306 lines
14 KiB
Plaintext
306 lines
14 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"#!/usr/bin/env python\n",
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"# This Python file uses the following encoding: utf-8\n",
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"# Copyright 2015 Tin Arm Engineering AB\n",
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"# Copyright 2018 Google LLC\n",
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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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"\"\"\"Capacitated Vehicle Routing Problem with Time Windows (CVRPTW).\n",
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"\n",
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" This is a sample using the routing library python wrapper to solve a CVRPTW\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 and time in minutes.\n",
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"\"\"\"\n",
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"\n",
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"from __future__ import print_function\n",
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"\n",
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"from functools import partial\n",
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"from six.moves import xrange\n",
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"\n",
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"from ortools.constraint_solver import pywrapcp\n",
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"from ortools.constraint_solver import routing_enums_pb2\n",
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"\n",
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"\n",
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"###########################\n",
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"# Problem Data Definition #\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), (8, 0), # locations to visit\n",
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" (0, 1), (1, 1),\n",
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" (5, 2), (7, 2),\n",
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" (3, 3), (6, 3),\n",
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" (5, 5), (8, 5),\n",
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" (1, 6), (2, 6),\n",
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" (3, 7), (6, 7),\n",
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" (0, 8), (7, 8)]\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['time_windows'] = \\\n",
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" [(0, 0),\n",
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" (75, 85), (75, 85), # 1, 2\n",
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" (60, 70), (45, 55), # 3, 4\n",
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" (0, 8), (50, 60), # 5, 6\n",
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" (0, 10), (10, 20), # 7, 8\n",
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" (0, 10), (75, 85), # 9, 10\n",
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" (85, 95), (5, 15), # 11, 12\n",
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" (15, 25), (10, 20), # 13, 14\n",
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" (45, 55), (30, 40)] # 15, 16\n",
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" data['demands'] = \\\n",
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" [0, # depot\n",
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" 1, 1, # 1, 2\n",
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" 2, 4, # 3, 4\n",
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" 2, 4, # 5, 6\n",
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" 8, 8, # 7, 8\n",
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" 1, 2, # 9,10\n",
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" 1, 2, # 11,12\n",
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" 4, 4, # 13, 14\n",
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" 8, 8] # 15, 16\n",
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" data['time_per_demand_unit'] = 5 # 5 minutes/unit\n",
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" data['num_vehicles'] = 4\n",
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" data['vehicle_capacity'] = 15\n",
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" data['vehicle_speed'] = 83 # Travel speed: 5km/h converted in m/min\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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"# 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 (\n",
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" abs(position_1[0] - position_2[0]) + 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 xrange(data['num_locations']):\n",
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" _distances[from_node] = {}\n",
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" for to_node in xrange(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_node, to_node):\n",
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" \"\"\"Returns the manhattan distance between the two nodes\"\"\"\n",
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" return _distances[manager.IndexToNode(from_node)][manager.IndexToNode(\n",
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" 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 create_demand_evaluator(data):\n",
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" \"\"\"Creates callback to get demands at each location.\"\"\"\n",
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" _demands = data['demands']\n",
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"\n",
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" def demand_evaluator(manager, node):\n",
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" \"\"\"Returns the demand of the current node\"\"\"\n",
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" return _demands[manager.IndexToNode(node)]\n",
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"\n",
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" return demand_evaluator\n",
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"\n",
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"\n",
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"def add_capacity_constraints(routing, data, demand_evaluator_index):\n",
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" \"\"\"Adds capacity constraint\"\"\"\n",
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" capacity = 'Capacity'\n",
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" routing.AddDimension(\n",
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" demand_evaluator_index,\n",
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" 0, # null capacity slack\n",
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" data['vehicle_capacity'],\n",
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" True, # start cumul to zero\n",
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" capacity)\n",
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"\n",
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"\n",
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"def create_time_evaluator(data):\n",
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" \"\"\"Creates callback to get total times between locations.\"\"\"\n",
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"\n",
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" def service_time(data, node):\n",
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" \"\"\"Gets the service time for the specified location.\"\"\"\n",
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" return data['demands'][node] * data['time_per_demand_unit']\n",
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"\n",
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" def travel_time(data, from_node, to_node):\n",
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" \"\"\"Gets the travel times between two locations.\"\"\"\n",
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" if from_node == to_node:\n",
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" travel_time = 0\n",
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" else:\n",
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" travel_time = manhattan_distance(data['locations'][from_node], data[\n",
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" 'locations'][to_node]) / data['vehicle_speed']\n",
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" return travel_time\n",
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"\n",
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" _total_time = {}\n",
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" # precompute total time to have time callback in O(1)\n",
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" for from_node in xrange(data['num_locations']):\n",
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" _total_time[from_node] = {}\n",
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" for to_node in xrange(data['num_locations']):\n",
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" if from_node == to_node:\n",
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" _total_time[from_node][to_node] = 0\n",
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" else:\n",
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" _total_time[from_node][to_node] = int(\n",
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" service_time(data, from_node) + travel_time(\n",
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" data, from_node, to_node))\n",
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"\n",
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" def time_evaluator(manager, from_node, to_node):\n",
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" \"\"\"Returns the total time between the two nodes\"\"\"\n",
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" return _total_time[manager.IndexToNode(from_node)][manager.IndexToNode(\n",
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" to_node)]\n",
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"\n",
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" return time_evaluator\n",
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"\n",
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"\n",
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"def add_time_window_constraints(routing, manager, data, time_evaluator_index):\n",
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" \"\"\"Add Global Span constraint\"\"\"\n",
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" time = 'Time'\n",
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" horizon = 120\n",
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" routing.AddDimension(\n",
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" time_evaluator_index,\n",
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" horizon, # allow waiting time\n",
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" horizon, # maximum time per vehicle\n",
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" False, # don't force start cumul to zero since we are giving TW to start nodes\n",
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" time)\n",
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" time_dimension = routing.GetDimensionOrDie(time)\n",
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" # Add time window constraints for each location except depot\n",
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" # and 'copy' the slack var in the solution object (aka Assignment) to print it\n",
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" for location_idx, time_window in enumerate(data['time_windows']):\n",
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" if location_idx == 0:\n",
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" continue\n",
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" index = manager.NodeToIndex(location_idx)\n",
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" time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])\n",
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" routing.AddToAssignment(time_dimension.SlackVar(index))\n",
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" # Add time window constraints for each vehicle start node\n",
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" # and 'copy' the slack var in the solution object (aka Assignment) to print it\n",
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" for vehicle_id in xrange(data['num_vehicles']):\n",
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" index = routing.Start(vehicle_id)\n",
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" time_dimension.CumulVar(index).SetRange(data['time_windows'][0][0],\n",
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" data['time_windows'][0][1])\n",
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" routing.AddToAssignment(time_dimension.SlackVar(index))\n",
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" # Warning: Slack var is not defined for vehicle's end node\n",
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" #routing.AddToAssignment(time_dimension.SlackVar(self.routing.End(vehicle_id)))\n",
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"\n",
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"\n",
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"###########\n",
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"# Printer #\n",
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"###########\n",
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"def print_solution(data, manager, routing, assignment): # pylint:disable=too-many-locals\n",
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" \"\"\"Prints assignment on console\"\"\"\n",
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" print('Objective: {}'.format(assignment.ObjectiveValue()))\n",
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" total_distance = 0\n",
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" total_load = 0\n",
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" total_time = 0\n",
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" capacity_dimension = routing.GetDimensionOrDie('Capacity')\n",
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" time_dimension = routing.GetDimensionOrDie('Time')\n",
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" for vehicle_id in xrange(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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" distance = 0\n",
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" while not routing.IsEnd(index):\n",
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" load_var = capacity_dimension.CumulVar(index)\n",
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" time_var = time_dimension.CumulVar(index)\n",
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" slack_var = time_dimension.SlackVar(index)\n",
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" plan_output += ' {0} Load({1}) Time({2},{3}) Slack({4},{5}) ->'.format(\n",
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" manager.IndexToNode(index),\n",
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" assignment.Value(load_var),\n",
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" assignment.Min(time_var),\n",
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" assignment.Max(time_var),\n",
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" assignment.Min(slack_var), assignment.Max(slack_var))\n",
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" previous_index = index\n",
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" index = assignment.Value(routing.NextVar(index))\n",
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" distance += routing.GetArcCostForVehicle(previous_index, index,\n",
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" vehicle_id)\n",
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" load_var = capacity_dimension.CumulVar(index)\n",
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" time_var = time_dimension.CumulVar(index)\n",
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" slack_var = time_dimension.SlackVar(index)\n",
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" plan_output += ' {0} Load({1}) Time({2},{3})\\n'.format(\n",
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" manager.IndexToNode(index),\n",
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" assignment.Value(load_var),\n",
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" assignment.Min(time_var), assignment.Max(time_var))\n",
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" plan_output += 'Distance of the route: {0}m\\n'.format(distance)\n",
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" plan_output += 'Load of the route: {}\\n'.format(\n",
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" assignment.Value(load_var))\n",
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" plan_output += 'Time of the route: {}\\n'.format(\n",
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" assignment.Value(time_var))\n",
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" print(plan_output)\n",
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" total_distance += distance\n",
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" total_load += assignment.Value(load_var)\n",
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" total_time += assignment.Value(time_var)\n",
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" print('Total Distance of all routes: {0}m'.format(total_distance))\n",
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" print('Total Load of all routes: {}'.format(total_load))\n",
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" print('Total Time of all routes: {0}min'.format(total_time))\n",
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"\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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"\"\"\"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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" partial(create_distance_evaluator(data), manager))\n",
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"routing.SetArcCostEvaluatorOfAllVehicles(distance_evaluator_index)\n",
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"\n",
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"# Add Capacity constraint\n",
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"demand_evaluator_index = routing.RegisterUnaryTransitCallback(\n",
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" partial(create_demand_evaluator(data), manager))\n",
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"add_capacity_constraints(routing, data, demand_evaluator_index)\n",
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"\n",
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"# Add Time Window constraint\n",
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"time_evaluator_index = routing.RegisterTransitCallback(\n",
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" partial(create_time_evaluator(data), manager))\n",
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"add_time_window_constraints(routing, manager, data, time_evaluator_index)\n",
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"\n",
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"# Setting first solution heuristic (cheapest addition).\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) # pylint: disable=no-member\n",
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"# Solve the problem.\n",
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"assignment = routing.SolveWithParameters(search_parameters)\n",
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"print_solution(data, manager, routing, assignment)\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": 4
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}
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