464 lines
20 KiB
Plaintext
464 lines
20 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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"# cvrp_reload"
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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/cvrp_reload.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/cvrp_reload.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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"Capacitated Vehicle Routing Problem (CVRP).\n",
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"\n",
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" This is a sample using the routing library python wrapper to solve a CVRP\n",
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" problem while allowing multiple trips, i.e., vehicles can return to a depot\n",
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" to reset their load (\"reload\").\n",
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"\n",
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" A description of the CVRP 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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" In order to implement multiple trips, new nodes are introduced at the same\n",
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" locations of the original depots. These additional nodes can be dropped\n",
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" from the schedule at 0 cost.\n",
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"\n",
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" The max_slack parameter associated to the capacity constraints of all nodes\n",
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" can be set to be the maximum of the vehicles' capacities, rather than 0 like\n",
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" in a traditional CVRP. Slack is required since before a solution is found,\n",
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" it is not known how much capacity will be transferred at the new nodes. For\n",
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" all the other (original) nodes, the slack is then re-set to 0.\n",
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"\n",
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" The above two considerations are implemented in `add_capacity_constraints()`.\n",
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"\n",
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" Last, it is useful to set a large distance between the initial depot and the\n",
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" new nodes introduced, to avoid schedules having spurious transits through\n",
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" those new nodes unless it's necessary to reload. This consideration is taken\n",
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" into account in `create_distance_evaluator()`.\n",
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"\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 functools import partial\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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" _capacity = 15\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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" (4, 4), # unload depot_first\n",
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" (4, 4), # unload depot_second\n",
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" (4, 4), # unload depot_third\n",
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" (4, 4), # unload depot_fourth\n",
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" (4, 4), # unload depot_fifth\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['demands'] = \\\n",
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" [0, # depot\n",
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" -_capacity, # unload depot_first\n",
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" -_capacity, # unload depot_second\n",
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" -_capacity, # unload depot_third\n",
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" -_capacity, # unload depot_fourth\n",
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" -_capacity, # unload depot_fifth\n",
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" 3, 3, # 1, 2\n",
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" 3, 4, # 3, 4\n",
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" 3, 4, # 5, 6\n",
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" 8, 8, # 7, 8\n",
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" 3, 3, # 9,10\n",
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" 3, 3, # 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['time_windows'] = \\\n",
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" [(0, 0), # depot\n",
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" (0, 1000), # unload depot_first\n",
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" (0, 1000), # unload depot_second\n",
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" (0, 1000), # unload depot_third\n",
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" (0, 1000), # unload depot_fourth\n",
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" (0, 1000), # unload depot_fifth\n",
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" (75, 850), (75, 850), # 1, 2\n",
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" (60, 700), (45, 550), # 3, 4\n",
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" (0, 800), (50, 600), # 5, 6\n",
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" (0, 1000), (10, 200), # 7, 8\n",
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" (0, 1000), (75, 850), # 9, 10\n",
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" (85, 950), (5, 150), # 11, 12\n",
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" (15, 250), (10, 200), # 13, 14\n",
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" (45, 550), (30, 400)] # 15, 16\n",
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" data['num_vehicles'] = 3\n",
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" data['vehicle_capacity'] = _capacity\n",
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" data['vehicle_max_distance'] = 10_000\n",
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" data['vehicle_max_time'] = 1_500\n",
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" data[\n",
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" 'vehicle_speed'] = 5 * 60 / 3.6 # Travel speed: 5km/h to convert 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 (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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" # Forbid start/end/reload node to be consecutive.\n",
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" elif from_node in range(6) and to_node in range(6):\n",
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" _distances[from_node][to_node] = data['vehicle_max_distance']\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 add_distance_dimension(routing, manager, data, 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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" data['vehicle_max_distance'], # 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 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, from_node):\n",
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" \"\"\"Returns the demand of the current node\"\"\"\n",
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" return _demands[manager.IndexToNode(from_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, manager, data, demand_evaluator_index):\n",
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" \"\"\"Adds capacity constraint\"\"\"\n",
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" vehicle_capacity = data['vehicle_capacity']\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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" vehicle_capacity,\n",
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" 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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" # Add Slack for reseting to zero unload depot nodes.\n",
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" # e.g. vehicle with load 10/15 arrives at node 1 (depot unload)\n",
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" # so we have CumulVar = 10(current load) + -15(unload) + 5(slack) = 0.\n",
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" capacity_dimension = routing.GetDimensionOrDie(capacity)\n",
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" # Allow to drop reloading nodes with zero cost.\n",
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" for node in [1, 2, 3, 4, 5]:\n",
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" node_index = manager.NodeToIndex(node)\n",
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" routing.AddDisjunction([node_index], 0)\n",
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"\n",
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" # Allow to drop regular node with a cost.\n",
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" for node in range(6, len(data['demands'])):\n",
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" node_index = manager.NodeToIndex(node)\n",
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" capacity_dimension.SlackVar(node_index).SetValue(0)\n",
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" routing.AddDisjunction([node_index], 100_000)\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 abs(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(\n",
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" data['locations'][from_node], data['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 range(data['num_locations']):\n",
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" _total_time[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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" _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):\n",
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" \"\"\"Add Time windows constraint\"\"\"\n",
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" time = 'Time'\n",
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" max_time = data['vehicle_max_time']\n",
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" routing.AddDimension(\n",
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" time_evaluator,\n",
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" max_time, # allow waiting time\n",
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" max_time, # 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 range(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(f'Objective: {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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" dropped = []\n",
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" for order in range(6, routing.nodes()):\n",
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" index = manager.NodeToIndex(order)\n",
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" if assignment.Value(routing.NextVar(index)) == index:\n",
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" dropped.append(order)\n",
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" print(f'dropped orders: {dropped}')\n",
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" for reload in range(1, 6):\n",
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" index = manager.NodeToIndex(reload)\n",
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" if assignment.Value(routing.NextVar(index)) == index:\n",
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" dropped.append(reload)\n",
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" print(f'dropped reload stations: {dropped}')\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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" 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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" plan_output += ' {0} Load({1}) Time({2},{3}) ->'.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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" 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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" 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 += f'Distance of the route: {distance}m\\n'\n",
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" plan_output += f'Load of the route: {assignment.Value(load_var)}\\n'\n",
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" plan_output += f'Time of the route: {assignment.Value(time_var)}min\\n'\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: {}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: {}min'.format(total_time))\n",
|
|
"\n",
|
|
"\n",
|
|
"########\n",
|
|
"# Main #\n",
|
|
"########\n",
|
|
"def main():\n",
|
|
" \"\"\"Entry point of the program\"\"\"\n",
|
|
" # Instantiate the data problem.\n",
|
|
" data = create_data_model()\n",
|
|
"\n",
|
|
" # Create the routing index manager\n",
|
|
" manager = pywrapcp.RoutingIndexManager(data['num_locations'],\n",
|
|
" data['num_vehicles'], data['depot'])\n",
|
|
"\n",
|
|
" # Create Routing Model\n",
|
|
" routing = pywrapcp.RoutingModel(manager)\n",
|
|
"\n",
|
|
" # Define weight of each edge\n",
|
|
" distance_evaluator_index = routing.RegisterTransitCallback(\n",
|
|
" partial(create_distance_evaluator(data), manager))\n",
|
|
" routing.SetArcCostEvaluatorOfAllVehicles(distance_evaluator_index)\n",
|
|
"\n",
|
|
" # Add Distance constraint to minimize the longuest route\n",
|
|
" add_distance_dimension(routing, manager, data, distance_evaluator_index)\n",
|
|
"\n",
|
|
" # Add Capacity constraint\n",
|
|
" demand_evaluator_index = routing.RegisterUnaryTransitCallback(\n",
|
|
" partial(create_demand_evaluator(data), manager))\n",
|
|
" add_capacity_constraints(routing, manager, data, demand_evaluator_index)\n",
|
|
"\n",
|
|
" # Add Time Window constraint\n",
|
|
" time_evaluator_index = routing.RegisterTransitCallback(\n",
|
|
" partial(create_time_evaluator(data), manager))\n",
|
|
" add_time_window_constraints(routing, manager, data, time_evaluator_index)\n",
|
|
"\n",
|
|
" # Setting first solution heuristic (cheapest addition).\n",
|
|
" search_parameters = pywrapcp.DefaultRoutingSearchParameters()\n",
|
|
" search_parameters.first_solution_strategy = (\n",
|
|
" routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC) # pylint: disable=no-member\n",
|
|
" search_parameters.local_search_metaheuristic = (\n",
|
|
" routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)\n",
|
|
" search_parameters.time_limit.FromSeconds(3)\n",
|
|
"\n",
|
|
" # Solve the problem.\n",
|
|
" solution = routing.SolveWithParameters(search_parameters)\n",
|
|
" if solution:\n",
|
|
" print_solution(data, manager, routing, solution)\n",
|
|
" else:\n",
|
|
" print(\"No solution found !\")\n",
|
|
"\n",
|
|
"\n",
|
|
"main()\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|