minimum distance constraint in vehicle routing using or tools

Question

I am trying to solve the vehicle routing problem using or tools and i want to modify the below solution such that each vehicle at least cover 100 unit of distance before moving on to next vehicle.

Below is my code so far : The distance matrix is passed as variable data.

def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    max_route_distance = 0
    
    for vehicle_id in range(data['num_vehicles']):
        sap_index = []
        index = routing.Start(vehicle_id)
        print(routing.IsEnd(index))
        plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
        route_distance = 0
        while not routing.IsEnd(index):
            plan_output += ' {} -> '.format(manager.IndexToNode(index))
            sap_index.append(manager.IndexToNode(index))
            previous_index = index
            index = solution.Value(routing.NextVar(index))
            route_distance += routing.GetArcCostForVehicle(
                previous_index, index, vehicle_id)
        plan_output += '{}\n'.format(manager.IndexToNode(index))
        sap_index.append(manager.IndexToNode(index))
        plan_output += 'Distance of the route: {}\n'.format(route_distance)
        print(plan_output)
        for z in sap_index:
            print(sapids[z],end=" -> ")
        print("\n")
        max_route_distance = max(route_distance, max_route_distance)
    print('Maximum of the route distances: {}'.format(max_route_distance))




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
        100,  # vehicle maximum travel distance
        True,  # start cumul to zero
        dimension_name)
    distance_dimension = routing.GetDimensionOrDie(dimension_name)
    distance_dimension.SetGlobalSpanCostCoefficient(100)

    # Setting first solution heuristic.
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)

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

    # Print solution on console.
    if solution:
        print_solution(data, manager, routing, solution)


if __name__ == '__main__':
    main()

answer for 50 sites and 4 vehicle is coming as under :

Route for vehicle 0:
 0 ->  22 ->  11 ->  21 ->  39 ->  49 ->  24 ->  41 ->  35 -> 0
Distance of the route: 13

Route for vehicle 1:
 0 -> 0
Distance of the route: 0

Route for vehicle 2:
 0 ->  10 ->  43 ->  38 ->  6 ->  17 ->  36 ->  37 ->  14 ->  19 ->  15 ->  20 ->  40 ->  18 ->  16 ->  34 ->  12 ->  13 ->  5 ->  7 ->  8 ->  42
-> 0
Distance of the route: 20

Route for vehicle 3:
 0 ->  23 ->  27 ->  26 ->  1 ->  48 ->  46 ->  47 ->  45 ->  30 ->  2 ->  33 ->  32 ->  31 ->  9 ->  28 ->  25 ->  29 ->  3 ->  44 ->  4 -> 0
Distance of the route: 25

Maximum of the route distances: 25

in the def print_solution function i tried giving route_distance < 100 condition in while loop along with not routing.IsEnd(index) but that did not work.

Need help!

Answer 1

in your sample, you have used:

       100,  # vehicle maximum travel distance

i.e. the hard upper bound for each vehicle is 100, so how you can expect vehicle to travel more than its limit ?

Also you should comment out the GlobalSpan coefficient which currently give incentive to the solver to limit the maximum route length (it is the dominant factor here)...

Answer 2

This is a bad idea. You will create unfeasible problems very easily. You need to get the end var of each vehicle, and add a soft lower bound on that one.

See this doc entry