too many elements. + for cluster in best_res: + weight = 0 + if self.weights is not None: + for dest in cluster: + weight += self.weights[dest] + if len(cluster) > max_size or weight > max_weight: + best_res.remove(cluster) + best_res += self.recursive_dbscan(cluster, costs, 0., self.max_dist, 2, max_size, max_weight) + + # Removing singleton clusters while they are and there is more than clusters_num clusters. + if self.anti_noiser: + while len(best_res) > clusters_num: + singleton = [0] + for cluster in best_res: + if len(cluster) == 1: + singleton = cluster + break + + if singleton == [0]: + break + + best_res.remove(singleton) + + one = singleton[0] + best_cluster = [] + best_dist = self.max_dist + + for cluster in best_res: + if len(cluster) == max_size or cluster == singleton: + continue + + weight = 0 + min_dist = self.max_dist + + for dest in cluster: + if self.weights is not None: + weight += self.weights[dest] + min_dist = min(min_dist, costs[dest][one]) + if self.weights is None or weight + self.weights[one] <= max_weight: + if best_dist > min_dist: + best_dist = min_dist + best_cluster = cluster + + if best_cluster == []: + best_res.append(singleton) + break + best_res.remove(best_cluster) + best_res.append(best_cluster + singleton) + + self.solution = best_res + return best_res \ No newline at end of file diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/dbscan_solver.py b/Src/external/VRP-explorations/VRP/quantum/BQM_based/dbscan_solver.py new file mode 100644 index 0000000..813b514 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/dbscan_solver.py @@ -0,0 +1,151 @@ +import time +import numpy as np +import networkx as nx +import matplotlib.pyplot as plt + +from itertools import product +from collections import Counter +from matplotlib.colors import rgb2hex +from .vehicle_routing import VehicleRouter +from .dbscan import DBSCAN +from qiskit_optimization import QuadraticProgram + +class DBSCANSolver(VehicleRouter): + + """Density-Based Spatial Clustering of Applications with Noise (DBSCAN) Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, **params): + + """Initializes any required variables and calls init of super class.""" + + # Initialize cluster data + self.cluster = None + self.cluster_dict = None + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_clusters(self): + + """Sets up clusters for tsp solver.""" + + self.cluster = DBSCAN(self.cost) + dests = [i for i in range(1, self.n+1)] + self.cluster.dbscan(dests, self.cost) + print(self.cluster.solution) + self.m = len(self.cluster.solution) + self.cluster_dict = {i: self.cluster.solution[i] for i in range(self.m)} + + def build_quadratic_program(self): + + """Builds the required quadratic program and sets the names of variables in self.variables. Also runs + clustering prior to building quadratic program.""" + + # Build clusters and reinitialize clock + self.build_clusters() + + # Initialization + self.qp = QuadraticProgram(name='Vehicle Routing Problem') + + # Designate variable names + self.variables = [] + for i in range(self.m): + node_list = self.cluster_dict[i] + self.variables += [f'x.{i}.{j}.{k}' for k in range(1, len(node_list) + 1) for j in node_list] + self.variables = np.array(self.variables) + + # Add variables to quadratic program + for var in self.variables: + self.qp.binary_var(name=var) + + # Initialize objective function containers + obj_linear_a = {} + obj_linear_b = {} + obj_quadratic = {} + + # Build objective function + for i in range(self.m): + + # Extract cluster + node_list = self.cluster_dict[i] + edgelist = [(j, k) for j, k in product(node_list, repeat=2) if j != k] + + # Build quadratic terms + for j, k in edgelist: + for t in range(1, len(node_list)): + obj_quadratic[(f'x.{i}.{j}.{t}', f'x.{i}.{k}.{t + 1}')] = self.cost[j, k] + + # Build linear terms + for j in node_list: + obj_linear_a[f'x.{i}.{j}.{1}'] = self.cost[0, j] + obj_linear_b[f'x.{i}.{j}.{len(node_list)}'] = self.cost[j, 0] + + # Add objective to quadratic program + self.qp.minimize(linear=dict(Counter(obj_linear_a) + Counter(obj_linear_b)), quadratic=obj_quadratic) + + # Add constraints - single delivery per client + for i in range(self.m): + node_list = self.cluster_dict[i] + for j in node_list: + constraint_linear = {f'x.{i}.{j}.{k}': 1 for k in range(1, len(node_list) + 1)} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, name=f'single_delivery_{i}_{j}') + + # Add constraints - vehicle at one place at one time + for i in range(self.m): + node_list = self.cluster_dict[i] + for k in range(1, len(node_list) + 1): + constraint_linear = {f'x.{i}.{j}.{k}': 1 for j in node_list} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, name=f'single_location_{i}_{k}') + + def visualize(self, xc=None, yc=None): + + """Visualizes solution. + Args: + xc: x coordinates of nodes. Defaults to random values. + yc: y coordinates of nodes. Defaults to random values. + """ + + # Resolve coordinates + if xc is None: + xc = (np.random.rand(self.n + 1) - 0.5) * 10 + if yc is None: + yc = (np.random.rand(self.n + 1) - 0.5) * 10 + + # Initialize figure + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + cmap = plt.cm.get_cmap('Accent') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + node_colors = [None] * (self.n + 1) + node_colors[0] = rgb2hex(cmap(self.m)) + for i in range(self.m): + for j in self.cluster.solution[i]: + node_colors[j] = rgb2hex(cmap(i)) + + # Plot nodes + pos = {i: (xc[i], yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + nx.draw_networkx_nodes(G, pos=pos, ax=ax, node_color=node_colors, node_size=500, alpha=0.8) + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=16) + + # Evaluate active variables + active_vars = [self.variables[k] for k in range(len(self.variables)) if self.solution[k] == 1] + + # Loop over cars + for i in range(self.m): + + # Get route + route = [int(var.split('.')[2]) for var in active_vars if int(var.split('.')[1]) == i] + + # Plot edges + edgelist = [(0, route[0])] + [(route[j], route[j + 1]) for j in range(len(route) - 1)] + [(route[-1], 0)] + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=2, edge_color=rgb2hex(cmap(i))) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/VRP/quantum/BQM_based/full_qubo_solver.py b/Src/external/VRP-explorations/VRP/quantum/BQM_based/full_qubo_solver.py new file mode 100644 index 0000000..2e53ef9 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/BQM_based/full_qubo_solver.py @@ -0,0 +1,132 @@ +import numpy as np +import networkx as nx +import matplotlib.pyplot as plt + +from collections import Counter +from matplotlib.colors import rgb2hex +from qiskit_optimization import QuadraticProgram +from .vehicle_routing import VehicleRouter + + +class FullQuboSolver(VehicleRouter): + + """FQS Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, **params): + + """Initializes any required variables and calls init of super class.""" + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_quadratic_program(self): + + """Builds the required quadratic program and sets the names of variables in self.variables.""" + + # Initialization + self.qp = QuadraticProgram(name='Vehicle Routing Problem') + + # Designate variable names + self.variables = np.array([[['x.{}.{}.{}'.format(i, j, k) for k in range(1, self.n + 1)] + for j in range(self.n + 1)] for i in range(1, self.m + 1)]) + + # Add variables to quadratic program + for var in self.variables.reshape(-1): + self.qp.binary_var(name=var) + + # Build objective function + obj_linear_a = {self.variables[m, n, 0]: self.cost[0, n] for m in range(self.m) for n in range(1, self.n + 1)} + obj_linear_b = {self.variables[m, n, -1]: self.cost[n, 0] for m in range(self.m) for n in range(1, self.n + 1)} + obj_quadratic = {(self.variables[m, i, n], self.variables[m, j, n + 1]): self.cost[i, j] for m in range(self.m) + for n in range(self.n - 1) for i in range(self.n + 1) for j in range(self.n + 1)} + + # Add objective to quadratic program + self.qp.minimize(linear=dict(Counter(obj_linear_a) + Counter(obj_linear_b)), quadratic=obj_quadratic) + + # Add constraints - single delivery per client + for k in range(1, self.n + 1): + constraint_linear = {self.variables[i, k, j]: 1 for i in range(self.m) for j in range(self.n)} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, name=f'single_delivery_{k}') + + # Add constraints - vehicle at one place at one time + for m in range(self.m): + for n in range(self.n): + constraint_linear = {self.variables[m, k, n]: 1 for k in range(self.n + 1)} + self.qp.linear_constraint(linear=constraint_linear, sense='==', rhs=1, + name=f'single_location_{m + 1}_{n + 1}') + + def visualize(self, xc=None, yc=None): + + """Visualizes solution. + Args: + xc: x coordinates of nodes. Defaults to random values. + yc: y coordinates of nodes. Defaults to random values. + """ + + # Resolve coordinates + if xc is None: + xc = (np.random.rand(self.n + 1) - 0.5) * 10 + if yc is None: + yc = (np.random.rand(self.n + 1) - 0.5) * 10 + + # Initialize figure + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + cmap = plt.cm.get_cmap('Accent') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + # Plot nodes + pos = {i: (xc[i], yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + nx.draw_networkx_nodes(G, pos=pos, ax=ax, node_color='b', node_size=500, alpha=0.8) + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=16) + + # Loop over cars + for i in range(self.solution.shape[0]): + + # Get route + var_list = np.transpose(self.variables[i]).reshape(-1) + sol_list = np.transpose(self.solution[i]).reshape(-1) + active_vars = [var_list[k] for k in range(len(var_list)) if sol_list[k] == 1] + route = [int(var.split('.')[2]) for var in active_vars] + + # Plot edges + edgelist = [(0, route[0])] + [(route[j], route[j + 1]) for j in range(len(route) - 1)] + [(route[-1], 0)] + G.add_edges_from(edgelist) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist, width=2, edge_color=rgb2hex(cmap(i))) + + # Show plot + plt.grid(True) + plt.show() + + +class CapcFullQuboSolver(FullQuboSolver): + + """Capacitated FQS Solver implementation.""" + + def __init__(self, n_clients, n_vehicles, cost_matrix, capacity, demand, **params): + + """Initializes any required variables and calls init of super class.""" + + # Store capacity data + self.capacity = capacity + self.demand = demand + + # Call parent initializer + super().__init__(n_clients, n_vehicles, cost_matrix, **params) + + def build_quadratic_program(self): + + """Builds the required quadratic program and sets the names of variables in self.variables.""" + + # Build quadratic program without capacity + super().build_quadratic_program() + + # 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 5\n", + "m = 2\n", + "seed = 891\n", + "\n", + "instance, xc, yc = utility.generate_vrp_instance(n, seed)\n", + "sps = FQS(n, m, instance)\n", + "sps.solve(solver='neal')\n", + "sps.visualize(xc, yc)" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "1fddfe479357b1ca97118c3a6342535a6e6159876c04dae960732da936488d33" + }, + "kernelspec": { + "display_name": "Python 3.9.7 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Src/external/VRP-explorations/VRP/quantum/CQM_based/fqs.py b/Src/external/VRP-explorations/VRP/quantum/CQM_based/fqs.py new file mode 100644 index 0000000..560ceee --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/CQM_based/fqs.py @@ -0,0 +1,199 @@ +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import dimod +from neal import SimulatedAnnealingSampler +from dwave.system import LeapHybridCQMSampler + +''' +Solving a custom formulation (FQS) of VRP using LeapHybridCQMSampler +''' + +class FQS(): + '''Full Qubo Solver for Vehicle Routing Problem''' + + def __init__(self, n, m, cost, xc, yc): + self.n = n + self.m = m + self.cost = cost + self.xc = xc + self.yc = yc + self.sol = None + self.model = dimod.ConstrainedQuadraticModel() + self.formulate() + # self.solve() + # self.visualize() + + + def formulate(self): + '''Formulate the problem''' + + x = [[[None] * (self.m+1) for _ in range(self.n+self.m+1)] for __ in range(self.n+1)] + + + ##### Declare variables ##### + for i in range(self.n+1): + for t in range(1, self.n+self.m+1): + for k in range(1, self.m+1): + x[i][t][k] = dimod.Binary(label=f'x.{i}.{t}.{k}') + + + ##### OBJECTIVE ##### + self.model.set_objective( + sum(self.cost[0][i] * x[i][1][k] for i in range(1, self.n+1) for k in range(1, self.m+1)) + + sum(self.cost[i][0] * x[i][self.n+self.m][k] for i in range(1, self.n+1) for k in range(1, self.m+1)) + + sum(self.cost[i][j] * x[i][t][k] * x[j][t+1][k] for i in range(self.n+1) for j in range(self.n+1) if i != j for t in range(1, self.n+self.m) for k in range(1, self.m+1)) + + # If constraint 5 does not give a feasible solution, uncomment the following line and comment the above line and constraint 5 + # sum(self.cost[i][j] * x[i][ti][k] * x[j][tj][k] for i in range(1, self.n+1) for j in range(1, self.n+1) if i != j for ti in range(1, self.n) for tj in range(1, self.n) if tj > ti for k in range(1, self.m+1)) + ) + + + ##### CONSTRAINTS ##### + # 1. Exactly one client/depot is visited by exactly one vehicle at any given instant. + for t in range(1, self.n+self.m+1): + self.model.add_constraint(sum(x[i][t][k] for i in range(self.n+1) for k in range(1, self.m+1)) == 1) + + # 2. Each client is visited by one vehicle throughout all the time steps. + for i in range(1, self.n+1): + self.model.add_constraint(sum(x[i][t][k] for t in range(1, self.n+self.m+1) for k in range(1, self.m+1)) == 1) + + # 3. The depot is visited by each vehicle at some time step. + for k in range(1, self.m+1): + self.model.add_constraint(sum(x[0][t][k] for t in range(1, self.n+self.m+1)) == 1) + + # 4. Each vehicle visits at least one client. + for k in range(1, self.m+1): + self.model.add_constraint(sum(x[i][t][k] for i in range(1, self.n+1) for t in range(1, self.n+self.m+1)) >= 1) + + # 5. No other vehicle is allowed to start its journey when another vehicle is already in its journey. + for k in range(1, self.m+1): + for t in range(1, self.n+self.m): + for i in range(1, self.n+1): + # 5a. If a vehicle has visited a client in time step t, then it must visit another client or the depot in the next time step. + self.model.add_constraint(x[i][t][k] * (1 - sum(x[j][t+1][k] for j in range(self.n+1) if j != i)) == 0) + + # 5b. If a vehicle has visited the depot in time step t, then the journey for that vehicle is over. + self.model.add_constraint(x[0][t][k] * sum(x[i][t1][k] for t1 in range(t+1, self.n+self.m+1) for i in range(1, self.n+1)) == 0) + + def solve(self, **params): + '''Solve the problem''' + + sampler = LeapHybridCQMSampler() + sampleset = sampler.sample_cqm(self.model, label=f'Vehicle Routing Problem ({self.n} Clients, {self.m} Vehicles) - FQS', time_limit=params['time_limit']) + feasible_sampleset = sampleset.filter(lambda row: row.is_feasible) + + print('\nFULL QUBO SOLVER (Constrained Quadratic Model)') + + tot_cost = None + if len(feasible_sampleset): + self.sol = feasible_sampleset.first + print("{} feasible solutions of {}.".format(len(feasible_sampleset), len(sampleset))) + + # !Does not give the correct minimum cost for some reason. + # print(f'Minimum total cost: {self.sol.energy} ____(X)') + + # Evaluate cost of the solution ___________________________________________________________________________(1) + # x = [[[None] * (self.m+1) for _ in range(self.n+1)] for __ in range(self.n+1)] + # varList = [var for var in self.sol.sample] + # for var in varList: + # i=int(var.split('.')[1]) + # t=int(var.split('.')[2]) + # k=int(var.split('.')[3]) + # x[i][t][k] = self.sol.sample[var] + # tot_cost = sum(self.cost[0][i] * x[i][1][k] for i in range(1, self.n+1) for k in range(1, self.m+1)) + sum(self.cost[i][0] * x[i][self.n][k] for i in range(1, self.n+1) for k in range(1, self.m+1)) + sum(self.cost[i][j] * x[i][t][k] * x[j][t+1][k] for i in range(1, self.n+1) for j in range(1, self.n+1) if i != j for t in range(1, self.n) for k in range(1, self.m+1)) + # tot_cost = sum(self.cost[0][i] * x[i][1][k] for i in range(1, self.n+1) for k in range(1, self.m+1)) + sum(self.cost[i][0] * x[i][self.n][k] for i in range(1, self.n+1) for k in range(1, self.m+1)) + sum(self.cost[i][j] * x[i][ti][k] * x[j][tj][k] for i in range(1, self.n+1) for j in range(1, self.n+1) if i != j for ti in range(1, self.n) for tj in range(1, self.n) if tj > ti for k in range(1, self.m+1)) + + # Evaluate cost of the solution ___________________________________________________________________________(2) + activeVarList = [[] for _ in range(self.m+1)] + for i in self.sol.sample: + if self.sol.sample[i] == 1: + activeVarList[int(i.split('.')[3])].append((int(i.split('.')[1]), int(i.split('.')[2]))) + + for i in range(self.m+1): + activeVarList[i] = sorted(activeVarList[i], key=lambda x: x[1]) + + tot_cost = 0.0 + for i in range(1, self.m+1): + tmp = 0 + for var in activeVarList[i]: + if var[0] != tmp: + tot_cost += self.cost[tmp][var[0]] + tmp = var[0] + tot_cost += self.cost[tmp][0] + print(f'Minimum total cost: {tot_cost}') + else: + print("No feasible solutions.") + + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + + return dict({ + 'min_cost': tot_cost, + 'runtime': sampleset.info['run_time']/1000, + 'num_vars': len(sampleset.variables) + }) + + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + activeVarList = [[] for _ in range(self.m+1)] + for i in self.sol.sample: + if self.sol.sample[i] == 1: + activeVarList[int(i.split('.')[3])].append((int(i.split('.')[1]), int(i.split('.')[2]))) + + for i in range(self.m+1): + activeVarList[i] = sorted(activeVarList[i], key=lambda x: x[1]) + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C0', node_shape='s') + + nodelist = [[] for _ in range(self.m+1)] + edgelist = [[] for _ in range(self.m+1)] + for i in range(1, self.m+1): + tmp = 0 + for var in activeVarList[i]: + if var[0] != tmp: + if var[0]: + nodelist[i].append(var[0]) + edgelist[i].append((tmp, var[0])) + tmp = var[0] + edgelist[i].append((tmp, 0)) + + # Loop over cars and plot other nodes and edges + for k in range(1, self.m+1): + + # Get edges and nodes for this car + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist[k], ax=ax, alpha=0.75, node_size=300, node_color=f'C{k}') + + G.add_edges_from(edgelist[k]) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist[k], width=1.5, edge_color=f'C{k}') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/VRP/quantum/CQM_based/gps.py b/Src/external/VRP-explorations/VRP/quantum/CQM_based/gps.py new file mode 100644 index 0000000..10a4907 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/CQM_based/gps.py @@ -0,0 +1,187 @@ +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import dimod +from neal import SimulatedAnnealingSampler +from dwave.system import LeapHybridCQMSampler + +''' +Solving a custom formulation (GPS) of VRP using LeapHybridCQMSampler +''' + +class GPS(): + '''Guillermo Alonso-Linaje, Parfait Atchade-Adelomou, and Saúl Gonzalez-Bermejo''' + + def __init__(self, n, m, cost, xc, yc): + self.n = n + self.m = m + self.cost = cost + self.xc = xc + self.yc = yc + self.sol = None + self.model = dimod.ConstrainedQuadraticModel() + self.formulate() + # self.solve() + # self.visualize() + + + def formulate(self): + '''Formulate the problem''' + + ##### Declare Variables ##### + x = [[[[None] * (self.m+1) for _ in range(3)] for __ in range(self.n+1)] for ___ in range(self.n+1)] + a = [[None] * (self.n+1) for _ in range(self.n+1)] + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + a[i][j] = dimod.Binary(f'a.{i}.{j}') + for r in range(3): + for k in range(1, self.m+1): + x[i][j][r][k] = dimod.Binary(f'x.{i}.{j}.{r}.{k}') + + + ##### OBJECTIVE ##### + self.model.set_objective(sum(self.cost[i][j] * x[i][j][1][k] for i in range(self.n+1) for j in range(self.n+1) if i != j for k in range(1, self.m+1)) + + # Objective function for Constraint-7 + # + sum(a[i][j]*a[j][k] - a[i][j]*a[i][k] - a[j][k]*a[i][k] + a[i][k]*a[i][k] for i in range(1, self.n+1) for j in range(1, self.n+1) for k in range(1, self.n+1) if i != j and j != k and k != i) + ) + + + ##### CONSTRAINTS ##### + # Constraint 1: For each i, j, q, one and only one of the possibilities must be met for r. + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + for k in range(1, self.m+1): + self.model.add_constraint(sum(x[i][j][r][k] for r in range(3)) == 1) + + # Constraint 2a: Each vehicle must leave the depot in the beginning. + for k in range(1, self.m+1): + self.model.add_constraint(sum(x[0][j][1][k] for j in range(1, self.n+1)) == 1) + + # Constraint 2b: Each vehicle must reach the depot in the end. + for k in range(1, self.m+1): + self.model.add_constraint(sum(x[i][0][1][k] for i in range(1, self.n+1)) == 1) + + # Constraint 3a: Every vehicle must arrive at each city once and only once. + for j in range(1, self.n+1): + self.model.add_constraint(sum(x[i][j][1][k] for i in range(self.n+1) if i != j for k in range(1, self.m+1)) == 1) + + # Constraint 3b: Every vehicle must leave each city once and only once. + for i in range(1, self.n+1): + self.model.add_constraint(sum(x[i][j][1][k] for j in range(self.n+1) if i != j for k in range(1, self.m+1)) == 1) + + # Constraint 4: A city i can either be reached earlier or later than a city j. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + self.model.add_constraint(sum(x[i][j][r][k] for r in range(2) for k in range(1, self.m+1)) - a[i][j] * self.m == 0) + self.model.add_constraint(a[i][j] + a[j][i] == 1) + + # Constraint 5: If the vehicle q arrives in the city j, then the vehicle q must leave the city j + for i in range(self.n+1): + for j in range(1, self.n+1): + if i != j: + for l in range(1, self.m+1): + self.model.add_constraint(x[i][j][1][l] * (1 - sum(x[j][k][1][l] for k in range(self.n+1) if k != j)) == 0) + + # Constraint 6: A vehicle can either arrive at city i before city j or arrive at city j before city i. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + for k in range(1, self.m+1): + self.model.add_constraint(sum(x[i][j][r][k] for r in range(2)) + sum(x[j][i][r][k] for r in range(2)) == 1) + + # Constraint 7: If city i is reached before city j, and city j is reached before city k, then city i must be reached before city k. + for i in range(1, self.n+1): + for j in range(1, self.n+1): + for k in range(1, self.n+1): + if i != j and j != k and k != i: + self.model.add_constraint(a[i][j]*a[j][k] - a[i][j]*a[i][k] - a[j][k]*a[i][k] + a[i][k]*a[i][k] == 0) + + + def solve(self, **params): + '''Solve the problem''' + + sampler = LeapHybridCQMSampler() + sampleset = sampler.sample_cqm(self.model, label=f"Vehicle Routing Problem ({self.n} Clients, {self.m} Vehicles) - GPS", time_limit=params['time_limit']) + feasible_sampleset = sampleset.filter(lambda row: row.is_feasible) + + print('\nGUILLERMO, PARFAIT, SAÚL SOLVER (Constrained Quadratic Model)') + if len(feasible_sampleset): + print("{} feasible solutions of {}.".format(len(feasible_sampleset), len(sampleset))) + self.sol = feasible_sampleset.first + print(f'Minimum total cost: {self.sol.energy}') + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + + return { + 'min_cost': self.sol.energy, + 'runtime': sampleset.info['run_time']/1000, + 'num_vars': len(sampleset.variables) + } + + print("No feasible solutions.") + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + + return { + 'min_cost': None, + 'runtime': sampleset.info['run_time']/1000, + 'num_vars': len(sampleset.variables) + } + + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + activeVarList = [i for i in self.sol.sample if self.sol.sample[i] == 1] + activeVarList = [(int(i.split('.')[4]), int(i.split('.')[1]), int(i.split('.')[2])) for i in activeVarList if i.split('.')[0] == 'x' and i.split('.')[3] == '1'] + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C0', node_shape='s') + + edgelist = [[] for _ in range(self.m+1)] + nodelist = [[] for _ in range(self.m+1)] + for var in activeVarList: + if var[1]: + nodelist[var[0]].append(var[1]) + edgelist[var[0]].append((var[1], var[2])) + + # Loop over cars and plot other nodes and edges + for k in range(1, self.m+1): + + # Get edges and nodes for this car + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist[k], ax=ax, alpha=0.75, node_size=300, node_color=f'C{k}') + + G.add_edges_from(edgelist[k]) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist[k], width=1.5, edge_color=f'C{k}') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/VRP/quantum/CQM_based/ras.py b/Src/external/VRP-explorations/VRP/quantum/CQM_based/ras.py new file mode 100644 index 0000000..01e3371 --- /dev/null +++ b/Src/external/VRP-explorations/VRP/quantum/CQM_based/ras.py @@ -0,0 +1,187 @@ +from dimod.reference.samplers.exact_solver import ExactCQMSolver +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +import networkx as nx +import dimod +from neal import SimulatedAnnealingSampler +from dwave.system import LeapHybridCQMSampler + +''' +Solving a custom formulation (RAS) of VRP using LeapHybridCQMSampler +''' + +class RAS(): + '''Route Activation Solver (Method-1)''' + + def __init__(self, n, m, cost, xc, yc): + self.n = n + self.m = m + self.cost = cost + self.xc = xc + self.yc = yc + self.T_max = max(self.n-self.m+1, 1) + self.B = 2*self.n + self.sol = None + self.model = dimod.ConstrainedQuadraticModel() + self.formulate() + # self.solve() + # self.visualize() + + + def formulate(self): + '''Formulate the problem''' + + x = [[None] * (self.n+1) for _ in range(self.n+1)] + y = [[None] * (self.m+1) for _ in range(self.n+1)] + t = [None] * (self.n+1) + + + ##### Declare variables ##### + for i in range(self.n+1): + for j in range(self.n+1): + if i != j: + x[i][j] = dimod.Binary(label=f'x.{i}.{j}') + + for i in range(1, self.n+1): + t[i] = dimod.Integer(lower_bound=1, upper_bound=self.T_max, label=f't.{i}') + for k in range(1, self.m+1): + y[i][k] = dimod.Binary(label=f'y.{i}.{k}') + + + ##### OBJECTIVE ##### + self.model.set_objective(sum(self.cost[i][j]*x[i][j] for i in range(self.n+1) for j in range(self.n+1) if i != j)) + + + ##### CONSTRAINTS ##### + for i in range(1, self.n+1): + + # Each client node must have exactly one edge directed away from it + self.model.add_constraint(sum(x[i][j] for j in range(self.n+1) if j != i) == 1) + + # Each client node must have exactly one edge directed towards it + self.model.add_constraint(sum(x[j][i] for j in range(self.n+1) if j != i) == 1) + + # Each client must be visited by exactly one vehicle + self.model.add_constraint(sum(y[i][k] for k in range(1, self.m+1)) == 1) + + # m vehicles coming from depot + self.model.add_constraint(sum(x[0][i] for i in range(1, self.n+1)) == self.m) + + # m vehicles going to depot + self.model.add_constraint(sum(x[i][0] for i in range(1, self.n+1)) == self.m) + + # If there is an edge from node i to node j, then both ith and jth node must be visited by the same vehicle + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + for k in range(1, self.m+1): + self.model.add_constraint(y[i][k] - y[j][k] + (1 - x[i][j]) >= 0) + self.model.add_constraint(y[j][k] - y[i][k] + (1 - x[i][j]) >= 0) + + # Each vehicle must be used at least once + for k in range(1, self.m+1): + self.model.add_constraint(sum(y[i][k] for i in range(1, self.n+1)) >= 1) + + # Eliminate subtours - MTZ constraint + for i in range(1, self.n+1): + for j in range(1, self.n+1): + if i != j: + for k in range(1, self.m+1): + self.model.add_constraint(t[j] * y[j][k] - (t[i] + 1) * y[i][k] + self.B*(1 - x[i][j])>= 0) + + + def solve(self, **params): + '''Solve the problem''' + + sampler = LeapHybridCQMSampler() + sampleset = sampler.sample_cqm(self.model, label=f"Vehicle Routing Problem ({self.n} Clients, {self.m} Vehicles) - RAS", time_limit=params['time_limit']) + feasible_sampleset = sampleset.filter(lambda row: row.is_feasible) + + print('\nROUTE ACTIVATION SOLVER (Constrained Quadratic Model)') + if len(feasible_sampleset): + self.sol = feasible_sampleset.first + print("{} feasible solutions of {}.".format(len(feasible_sampleset), len(sampleset))) + print(f'Minimum total cost: {self.sol.energy}') + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + + return { + 'min_cost': self.sol.energy, + 'runtime': sampleset.info['run_time']/1000, + 'num_vars': len(sampleset.variables) + } + + print("No feasible solutions.") + print(f"Number of variables: {len(sampleset.variables)}") + print(f"Runtime: {sampleset.info['run_time']/1000:.3f} ms") + return { + 'min_cost': None, + 'runtime': sampleset.info['run_time']/1000, + 'num_vars': len(sampleset.variables) + } + + + def visualize(self): + '''Visualize solution''' + + if self.sol is None: + print('No solution to show!') + return + + activeVarList = [i for i in self.sol.sample if self.sol.sample[i] == 1] + activeXList = [(int(i.split('.')[1]), int(i.split('.')[2])) for i in activeVarList if i.split('.')[0] == 'x'] + activeYList = [(int(i.split('.')[1]), int(i.split('.')[2])) for i in activeVarList if i.split('.')[0] == 'y'] + + if self.xc is None or self.yc is None: + self.xc = (np.random.rand(self.n + 1) - 0.5) * 20 + self.yc = (np.random.rand(self.n + 1) - 0.5) * 20 + + # Initialize figure + mpl.style.use('seaborn') + plt.figure() + ax = plt.gca() + ax.set_title(f'Vehicle Routing Problem - {self.n} Clients & {self.m} Cars') + + # Build graph + G = nx.MultiDiGraph() + G.add_nodes_from(range(self.n + 1)) + + pos = {i: (self.xc[i], self.yc[i]) for i in range(self.n + 1)} + labels = {i: str(i) for i in range(self.n + 1)} + + # Plot depot node + nx.draw_networkx_nodes(G, pos=pos, nodelist=[0], ax=ax, alpha=0.75, node_size=300, node_color=f'C0', node_shape='s') + + next_node = [[]] + [None for _ in range(1, self.n + 1)] + node_id = [None] * (self.n + 1) + for from_node, to_node in activeXList: + if from_node: + next_node[from_node] = to_node + else: + next_node[from_node].append(to_node) + + nodelist = [[] for _ in range(self.m+1)] + edgelist = [[] for _ in range(self.m+1)] + for i, k in activeYList: + nodelist[k].append(i) + node_id[i] = k + edgelist[k].append((i, next_node[i])) + + for i in next_node[0]: + edgelist[node_id[i]].append((0, i)) + + # Loop over cars and plot other nodes and edges + for k in range(1, self.m+1): + + # Get edges and nodes for this car + nx.draw_networkx_nodes(G, pos=pos, nodelist=nodelist[k], ax=ax, alpha=0.75, node_size=300, node_color=f'C{k}') + + G.add_edges_from(edgelist[k]) + nx.draw_networkx_edges(G, pos=pos, edgelist=edgelist[k], width=1.5, edge_color=f'C{k}') + + nx.draw_networkx_labels(G, pos=pos, labels=labels, font_size=12) + + # Show plot + plt.grid(True) + plt.show() diff --git a/Src/external/VRP-explorations/datasets/dataset.csv b/Src/external/VRP-explorations/datasets/dataset.csv new file mode 100644 index 0000000..27658e5 --- /dev/null +++ b/Src/external/VRP-explorations/datasets/dataset.csv @@ -0,0 +1,4360 @@ +,,0,1 +x_2_0,0,22.381612842583515, +x_2_0,1,-13.67262894341385, +y_2_0,0,4.721007219556627, +y_2_0,1,-3.584565753515262, +wm_2_0,0,0.0,1368.8908931741805 +wm_2_0,1,1368.8908931741805,0.0 +,,0,1 +x_2_1,0,-19.304770033978834, +x_2_1,1,12.394041135959572, +y_2_1,0,5.552969764497146, +y_2_1,1,15.484590169571794, +wm_2_1,0,0.0,1103.4517134579069 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0000000..0b01da5 --- /dev/null +++ b/Src/external/VRP-explorations/datasets/generate_dataset_for_vrp.ipynb @@ -0,0 +1,323 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "d47c6802-5846-4830-ba6c-66a678e6ad13", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "9308e40c-493e-4962-93b2-95c82d7b7c2b", + "metadata": {}, + "outputs": [], + "source": [ + "class Initializer:\n", + "\n", + " def __init__(self, n, a, b):\n", + " self.n = n\n", + " self.a = a\n", + " self.b = b\n", + "\n", + " def generate_nodes_and_weight_matrix(self):\n", + "\n", + " n = self.n\n", + " a = self.a\n", + " b = self.b\n", + " \n", + " np.random.seed(100*a + b)\n", + "\n", + " x = (np.random.rand(n) - 0.5) * 50\n", + " y = (np.random.rand(n) - 0.5) * 50\n", + "\n", + " weight_matrix = np.zeros([n, n])\n", + " for i in range(n):\n", + " for j in range(i+1, n):\n", + " weight_matrix[i, j] = (x[i] - x[j]) ** 2 + (y[i] - y[j]) ** 2\n", + " weight_matrix[j, i] = weight_matrix[i, j]\n", + "\n", + " return x, y, weight_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f2a2505f-c24e-4ccd-a86f-9c66b3589b42", + "metadata": {}, + "outputs": [], + "source": [ + "for i in range(2,16): ### Here, (2,16) could be replaced with the some other range of no. of locations you want.\n", + " for j in range(10): ### Here, (10) could be replaced with some other number of instcnces you want to generate for a particular no. of locations.\n", + " initializer = Initializer(i, i, j)\n", + " x,y,weight_matrix = initializer.generate_nodes_and_weight_matrix()\n", + " df_x = pd.DataFrame(x)\n", + " df_y = pd.DataFrame(y)\n", + " df_wm = pd.DataFrame(weight_matrix)\n", + " with open (\"dataset.csv\", 'a') as f:\n", + " df = pd.concat([df_x, df_y, df_wm], keys = [\"x_\" + str(i) + '_' + str(j), \"y_\" + str(i) + '_' + str(j), \"wm_\" + str(i) + '_' + 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Circuit Properties

" + } + } + }, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Src/external/VRP-explorations/post_processing_results.ipynb b/Src/external/VRP-explorations/post_processing_results.ipynb new file mode 100644 index 0000000..ca1cf4e --- /dev/null +++ b/Src/external/VRP-explorations/post_processing_results.ipynb @@ -0,0 +1,313 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "\n", + "with open('Results/sol9_2.log', 'r') as file:\n", + " data = file.read()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "rows_list = []\n", + "for dline in data.split('\\n\\n'):\n", + " if dline.startswith('n = '):\n", + " lines=dline.split('\\n')\n", + " for line in lines:\n", + " if line.startswith('n = '):\n", + " words=line.split(', ')\n", + " for word in words:\n", + " if word.startswith('n = '):\n", + " n=int(word.strip('n = '))\n", + " if word.startswith('m = '):\n", + " k=int(word.strip('m = '))\n", + " if word.startswith('instance = '):\n", + " instance=word.strip('instance = ')\n", + " \n", + " if line.startswith('Classical cost from best known solution: '):\n", + " classical_cost=f\"{float(line.strip('Classical cost from best known solution: ')):.5f}\"\n", + "\n", + " if line.startswith('RAS: '):\n", + " words=line.split(' \\t ')\n", + " for word in words:\n", + " if word.startswith('quantum cost = '):\n", + " ras_quantum_cost=f\"{float(word.strip('quantum cost = ')):.5f}\" if word.strip('quantum cost = ') != 'None' else None\n", + " if word.startswith('approximation ratio = '):\n", + " ras_approximation_ratio=f\"{float(word.strip('approximation ratio = ')):.5f}\" if word.strip('approximation ratio = ') != 'None' else None\n", + " if word.startswith('number of variables = '):\n", + " ras_no_of_variables=int(word.strip('number of variables = '))\n", + " if word.startswith('runtime = '):\n", + " ras_runtime=f\"{float(word.strip('runtime = ')):.5f}\"\n", + " \n", + " if line.startswith('FQS: '):\n", + " words=line.split(' \\t ')\n", + " for word in words:\n", + " if word.startswith('quantum cost = '):\n", + " fqs_quantum_cost=f\"{float(word.strip('quantum cost = ')):.5f}\" if word.strip('quantum cost = ') != 'None' else None\n", + " if word.startswith('approximation ratio = '):\n", + " fqs_approximation_ratio=f\"{float(word.strip('approximation ratio = ')):.5f}\" if word.strip('approximation ratio = ') != 'None' else None\n", + " if word.startswith('number of variables = '):\n", + " fqs_no_of_variables=int(word.strip('number of variables = '))\n", + " if word.startswith('runtime = '):\n", + " fqs_runtime=f\"{float(word.strip('runtime = ')):.5f}\"\n", + " \n", + " if line.startswith('GPS: '):\n", + " words=line.split(' \\t ')\n", + " for word in words:\n", + " if word.startswith('quantum cost = '):\n", + " gps_quantum_cost=f\"{float(word.strip('quantum cost = ')):.5f}\" if word.strip('quantum cost = ') != 'None' else None\n", + " if word.startswith('approximation ratio = '):\n", + " gps_approximation_ratio=f\"{float(word.strip('approximation ratio = ')):.5f}\" if word.strip('approximation ratio = ') != 'None' else None\n", + " if word.startswith('number of variables = '):\n", + " gps_no_of_variables=int(word.strip('number of variables = '))\n", + " if word.startswith('runtime = '):\n", + " gps_runtime=f\"{float(word.strip('runtime = ')):.5f}\"\n", + " \n", + " rows_list.append({'n': n, 'k': k, 'instance': instance, 'Classical Cost': classical_cost, 'RAS: Quantum Cost': ras_quantum_cost, 'RAS: Approximation Ratio': ras_approximation_ratio, 'RAS: No. of Variables': ras_no_of_variables, 'RAS: Runtime': ras_runtime, 'FQS: Quantum Cost': fqs_quantum_cost, 'FQS: Approximation Ratio': fqs_approximation_ratio, 'FQS: No. of Variables': fqs_no_of_variables, 'FQS: Runtime': fqs_runtime, 'GPS: Quantum Cost': gps_quantum_cost, 'GPS: Approximation Ratio': gps_approximation_ratio, 'GPS: No. of Variables': gps_no_of_variables, 'GPS: Runtime': gps_runtime})" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "df = pd.DataFrame(rows_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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3853.37937 1.24371 272 \n", + "24 2650.11637 1.00000 272 \n", + "1 4553.22378 1.91146 488 \n", + "\n", + " GPS: Runtime \n", + "0 18020.55200 \n", + "8 18042.71700 \n", + "16 17994.78600 \n", + "24 17992.76200 \n", + "1 18061.10500 " + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.sort_values(by=['n', 'k', 'instance'], inplace=True)\n", + "df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "df.to_csv('Results/sol9_2.csv', index=False)" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "a2afd0ddbcfb87ec4f087e6612d43180006366a8f4c127a029466ae157c416c8" + }, + "kernelspec": { + "display_name": "Python 3.9.7 64-bit ('_venv_': venv)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Src/external/VRP-explorations/presentations/README.md b/Src/external/VRP-explorations/presentations/README.md new file mode 100644 index 0000000..cfbf836 --- /dev/null +++ b/Src/external/VRP-explorations/presentations/README.md @@ -0,0 +1,13 @@ +# Presentations +For a description of the RAS (Route Activation Solver) look at `notebook_4.ipynb`. +It describes 3 approaches of RAS and their advantages and disadvantages. + +For a description of the DBSCAN (Density-Based Spatial Clustering Of Applications with Noise) Solver look at `vrp_presentation_asish.ipynb`. + +If you wish to see the slides of the presentation: +Run the following commands: +```bash +pip install nbconvert # Install nbconvert +bash presentation.sh # Run the script to generate the slides +``` +> The nbconvert tool allows you to convert an .ipynb notebook 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