如何在Google OR Tools中为CVRP添加最长路径长度约束

要给基于OR-Tools的带容量约束车辆路径问题（CVRP）添加最长路径长度上限，只需通过OR-Tools的维度（Dimension）机制，新增一个跟踪路径距离的维度并设置上限即可。以下是具体实现步骤和修改后的完整代码：

实现步骤 #

1. 在数据模型中添加路径上限参数：在create_data_model()函数里新增max_route_distance字段，定义单辆车允许的最长路径长度。
2. 注册距离维度约束：利用已有的距离回调函数，通过AddDimension方法创建距离维度，限制每辆车的累积路径长度不超过设定上限。

修改后的完整代码 #

from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp

def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    print(f"Objective: {solution.ObjectiveValue()}")
    total_distance = 0
    total_load = 0
    for vehicle_id in range(data["num_vehicles"]):
        index = routing.Start(vehicle_id)
        plan_output = f"Route for vehicle {vehicle_id}:\n"
        route_distance = 0
        route_load = 0
        while not routing.IsEnd(index):
            node_index = manager.IndexToNode(index)
            route_load += data["demands"][node_index]
            plan_output += f" {node_index} Load({route_load}) -> "
            previous_index = index
            index = solution.Value(routing.NextVar(index))
            route_distance += routing.GetArcCostForVehicle(
                previous_index, index, vehicle_id
            )
        plan_output += f" {manager.IndexToNode(index)} Load({route_load})\n"
        plan_output += f"Distance of the route: {route_distance}m\n"
        plan_output += f"Load of the route: {route_load}\n"
        print(plan_output)
        total_distance += route_distance
        total_load += route_load
    print(f"Total distance of all routes: {total_distance}m")
    print(f"Total load of all routes: {total_load}")

def create_data_model():
    """Stores the data for the problem."""
    data = {}
    # 示例距离矩阵，可根据实际需求替换
    data["distance_matrix"] = [
        [0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468],
        [548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016],
        [776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788],
        [696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164],
        [582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050],
        [274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514],
        [502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514],
        [194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662],
        [308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320],
        [194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274],
        [536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388],
        [502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650],
        [388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536],
        [354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 388],
        [468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 388, 0],
    ]
    data["demands"] = [0, 1, 1, 2, 4, 2, 4, 8, 8, 1, 2, 1, 2, 4, 4]
    data["vehicle_capacities"] = [15, 15, 15]
    data["num_vehicles"] = 3
    data["depot"] = 0
    # 新增：单辆车允许的最长路径长度，可根据实际需求调整
    data["max_route_distance"] = 10000
    return data

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 Capacity constraint.
    def demand_callback(from_index):
        """Returns the demand of the node."""
        # Convert from routing variable Index to demands NodeIndex.
        from_node = manager.IndexToNode(from_index)
        return data["demands"][from_node]

    demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback)
    routing.AddDimensionWithVehicleCapacity(
        demand_callback_index,
        0,  # null capacity slack
        data["vehicle_capacities"],  # vehicle maximum capacities
        True,  # start cumul to zero
        "Capacity",
    )

    # 新增：添加最长路径距离约束
    distance_dimension = routing.AddDimension(
        transit_callback_index,
        0,  # 允许的松弛距离（设为0表示严格不超过上限）
        data["max_route_distance"],  # 每个车辆的最大路径长度
        True,  # 起始节点的累积距离为0
        "Distance"
    )

    # 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.time_limit.FromSeconds(1)

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

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

if __name__ == "__main__":
    main()

关键说明 #

• AddDimension方法会自动跟踪每辆车的累积路径长度，确保其不超过max_route_distance设定的值。
• 如果需要为不同车辆设置不同的路径上限，可以将第三个参数替换为列表（如data["max_route_distances"] = [10000, 8000, 12000]），列表长度需与车辆数一致。
• 松弛参数设为0表示不允许路径长度超过上限，若需一定弹性可设置大于0的值。

内容的提问来源于stack exchange，提问作者Santosh Kumar Mandal