367 lines
15 KiB
Plaintext
367 lines
15 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "google",
|
|
"metadata": {},
|
|
"source": [
|
|
"##### Copyright 2023 Google LLC."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "apache",
|
|
"metadata": {},
|
|
"source": [
|
|
"Licensed under the Apache License, Version 2.0 (the \"License\");\n",
|
|
"you may not use this file except in compliance with the License.\n",
|
|
"You may obtain a copy of the License at\n",
|
|
"\n",
|
|
" http://www.apache.org/licenses/LICENSE-2.0\n",
|
|
"\n",
|
|
"Unless required by applicable law or agreed to in writing, software\n",
|
|
"distributed under the License is distributed on an \"AS IS\" BASIS,\n",
|
|
"WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
|
|
"See the License for the specific language governing permissions and\n",
|
|
"limitations under the License.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "basename",
|
|
"metadata": {},
|
|
"source": [
|
|
"# cvrptw"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "link",
|
|
"metadata": {},
|
|
"source": [
|
|
"<table align=\"left\">\n",
|
|
"<td>\n",
|
|
"<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/constraint_solver/cvrptw.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
|
|
"</td>\n",
|
|
"<td>\n",
|
|
"<a href=\"https://github.com/google/or-tools/blob/main/ortools/constraint_solver/samples/cvrptw.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
|
|
"</td>\n",
|
|
"</table>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "doc",
|
|
"metadata": {},
|
|
"source": [
|
|
"First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "install",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"%pip install ortools"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "description",
|
|
"metadata": {},
|
|
"source": [
|
|
"Capacitated Vehicle Routing Problem with Time Windows (CVRPTW).\n",
|
|
"\n",
|
|
" This is a sample using the routing library python wrapper to solve a CVRPTW\n",
|
|
" problem.\n",
|
|
" A description of the problem can be found here:\n",
|
|
" http://en.wikipedia.org/wiki/Vehicle_routing_problem.\n",
|
|
"\n",
|
|
" Distances are in meters and time in minutes.\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "code",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from functools import partial\n",
|
|
"from ortools.constraint_solver import routing_enums_pb2\n",
|
|
"from ortools.constraint_solver import pywrapcp\n",
|
|
"\n",
|
|
"\n",
|
|
"def create_data_model():\n",
|
|
" \"\"\"Stores the data for the problem.\"\"\"\n",
|
|
" data = {}\n",
|
|
" # Locations in block unit\n",
|
|
" _locations = \\\n",
|
|
" [(4, 4), # depot\n",
|
|
" (2, 0), (8, 0), # locations to visit\n",
|
|
" (0, 1), (1, 1),\n",
|
|
" (5, 2), (7, 2),\n",
|
|
" (3, 3), (6, 3),\n",
|
|
" (5, 5), (8, 5),\n",
|
|
" (1, 6), (2, 6),\n",
|
|
" (3, 7), (6, 7),\n",
|
|
" (0, 8), (7, 8)]\n",
|
|
" # Compute locations in meters using the block dimension defined as follow\n",
|
|
" # Manhattan average block: 750ft x 264ft -> 228m x 80m\n",
|
|
" # here we use: 114m x 80m city block\n",
|
|
" # src: https://nyti.ms/2GDoRIe \"NY Times: Know Your distance\"\n",
|
|
" data['locations'] = [(l[0] * 114, l[1] * 80) for l in _locations]\n",
|
|
" data['num_locations'] = len(data['locations'])\n",
|
|
" data['time_windows'] = \\\n",
|
|
" [(0, 0),\n",
|
|
" (75, 85), (75, 85), # 1, 2\n",
|
|
" (60, 70), (45, 55), # 3, 4\n",
|
|
" (0, 8), (50, 60), # 5, 6\n",
|
|
" (0, 10), (10, 20), # 7, 8\n",
|
|
" (0, 10), (75, 85), # 9, 10\n",
|
|
" (85, 95), (5, 15), # 11, 12\n",
|
|
" (15, 25), (10, 20), # 13, 14\n",
|
|
" (45, 55), (30, 40)] # 15, 16\n",
|
|
" data['demands'] = \\\n",
|
|
" [0, # depot\n",
|
|
" 1, 1, # 1, 2\n",
|
|
" 2, 4, # 3, 4\n",
|
|
" 2, 4, # 5, 6\n",
|
|
" 8, 8, # 7, 8\n",
|
|
" 1, 2, # 9,10\n",
|
|
" 1, 2, # 11,12\n",
|
|
" 4, 4, # 13, 14\n",
|
|
" 8, 8] # 15, 16\n",
|
|
" data['time_per_demand_unit'] = 5 # 5 minutes/unit\n",
|
|
" data['num_vehicles'] = 4\n",
|
|
" data['vehicle_capacity'] = 15\n",
|
|
" data['vehicle_speed'] = 83 # Travel speed: 5km/h converted in m/min\n",
|
|
" data['depot'] = 0\n",
|
|
" return data\n",
|
|
"\n",
|
|
"\n",
|
|
"#######################\n",
|
|
"# Problem Constraints #\n",
|
|
"#######################\n",
|
|
"def manhattan_distance(position_1, position_2):\n",
|
|
" \"\"\"Computes the Manhattan distance between two points\"\"\"\n",
|
|
" return (abs(position_1[0] - position_2[0]) +\n",
|
|
" abs(position_1[1] - position_2[1]))\n",
|
|
"\n",
|
|
"\n",
|
|
"def create_distance_evaluator(data):\n",
|
|
" \"\"\"Creates callback to return distance between points.\"\"\"\n",
|
|
" _distances = {}\n",
|
|
" # precompute distance between location to have distance callback in O(1)\n",
|
|
" for from_node in range(data['num_locations']):\n",
|
|
" _distances[from_node] = {}\n",
|
|
" for to_node in range(data['num_locations']):\n",
|
|
" if from_node == to_node:\n",
|
|
" _distances[from_node][to_node] = 0\n",
|
|
" else:\n",
|
|
" _distances[from_node][to_node] = (manhattan_distance(\n",
|
|
" data['locations'][from_node], data['locations'][to_node]))\n",
|
|
"\n",
|
|
" def distance_evaluator(manager, from_node, to_node):\n",
|
|
" \"\"\"Returns the manhattan distance between the two nodes\"\"\"\n",
|
|
" return _distances[manager.IndexToNode(from_node)][manager.IndexToNode(\n",
|
|
" to_node)]\n",
|
|
"\n",
|
|
" return distance_evaluator\n",
|
|
"\n",
|
|
"\n",
|
|
"def create_demand_evaluator(data):\n",
|
|
" \"\"\"Creates callback to get demands at each location.\"\"\"\n",
|
|
" _demands = data['demands']\n",
|
|
"\n",
|
|
" def demand_evaluator(manager, node):\n",
|
|
" \"\"\"Returns the demand of the current node\"\"\"\n",
|
|
" return _demands[manager.IndexToNode(node)]\n",
|
|
"\n",
|
|
" return demand_evaluator\n",
|
|
"\n",
|
|
"\n",
|
|
"def add_capacity_constraints(routing, data, demand_evaluator_index):\n",
|
|
" \"\"\"Adds capacity constraint\"\"\"\n",
|
|
" capacity = 'Capacity'\n",
|
|
" routing.AddDimension(\n",
|
|
" demand_evaluator_index,\n",
|
|
" 0, # null capacity slack\n",
|
|
" data['vehicle_capacity'],\n",
|
|
" True, # start cumul to zero\n",
|
|
" capacity)\n",
|
|
"\n",
|
|
"\n",
|
|
"def create_time_evaluator(data):\n",
|
|
" \"\"\"Creates callback to get total times between locations.\"\"\"\n",
|
|
"\n",
|
|
" def service_time(data, node):\n",
|
|
" \"\"\"Gets the service time for the specified location.\"\"\"\n",
|
|
" return data['demands'][node] * data['time_per_demand_unit']\n",
|
|
"\n",
|
|
" def travel_time(data, from_node, to_node):\n",
|
|
" \"\"\"Gets the travel times between two locations.\"\"\"\n",
|
|
" if from_node == to_node:\n",
|
|
" travel_time = 0\n",
|
|
" else:\n",
|
|
" travel_time = manhattan_distance(\n",
|
|
" data['locations'][from_node],\n",
|
|
" data['locations'][to_node]) / data['vehicle_speed']\n",
|
|
" return travel_time\n",
|
|
"\n",
|
|
" _total_time = {}\n",
|
|
" # precompute total time to have time callback in O(1)\n",
|
|
" for from_node in range(data['num_locations']):\n",
|
|
" _total_time[from_node] = {}\n",
|
|
" for to_node in range(data['num_locations']):\n",
|
|
" if from_node == to_node:\n",
|
|
" _total_time[from_node][to_node] = 0\n",
|
|
" else:\n",
|
|
" _total_time[from_node][to_node] = int(\n",
|
|
" service_time(data, from_node) +\n",
|
|
" travel_time(data, from_node, to_node))\n",
|
|
"\n",
|
|
" def time_evaluator(manager, from_node, to_node):\n",
|
|
" \"\"\"Returns the total time between the two nodes\"\"\"\n",
|
|
" return _total_time[manager.IndexToNode(from_node)][manager.IndexToNode(\n",
|
|
" to_node)]\n",
|
|
"\n",
|
|
" return time_evaluator\n",
|
|
"\n",
|
|
"\n",
|
|
"def add_time_window_constraints(routing, manager, data, time_evaluator_index):\n",
|
|
" \"\"\"Add Global Span constraint\"\"\"\n",
|
|
" time = 'Time'\n",
|
|
" horizon = 120\n",
|
|
" routing.AddDimension(\n",
|
|
" time_evaluator_index,\n",
|
|
" horizon, # allow waiting time\n",
|
|
" horizon, # maximum time per vehicle\n",
|
|
" False, # don't force start cumul to zero since we are giving TW to start nodes\n",
|
|
" time)\n",
|
|
" time_dimension = routing.GetDimensionOrDie(time)\n",
|
|
" # Add time window constraints for each location except depot\n",
|
|
" # and 'copy' the slack var in the solution object (aka Assignment) to print it\n",
|
|
" for location_idx, time_window in enumerate(data['time_windows']):\n",
|
|
" if location_idx == 0:\n",
|
|
" continue\n",
|
|
" index = manager.NodeToIndex(location_idx)\n",
|
|
" time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])\n",
|
|
" routing.AddToAssignment(time_dimension.SlackVar(index))\n",
|
|
" # Add time window constraints for each vehicle start node\n",
|
|
" # and 'copy' the slack var in the solution object (aka Assignment) to print it\n",
|
|
" for vehicle_id in range(data['num_vehicles']):\n",
|
|
" index = routing.Start(vehicle_id)\n",
|
|
" time_dimension.CumulVar(index).SetRange(data['time_windows'][0][0],\n",
|
|
" data['time_windows'][0][1])\n",
|
|
" routing.AddToAssignment(time_dimension.SlackVar(index))\n",
|
|
" # Warning: Slack var is not defined for vehicle's end node\n",
|
|
" #routing.AddToAssignment(time_dimension.SlackVar(self.routing.End(vehicle_id)))\n",
|
|
"\n",
|
|
"\n",
|
|
"def print_solution(manager, routing, assignment): # pylint:disable=too-many-locals\n",
|
|
" \"\"\"Prints assignment on console\"\"\"\n",
|
|
" print(f'Objective: {assignment.ObjectiveValue()}')\n",
|
|
" time_dimension = routing.GetDimensionOrDie('Time')\n",
|
|
" capacity_dimension = routing.GetDimensionOrDie('Capacity')\n",
|
|
" total_distance = 0\n",
|
|
" total_load = 0\n",
|
|
" total_time = 0\n",
|
|
" for vehicle_id in range(manager.GetNumberOfVehicles()):\n",
|
|
" index = routing.Start(vehicle_id)\n",
|
|
" plan_output = f'Route for vehicle {vehicle_id}:\\n'\n",
|
|
" distance = 0\n",
|
|
" while not routing.IsEnd(index):\n",
|
|
" load_var = capacity_dimension.CumulVar(index)\n",
|
|
" time_var = time_dimension.CumulVar(index)\n",
|
|
" slack_var = time_dimension.SlackVar(index)\n",
|
|
" plan_output += (\n",
|
|
" f' {manager.IndexToNode(index)} '\n",
|
|
" f'Load({assignment.Value(load_var)}) '\n",
|
|
" f'Time({assignment.Min(time_var)},{assignment.Max(time_var)}) '\n",
|
|
" f'Slack({assignment.Min(slack_var)},{assignment.Max(slack_var)}) ->'\n",
|
|
" )\n",
|
|
" previous_index = index\n",
|
|
" index = assignment.Value(routing.NextVar(index))\n",
|
|
" distance += routing.GetArcCostForVehicle(previous_index, index,\n",
|
|
" vehicle_id)\n",
|
|
" load_var = capacity_dimension.CumulVar(index)\n",
|
|
" time_var = time_dimension.CumulVar(index)\n",
|
|
" slack_var = time_dimension.SlackVar(index)\n",
|
|
" plan_output += (\n",
|
|
" f' {manager.IndexToNode(index)} '\n",
|
|
" f'Load({assignment.Value(load_var)}) '\n",
|
|
" f'Time({assignment.Min(time_var)},{assignment.Max(time_var)})\\n')\n",
|
|
" plan_output += f'Distance of the route: {distance}m\\n'\n",
|
|
" plan_output += f'Load of the route: {assignment.Value(load_var)}\\n'\n",
|
|
" plan_output += f'Time of the route: {assignment.Value(time_var)}\\n'\n",
|
|
" print(plan_output)\n",
|
|
" total_distance += distance\n",
|
|
" total_load += assignment.Value(load_var)\n",
|
|
" total_time += assignment.Value(time_var)\n",
|
|
" print(f'Total Distance of all routes: {total_distance}m')\n",
|
|
" print(f'Total Load of all routes: {total_load}')\n",
|
|
" print(f'Total Time of all routes: {total_time}min')\n",
|
|
"\n",
|
|
"\n",
|
|
"def main():\n",
|
|
" \"\"\"Solve the Capacitated VRP with time windows.\"\"\"\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",
|
|
"\n",
|
|
" # Define cost of each arc.\n",
|
|
" routing.SetArcCostEvaluatorOfAllVehicles(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, 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)\n",
|
|
" search_parameters.local_search_metaheuristic = (\n",
|
|
" routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)\n",
|
|
" search_parameters.time_limit.FromSeconds(2)\n",
|
|
" search_parameters.log_search = True\n",
|
|
"\n",
|
|
" # Solve the problem.\n",
|
|
" solution = routing.SolveWithParameters(search_parameters)\n",
|
|
"\n",
|
|
" # Print solution on console.\n",
|
|
" if solution:\n",
|
|
" print_solution(manager, routing, solution)\n",
|
|
" else:\n",
|
|
" print('No solution found!')\n",
|
|
"\n",
|
|
"\n",
|
|
"main()\n",
|
|
"\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|