Google OR-Tools VRP - 节点被不必要地删除

Question

我正在尝试解决具有时间 window 约束的车辆路径问题，如果找不到可行的解决方案，求解器可以删除节点。但是，我发现在添加析取后节点会被不必要地丢弃，即使在施加了很大的惩罚之后也是如此。

下面是一个简单的示例程序来说明这个问题。求解器丢弃节点 1 和 returns 0 -> 3 -> 2 -> 0 的解决方案。如果 routing.AddDisjunction([manager.NodeToIndex(node)], penalty) 代码被注释掉了。

我是不是走错了路？任何帮助将不胜感激。

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['time_matrix'] = [
        [0, 3, 2, 1], # depot
        [3, 0, 3, 3],
        [2, 3, 0, 2],
        [1, 3, 2, 0],
    ]
    data['time_windows'] = [
        (0, 0),  # depot
        (0, 3),  
        (0, 6),  
        (0, 9),  
    ]
    data['num_vehicles'] = 1
    data['depot'] = 0

    return data


def print_solution(data, manager, routing, solution):
    """Prints solution on console."""
    # Display dropped nodes.
    dropped_nodes = '\nDropped nodes:'
    for node in range(routing.Size()):
        if routing.IsStart(node) or routing.IsEnd(node):
            continue
        if solution.Value(routing.NextVar(node)) == node:
            dropped_nodes += ' {}'.format(manager.IndexToNode(node))
    print(dropped_nodes + '\n')

    time_dimension = routing.GetDimensionOrDie('Time')
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
        while not routing.IsEnd(index):
            time_var = time_dimension.CumulVar(index)
            plan_output += '{0} Time ({1}, {2}) -> '.format(
                manager.IndexToNode(index), 
                solution.Min(time_var),
                solution.Max(time_var))
            index = solution.Value(routing.NextVar(index))
        time_var = time_dimension.CumulVar(index)
        plan_output += '{0} Time({1},{2})\n'.format(manager.IndexToNode(index),
                                                    solution.Min(time_var),
                                                    solution.Max(time_var))
        plan_output += '\nTime of the route: {}min\n'.format(
            solution.Min(time_var))
        print(plan_output)



def main():
    """Solve the VRP with time windows."""
    # Instantiate the data problem.
    data = create_data_model()

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

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

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

    transit_callback_index = routing.RegisterTransitCallback(time_callback)

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

    # Add Time Windows constraint.
    time = 'Time'
    routing.AddDimension(
        transit_callback_index,
        9999999,  # maximum waiting time
        9999999,  # maximum travel time per vehicle
        False,  # Don't force start cumul to zero.
        time)
    time_dimension = routing.GetDimensionOrDie(time)

    # Add time window constraints for each location except depot.
    for location_idx, time_window in enumerate(data['time_windows']):
        if location_idx == data['depot']:
            continue
        index = manager.NodeToIndex(location_idx)
        time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
        
    # Add time window constraints for each vehicle start node.
    depot_idx = data['depot']
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        time_dimension.CumulVar(index).SetRange(
            data['time_windows'][depot_idx][0],
            data['time_windows'][depot_idx][1])

    # Instantiate route start and end times to produce feasible times.
    for i in range(data['num_vehicles']):
        routing.AddVariableMinimizedByFinalizer(
            time_dimension.CumulVar(routing.Start(i)))
        routing.AddVariableMinimizedByFinalizer(
            time_dimension.CumulVar(routing.End(i)))

    # Allow to drop nodes.
    penalty = 100000000000
    for node in range(1, len(data['time_matrix'])):
        routing.AddDisjunction([manager.NodeToIndex(node)], penalty)

    # Setting first solution heuristic.
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
    search_parameters.time_limit.seconds = 10

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

    # Print solution on console.
    if solution:
        print_solution(data, manager, routing, solution)
    else:
        print("\nNo solutions found")


if __name__ == '__main__':
    main()

Answer 1

你在添加析取的方向上做得很好，只是在最后错过了这行

    # 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 # to get some logs
-    search_parameters.time_limit.seconds = 10
+    search_parameters.time_limit.seconds = 1 # 1s is large enough ;)

即你忘记启用 Guided Local Search (GLS)，所以你最终只有第一个解决方案（节点 1 被删除）而你没有运行 GLS，所以求解器没有机会将它带回解决方案...

Google OR-Tools VRP - 节点被不必要地删除

Google OR-Tools VRP - Nodes getting dropped unnecessarily

python

optimization

or-tools

vehicle-routing