248 lines
8.8 KiB
Plaintext
248 lines
8.8 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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"# vrpgs"
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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/master/examples/notebook/constraint_solver/vrpgs.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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/master/ortools/constraint_solver/samples/vrpgs.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/master/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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"Simple Vehicles Routing Problem (VRP).\n",
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"\n",
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" This is a sample using the routing library python wrapper to solve a VRP\n",
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" problem.\n",
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" A description of the problem can be found here:\n",
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" http://en.wikipedia.org/wiki/Vehicle_routing_problem.\n",
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"\n",
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" Distances are in meters.\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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"import functools\n",
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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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" # Locations in block unit\n",
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" locations_ = [\n",
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" (4, 4), # depot\n",
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" (2, 0),\n",
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" (8, 0), # locations to visit\n",
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" (0, 1),\n",
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" (1, 1),\n",
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" (5, 2),\n",
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" (7, 2),\n",
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" (3, 3),\n",
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" (6, 3),\n",
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" (5, 5),\n",
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" (8, 5),\n",
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" (1, 6),\n",
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" (2, 6),\n",
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" (3, 7),\n",
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" (6, 7),\n",
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" (0, 8),\n",
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" (7, 8),\n",
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" ]\n",
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" # Compute locations in meters using the block dimension defined as follow\n",
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" # Manhattan average block: 750ft x 264ft -> 228m x 80m\n",
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" # here we use: 114m x 80m city block\n",
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" # src: https://nyti.ms/2GDoRIe 'NY Times: Know Your distance'\n",
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" data['locations'] = [(l[0] * 114, l[1] * 80) for l in locations_]\n",
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" data['num_locations'] = len(data['locations'])\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, assignment):\n",
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" \"\"\"Prints solution on console.\"\"\"\n",
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" print(f'Objective: {assignment.ObjectiveValue()}')\n",
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" total_distance = 0\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 = 'Route for vehicle {}:\\n'.format(vehicle_id)\n",
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" route_distance = 0\n",
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" while not routing.IsEnd(index):\n",
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" plan_output += ' {} ->'.format(manager.IndexToNode(index))\n",
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" previous_index = index\n",
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" index = assignment.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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" plan_output += ' {}\\n'.format(manager.IndexToNode(index))\n",
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" plan_output += 'Distance of the route: {}m\\n'.format(route_distance)\n",
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" print(plan_output)\n",
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" total_distance += route_distance\n",
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" print('Total Distance of all routes: {}m'.format(total_distance))\n",
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"\n",
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"\n",
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"\n",
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"#######################\n",
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"# Problem Constraints #\n",
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"#######################\n",
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"def manhattan_distance(position_1, position_2):\n",
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" \"\"\"Computes the Manhattan distance between two points.\"\"\"\n",
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" return (abs(position_1[0] - position_2[0]) +\n",
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" abs(position_1[1] - position_2[1]))\n",
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"\n",
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"\n",
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"def create_distance_evaluator(data):\n",
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" \"\"\"Creates callback to return distance between points.\"\"\"\n",
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" distances_ = {}\n",
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" # precompute distance between location to have distance callback in O(1)\n",
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" for from_node in range(data['num_locations']):\n",
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" distances_[from_node] = {}\n",
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" for to_node in range(data['num_locations']):\n",
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" if from_node == to_node:\n",
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" distances_[from_node][to_node] = 0\n",
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" else:\n",
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" distances_[from_node][to_node] = (manhattan_distance(\n",
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" data['locations'][from_node], data['locations'][to_node]))\n",
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"\n",
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" def distance_evaluator(manager, from_index, to_index):\n",
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" \"\"\"Returns the manhattan 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 distances_[from_node][to_node]\n",
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"\n",
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" return distance_evaluator\n",
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"\n",
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"\n",
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"def add_distance_dimension(routing, distance_evaluator_index):\n",
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" \"\"\"Add Global Span constraint.\"\"\"\n",
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" distance = 'Distance'\n",
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" routing.AddDimension(\n",
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" distance_evaluator_index,\n",
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" 0, # null slack\n",
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" 3000, # maximum distance per vehicle\n",
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" True, # start cumul to zero\n",
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" distance)\n",
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" distance_dimension = routing.GetDimensionOrDie(distance)\n",
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" # Try to minimize the max distance among vehicles.\n",
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" # /!\\ It doesn't mean the standard deviation is minimized\n",
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" distance_dimension.SetGlobalSpanCostCoefficient(100)\n",
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"\n",
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"\n",
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"def main():\n",
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" \"\"\"Entry point of the program.\"\"\"\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(data['num_locations'],\n",
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" data['num_vehicles'], data['depot'])\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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" # Define weight of each edge\n",
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" distance_evaluator_index = routing.RegisterTransitCallback(\n",
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" functools.partial(create_distance_evaluator(data), manager))\n",
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"\n",
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" # Define cost of each arc.\n",
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" routing.SetArcCostEvaluatorOfAllVehicles(distance_evaluator_index)\n",
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"\n",
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" # Add Distance constraint.\n",
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" add_distance_dimension(routing, distance_evaluator_index)\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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" # 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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