VRP with 2 Vehicles max for same physical locations

vrp_vmax.py

#!/usr/bin/env python3
"""Vehicles Routing Problem (VRP).

Some point are on the same physical location
No more than two vehicle to visit a physical location
"""
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp


def create_data_model():
    """Stores the data for the problem."""
    data = {}
    data['distance_matrix'] = [
        [
            0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354,
            468, 776, 662
        ],
        [
            548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480,
            674, 1016, 868, 1210
        ],
        [
            776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164,
            1130, 788, 1552, 754
        ],
        [
            696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628,
            822, 1164, 560, 1358
        ],
        [
            582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514,
            708, 1050, 674, 1244
        ],
        [
            274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628,
            514, 1050, 708
        ],
        [
            502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890,
            856, 514, 1278, 480
        ],
        [
            194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320,
            662, 742, 856
        ],
        [
            308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662,
            320, 1084, 514
        ],
        [
            194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388,
            274, 810, 468
        ],
        [
            536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764,
            730, 388, 1152, 354
        ],
        [
            502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114,
            308, 650, 274, 844
        ],
        [
            388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0,
            194, 536, 388, 730
        ],
        [
            354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194,
            0, 342, 422, 536
        ],
        [
            468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536,
            342, 0, 764, 194
        ],
        [
            776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274,
            388, 422, 764, 0, 798
        ],
        [
            662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730,
            536, 194, 798, 0
        ],
    ]
    data['locations'] = [
        [1,2,3,4,5],
        [6,7,8,9,10],
        [11,12,13,14,15,16],
    ]
    data['num_vehicles'] = 4
    data['depot'] = 0
    return data


def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    print(f"locations: {data['locations']}")
    print(f'Objective: {solution.ObjectiveValue()}')
    max_route_distance = 0

    for vehicle_id in range(data['num_vehicles']):
        plan_output = f'Route for vehicle {vehicle_id}:\n'
        route_distance = 0
        index = routing.Start(vehicle_id)
        while not routing.IsEnd(index):
            node = manager.IndexToNode(index)
            plan_output += f' N:{node} -> '
            previous_index = index
            index = solution.Value(routing.NextVar(index))
            route_distance += routing.GetArcCostForVehicle(
                previous_index, index, vehicle_id)
        node = manager.IndexToNode(index)
        plan_output += f'N:{node}\n'
        plan_output += f'Distance of the route: {route_distance}m\n'
        print(plan_output)
        max_route_distance = max(route_distance, max_route_distance)
    print(f'Maximum of the route distances: {max_route_distance}m')


def main():
    """Solve the CVRP problem."""
    # Instantiate the data problem.
    data = create_data_model()

    # Create the routing index manager.
    manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),
                                           data['num_vehicles'], data['depot'])

    # Create Routing Model.
    routing = pywrapcp.RoutingModel(manager)

    # Create and register a transit callback.
    def distance_callback(from_index, to_index):
        """Returns the distance between the two nodes."""
        # Convert from routing variable Index to distance matrix NodeIndex.
        from_node = manager.IndexToNode(from_index)
        to_node = manager.IndexToNode(to_index)
        return data['distance_matrix'][from_node][to_node]

    transit_callback_index = routing.RegisterTransitCallback(distance_callback)

    # Define cost of each arc.
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

    # Add Distance constraint.
    dimension_name = 'Distance'
    routing.AddDimension(
        transit_callback_index,
        0,  # no slack
        3_000,  # vehicle maximum travel distance
        True,  # start cumul to zero
        dimension_name)
    distance_dimension = routing.GetDimensionOrDie(dimension_name)
    distance_dimension.SetGlobalSpanCostCoefficient(10)


    b_vl = {}
    solver = routing.solver()
    for v in range(manager.GetNumberOfVehicles()):
        for l in range(len(data['locations'])):
            print(f'build b_vl[{v},{l}]...')
            test = []
            for location in data['locations'][l]:
                cond = routing.VehicleVar(manager.NodeToIndex(location)) == v
                test.append(cond)
                #test.append(cond.Var())
            b_vl[(v, l)] = solver.Sum(test) > 0

    for l in range(len(data['locations'])):
        solver.Add(solver.Sum([b_vl[(v, l)]
            for v in range(manager.GetNumberOfVehicles())]) <= 2)

    # Setting first solution heuristic.
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
    search_parameters.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    # search_parameters.log_search = True
    search_parameters.time_limit.FromSeconds(5)

    # Solve the problem.
    solution = routing.SolveWithParameters(search_parameters)

    # Print solution on console.
    if solution:
        print_solution(data, manager, routing, solution)
    else:
        print('No solution found !')


if __name__ == '__main__':
    main()

zz.md

Potential output:

./vrp_vmax.py
build b_vl[0,0]...
build b_vl[0,1]...
build b_vl[0,2]...
build b_vl[1,0]...
build b_vl[1,1]...
build b_vl[1,2]...
build b_vl[2,0]...
build b_vl[2,1]...
build b_vl[2,2]...
build b_vl[3,0]...
build b_vl[3,1]...
build b_vl[3,2]...
locations: [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16]]
Objective: 23648
Route for vehicle 0:
 N:0 ->  N:1 ->  N:4 ->  N:3 -> N:0
Distance of the route: 1552m

Route for vehicle 1:
 N:0 ->  N:5 ->  N:6 ->  N:2 ->  N:10 -> N:0
Distance of the route: 1712m

Route for vehicle 2:
 N:0 ->  N:13 ->  N:15 ->  N:11 ->  N:12 -> N:0
Distance of the route: 1552m

Route for vehicle 3:
 N:0 ->  N:9 ->  N:14 ->  N:16 ->  N:8 ->  N:7 -> N:0
Distance of the route: 1712m

Maximum of the route distances: 1712m