432 lines
17 KiB
Plaintext
432 lines
17 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 2025 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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"# cvrptw_break"
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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/cvrptw_break.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/cvrptw_break.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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"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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]
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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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"\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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" # fmt: off\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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" # fmt: on\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[\"numlocations_\"] = len(data[\"locations\"])\n",
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" data[\"time_windows\"] = [\n",
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" # fmt: off\n",
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" (0, 0), # depot\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),\n",
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" # 15, 16\n",
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" # fmt: on\n",
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" ]\n",
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" data[\"demands\"] = [\n",
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" # fmt: off\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,\n",
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" # 15, 16\n",
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" # fmt: on\n",
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" ]\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[\"breaks\"] = [(2, False), (2, False), (2, False), (2, False)]\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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"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]) + 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[\"numlocations_\"]):\n",
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" distances_[from_node] = {}\n",
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" for to_node in range(data[\"numlocations_\"]):\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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"\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(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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"\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 = (\n",
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" 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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" / data[\"vehicle_speed\"]\n",
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" )\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[\"numlocations_\"]):\n",
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" total_time_[from_node] = {}\n",
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" for to_node in range(data[\"numlocations_\"]):\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)\n",
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" + travel_time(data, from_node, to_node)\n",
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" )\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(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\n",
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" time,\n",
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" )\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 == data[\"depot\"]:\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(\n",
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" data[\"time_windows\"][0][0], data[\"time_windows\"][0][1]\n",
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" )\n",
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" routing.AddToAssignment(time_dimension.SlackVar(index))\n",
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" # The time window at the end node was impliclty set in the time dimension\n",
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" # definition to be [0, horizon].\n",
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" # Warning: Slack var is not defined for vehicle end nodes and should not\n",
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" # be added to the assignment.\n",
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"\n",
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"\n",
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"def print_solution(\n",
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" data, manager, routing, assignment\n",
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"): # 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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"\n",
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" print(\"Breaks:\")\n",
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" intervals = assignment.IntervalVarContainer()\n",
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" for i in range(intervals.Size()):\n",
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" brk = intervals.Element(i)\n",
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" if brk.PerformedValue() == 1:\n",
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" print(\n",
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" f\"{brk.Var().Name()}:\"\n",
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" f\" Start({brk.StartValue()}) Duration({brk.DurationValue()})\"\n",
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" )\n",
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" else:\n",
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" print(f\"{brk.Var().Name()}: Unperformed\")\n",
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"\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 range(data[\"num_vehicles\"]):\n",
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" if not routing.IsVehicleUsed(assignment, vehicle_id):\n",
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" continue\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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" slack_var = time_dimension.SlackVar(index)\n",
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" node = manager.IndexToNode(index)\n",
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" plan_output += (\n",
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" f\" {node}\"\n",
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" f\" Load({assignment.Value(load_var)})\"\n",
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" f\" Time({assignment.Min(time_var)}, {assignment.Max(time_var)})\"\n",
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" f\" Slack({assignment.Min(slack_var)}, {assignment.Max(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 = assignment.Value(routing.NextVar(index))\n",
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" distance += routing.GetArcCostForVehicle(previous_index, index, 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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" node = manager.IndexToNode(index)\n",
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" plan_output += (\n",
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" f\" {node}\"\n",
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" f\" Load({assignment.Value(load_var)})\"\n",
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" f\" Time({assignment.Min(time_var)}, {assignment.Max(time_var)})\\n\"\n",
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" )\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)}\\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(f\"Total Distance of all routes: {total_distance}m\")\n",
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" print(f\"Total Load of all routes: {total_load}\")\n",
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" print(f\"Total Time of all routes: {total_time}min\")\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(\n",
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" data[\"numlocations_\"], 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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" # 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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" 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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" functools.partial(create_demand_evaluator(data), manager)\n",
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" )\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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" functools.partial(create_time_evaluator(data), manager)\n",
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" )\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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" # Add breaks\n",
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" time_dimension = routing.GetDimensionOrDie(\"Time\")\n",
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" node_visit_transit = {}\n",
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" for index in range(routing.Size()):\n",
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" node = manager.IndexToNode(index)\n",
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" node_visit_transit[index] = int(\n",
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" data[\"demands\"][node] * data[\"time_per_demand_unit\"]\n",
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" )\n",
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"\n",
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" break_intervals = {}\n",
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" for v in range(data[\"num_vehicles\"]):\n",
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" vehicle_break = data[\"breaks\"][v]\n",
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" break_intervals[v] = [\n",
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" routing.solver().FixedDurationIntervalVar(\n",
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" 15,\n",
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" 100,\n",
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" vehicle_break[0],\n",
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" vehicle_break[1],\n",
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" f\"Break for vehicle {v}\",\n",
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" )\n",
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" ]\n",
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" time_dimension.SetBreakIntervalsOfVehicle(\n",
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" break_intervals[v], v, node_visit_transit.values()\n",
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" )\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\n",
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" ) # pylint: disable=no-member\n",
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"\n",
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" # Solve the problem.\n",
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" assignment = routing.SolveWithParameters(search_parameters)\n",
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"\n",
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" # Print solution on console.\n",
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" if assignment:\n",
|
|
" print_solution(data, manager, routing, assignment)\n",
|
|
" else:\n",
|
|
" print(\"No solution found!\")\n",
|
|
"\n",
|
|
"\n",
|
|
"main()\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"language_info": {
|
|
"name": "python"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|