322 lines
13 KiB
Plaintext
322 lines
13 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "google",
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"metadata": {},
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"source": [
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"##### Copyright 2022 Google LLC."
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]
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},
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{
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"cell_type": "markdown",
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"id": "apache",
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"metadata": {},
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"source": [
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"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
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"you may not use this file except in compliance with the License.\n",
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"You may obtain a copy of the License at\n",
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"\n",
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" http://www.apache.org/licenses/LICENSE-2.0\n",
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"\n",
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"Unless required by applicable law or agreed to in writing, software\n",
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"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
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"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
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"See the License for the specific language governing permissions and\n",
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"limitations under the License.\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "basename",
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"metadata": {},
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"source": [
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"# vrp_node_max"
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]
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},
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{
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"cell_type": "markdown",
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"id": "link",
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"metadata": {},
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"source": [
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"<table align=\"left\">\n",
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"<td>\n",
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"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/constraint_solver/vrp_node_max.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
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"</td>\n",
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"<td>\n",
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"<a href=\"https://github.com/google/or-tools/blob/main/ortools/constraint_solver/samples/vrp_node_max.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
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"</td>\n",
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"</table>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "doc",
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"metadata": {},
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"source": [
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"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "install",
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"metadata": {},
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"outputs": [],
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"source": [
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"!pip install ortools"
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]
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},
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{
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"cell_type": "markdown",
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"id": "description",
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"metadata": {},
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"source": [
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"\n",
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"Vehicles Routing Problem (VRP).\n",
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"\n",
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"Each route as an associated objective cost equal to the max node value along the\n",
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"road multiply by a constant factor (4200)\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "code",
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"metadata": {},
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"outputs": [],
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"source": [
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"from ortools.constraint_solver import routing_enums_pb2\n",
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"from ortools.constraint_solver import pywrapcp\n",
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"\n",
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"\n",
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"def create_data_model():\n",
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" \"\"\"Stores the data for the problem.\"\"\"\n",
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" data = {}\n",
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" data[\"distance_matrix\"] = [\n",
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" # fmt: off\n",
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" [0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468, 776, 662],\n",
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" [548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210],\n",
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" [776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754],\n",
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" [696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358],\n",
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" [582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244],\n",
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" [274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708],\n",
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" [502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480],\n",
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" [194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856],\n",
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" [308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514],\n",
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" [194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468],\n",
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" [536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354],\n",
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" [502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844],\n",
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" [388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730],\n",
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" [354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536],\n",
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" [468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194],\n",
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" [776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798],\n",
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" [662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0],\n",
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" # fmt: on\n",
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" ]\n",
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" data[\"value\"] = [\n",
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" 0, # depot\n",
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" 42, # 1\n",
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" 42, # 2\n",
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" 8, # 3\n",
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" 8, # 4\n",
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" 8, # 5\n",
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" 8, # 6\n",
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" 8, # 7\n",
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" 8, # 8\n",
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" 8, # 9\n",
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" 8, # 10\n",
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" 8, # 11\n",
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" 8, # 12\n",
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" 8, # 13\n",
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" 8, # 14\n",
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" 42, # 15\n",
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" 42, # 16\n",
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" ]\n",
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" assert len(data[\"distance_matrix\"]) == len(data[\"value\"])\n",
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" data[\"num_vehicles\"] = 4\n",
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" data[\"depot\"] = 0\n",
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" return data\n",
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"\n",
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"\n",
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"\n",
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"def print_solution(data, manager, routing, solution):\n",
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" \"\"\"Prints solution on console.\"\"\"\n",
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" print(f\"Objective: {solution.ObjectiveValue()}\")\n",
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" max_route_distance = 0\n",
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" dim_one = routing.GetDimensionOrDie(\"One\")\n",
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" dim_two = routing.GetDimensionOrDie(\"Two\")\n",
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"\n",
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" for vehicle_id in range(data[\"num_vehicles\"]):\n",
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" index = routing.Start(vehicle_id)\n",
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" plan_output = f\"Route for vehicle {vehicle_id}:\\n\"\n",
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" route_distance = 0\n",
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" while not routing.IsEnd(index):\n",
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" one_var = dim_one.CumulVar(index)\n",
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" one_slack_var = dim_one.SlackVar(index)\n",
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" two_var = dim_two.CumulVar(index)\n",
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" two_slack_var = dim_two.SlackVar(index)\n",
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" plan_output += (\n",
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" f\" N:{manager.IndexToNode(index)}\"\n",
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" f\" one:({solution.Value(one_var)}, {solution.Value(one_slack_var)})\"\n",
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" f\" two:({solution.Value(two_var)}, {solution.Value(two_slack_var)})\"\n",
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" \" -> \"\n",
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" )\n",
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" previous_index = index\n",
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" index = solution.Value(routing.NextVar(index))\n",
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" route_distance += routing.GetArcCostForVehicle(\n",
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" previous_index, index, vehicle_id\n",
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" )\n",
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" one_var = dim_one.CumulVar(index)\n",
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" two_var = dim_two.CumulVar(index)\n",
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" plan_output += (\n",
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" f\"N:{manager.IndexToNode(index)}\"\n",
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" f\" one:{solution.Value(one_var)}\"\n",
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" f\" two:{solution.Value(two_var)}\\n\"\n",
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" )\n",
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" plan_output += f\"Distance of the route: {route_distance}m\\n\"\n",
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" print(plan_output)\n",
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" max_route_distance = max(route_distance, max_route_distance)\n",
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" print(f\"Maximum of the route distances: {max_route_distance}m\")\n",
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"\n",
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"\n",
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"\n",
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"def main():\n",
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" \"\"\"Solve the CVRP problem.\"\"\"\n",
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" # Instantiate the data problem.\n",
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" data = create_data_model()\n",
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"\n",
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" # Create the routing index manager.\n",
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" manager = pywrapcp.RoutingIndexManager(\n",
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" len(data[\"distance_matrix\"]), data[\"num_vehicles\"], data[\"depot\"]\n",
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" )\n",
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"\n",
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" # Create Routing Model.\n",
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" routing = pywrapcp.RoutingModel(manager)\n",
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"\n",
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"\n",
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" # Create and register a transit callback.\n",
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" def distance_callback(from_index, to_index):\n",
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" \"\"\"Returns the distance between the two nodes.\"\"\"\n",
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" # Convert from routing variable Index to distance matrix NodeIndex.\n",
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" from_node = manager.IndexToNode(from_index)\n",
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" to_node = manager.IndexToNode(to_index)\n",
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" return data[\"distance_matrix\"][from_node][to_node]\n",
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"\n",
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" transit_callback_index = routing.RegisterTransitCallback(distance_callback)\n",
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"\n",
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" # Define cost of each arc.\n",
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" routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)\n",
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"\n",
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" # Add Distance constraint.\n",
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" dimension_name = \"Distance\"\n",
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" routing.AddDimension(\n",
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" transit_callback_index,\n",
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" 0, # no slack\n",
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" 3_000, # vehicle maximum travel distance\n",
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" True, # start cumul to zero\n",
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" dimension_name,\n",
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" )\n",
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" distance_dimension = routing.GetDimensionOrDie(dimension_name)\n",
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" distance_dimension.SetGlobalSpanCostCoefficient(10)\n",
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"\n",
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" # Max Node value Constraint.\n",
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" # Dimension One will be used to compute the max node value up to the node in\n",
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" # the route and store the result in the SlackVar of the node.\n",
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" routing.AddConstantDimensionWithSlack(\n",
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" 0, # transit 0\n",
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" 42 * 16, # capacity: be able to store PEAK*ROUTE_LENGTH in worst case\n",
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" 42, # slack_max: to be able to store peak in slack\n",
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" True, # Fix StartCumulToZero not really matter here\n",
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" \"One\",\n",
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" )\n",
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" dim_one = routing.GetDimensionOrDie(\"One\")\n",
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"\n",
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" # Dimension Two will be used to store the max node value in the route end node\n",
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" # CumulVar so we can use it as an objective cost.\n",
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" routing.AddConstantDimensionWithSlack(\n",
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" 0, # transit 0\n",
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" 42 * 16, # capacity: be able to have PEAK value in CumulVar(End)\n",
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" 42, # slack_max: to be able to store peak in slack\n",
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" True, # Fix StartCumulToZero YES here\n",
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" \"Two\",\n",
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" )\n",
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" dim_two = routing.GetDimensionOrDie(\"Two\")\n",
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"\n",
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" # force depot Slack to be value since we don't have any predecessor...\n",
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" for v in range(manager.GetNumberOfVehicles()):\n",
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" start = routing.Start(v)\n",
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" dim_one.SlackVar(start).SetValue(data[\"value\"][0])\n",
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" routing.AddToAssignment(dim_one.SlackVar(start))\n",
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"\n",
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" dim_two.SlackVar(start).SetValue(data[\"value\"][0])\n",
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" routing.AddToAssignment(dim_two.SlackVar(start))\n",
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"\n",
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" # Step by step relation\n",
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" # Slack(N) = max( Slack(N-1) , value(N) )\n",
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" solver = routing.solver()\n",
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" for node in range(1, 17):\n",
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" index = manager.NodeToIndex(node)\n",
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" routing.AddToAssignment(dim_one.SlackVar(index))\n",
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" routing.AddToAssignment(dim_two.SlackVar(index))\n",
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" test = []\n",
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" for v in range(manager.GetNumberOfVehicles()):\n",
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" previous_index = routing.Start(v)\n",
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" cond = routing.NextVar(previous_index) == index\n",
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" value = solver.Max(dim_one.SlackVar(previous_index), data[\"value\"][node])\n",
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" test.append((cond * value).Var())\n",
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" for previous in range(1, 17):\n",
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" previous_index = manager.NodeToIndex(previous)\n",
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" cond = routing.NextVar(previous_index) == index\n",
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" value = solver.Max(dim_one.SlackVar(previous_index), data[\"value\"][node])\n",
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" test.append((cond * value).Var())\n",
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" solver.Add(solver.Sum(test) == dim_one.SlackVar(index))\n",
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"\n",
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" # relation between dimensions, copy last node Slack from dim ONE to dim TWO\n",
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" for node in range(1, 17):\n",
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" index = manager.NodeToIndex(node)\n",
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" values = []\n",
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" for v in range(manager.GetNumberOfVehicles()):\n",
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" next_index = routing.End(v)\n",
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" cond = routing.NextVar(index) == next_index\n",
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" value = dim_one.SlackVar(index)\n",
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" values.append((cond * value).Var())\n",
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" solver.Add(solver.Sum(values) == dim_two.SlackVar(index))\n",
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"\n",
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" # Should force all others dim_two slack var to zero...\n",
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" for v in range(manager.GetNumberOfVehicles()):\n",
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" end = routing.End(v)\n",
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" dim_two.SetCumulVarSoftUpperBound(end, 0, 4200)\n",
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"\n",
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" # Setting first solution heuristic.\n",
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" search_parameters = pywrapcp.DefaultRoutingSearchParameters()\n",
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" search_parameters.first_solution_strategy = (\n",
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" routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC\n",
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" )\n",
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" search_parameters.local_search_metaheuristic = (\n",
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" routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH\n",
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" )\n",
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" # search_parameters.log_search = True\n",
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" search_parameters.time_limit.FromSeconds(5)\n",
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"\n",
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" # Solve the problem.\n",
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" solution = routing.SolveWithParameters(search_parameters)\n",
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"\n",
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" # Print solution on console.\n",
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" if solution:\n",
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" print_solution(data, manager, routing, solution)\n",
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" else:\n",
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" print(\"No solution found !\")\n",
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"\n",
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"\n",
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"main()\n",
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"\n"
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]
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}
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],
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"metadata": {},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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