这个 output 只是因为启发式而奇怪吗？

Question

I'm currently programming a tool to find a path with a set amount of stops. For that I'm using this answer. But when trying the code with the below data, a very strange path is generated:

As easily seen in the image, this is by far the most optimal path, even between just the visible points. And so I was wondering whether this is just a problem of heuristics, or if there is anything wrong with my code (Note: The path starts and ends at a given point, in the image that is the leftmost point):

from __future__ import print_function
from typing import List
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
import gpxpy
import gpxpy.gpx
from gpxpy.gpx import GPXWaypoint

START_LOCATION = GPXWaypoint(38.892743662408584, -77.03258470988436, name="Start")

def createOutputGpxRouteFile(stations:List):
    output = gpxpy.gpx.GPX()
    gpx_track = gpxpy.gpx.GPXTrack()
    output.tracks.append(gpx_track)
    gpx_segment = gpxpy.gpx.GPXTrackSegment()
    gpx_track.segments.append(gpx_segment)
    for station in stations:
        gpx_segment.points.append(gpxpy.gpx.GPXTrackPoint(latitude=station.latitude, longitude=station.longitude, name=station.name))
    print('Created GPX:', output.to_xml())

def readGpxData():
    """Reads the gpx data from a file and returns a list of the coordinates"""
    # Original code commented so it is reproducible
    #with open("Waypoints.gpx", "r") as gpx_file:
    #    gpx = gpxpy.parse(gpx_file)
    #gpx.waypoints.insert(0, START_LOCATION)
    waypoints = [
        GPXWaypoint(38.91965, -76.99145, name='GC7J4FJ', description='Cache Store by Shalacknar (2/1,5)'),
        GPXWaypoint(38.90755, -76.989483,  name='GC7CYPZ', description='West Virginia Ave.: The 50 States Project by UrbanAdventureSquad (1,5/1,5)'),
        GPXWaypoint(38.9242, -77.008083,  name='GC7R9Z9', description='Stronghold neighborhood by mellow_cello (2/1,5)'),
        GPXWaypoint(38.89614, -76.97886,  name='GC9XVTY', description='Take Something, Leave Something by DCSunshine11 (1/1)'),
        GPXWaypoint(38.91295, -77.000967, name='GC7FC8C', description='DC Hidden Murals #30: 28 Blocks by exmachina (2/1)'),
        GPXWaypoint(38.921817, -77.011167,  name='GC7JHBD', description='Catlandia by mellow_cello (1,5/1,5)'),
        GPXWaypoint(38.9037, -76.992583, name='GC78CZD', description='Florida Ave.: The 50 States Project by UrbanAdventureSquad (1,5/1,5)'),
        GPXWaypoint(38.9, -76.988753,  name='GC3PBQ2', description='DC Hidden Murals #17: Dusk of H Street by exmachina (2/1)'),
        GPXWaypoint(38.901917, -76.99155, name='GC9AYCF', description='A DC Saint? by poli1136 (1/1,5)'),
        GPXWaypoint(38.916983, -77.007967,  name='GC7R8YH', description='Rhode Island Ave.: The 50 States Project by UrbanAdventureSquad (2/1,5)'),
        GPXWaypoint(38.895096, -76.985681,  name='GC9GBFY', description='Triangles and Tribulations by urbnX (1,5/1,5)'),
        GPXWaypoint(38.917633, -77.010833,  name='GC7KD9P', description='Bloomingdale: Crispus Attucks Park by mellow_cello (2/1,5)'),
        GPXWaypoint(38.934617, -77.028583, name='GC4KRFJ', description='I thought he made elevators by zdonb & lilbru (1,5/1,5)'),
        GPXWaypoint(38.891967, -76.985233, name='GC9WRM2', description='Meet me at the crossroads by urbnX (1,5/1,5)'),
        GPXWaypoint(38.88075, -76.97475, name='GC6RP1W', description="Doug's Cache by puglisimclare (1,5/1,5)"),
        GPXWaypoint(38.907475, -77.003103,  name='GC8AT5F', description='SideTracked - NoMa-Gallaudet U Station by mellow_cello (2/1,5)'),
        GPXWaypoint(38.896342, -76.992444,  name='GC7CYPA', description='Maryland Ave.: The 50 States Project by UrbanAdventureSquad (2,5/1,5)'),
        GPXWaypoint(38.89215, -76.988133, name='GC9EKPE', description='17 years underground by urbnX (2/1,5)'),
        GPXWaypoint(38.93015, -77.028083,  name='GC34NZ3', description='DC Hidden Murals #2: Wonderland by exmachina (2/1)'),
        GPXWaypoint(38.883071, -76.979078,  name='GC98F36', description='What’s Next? by alexcran421 (2/1,5)'),
        GPXWaypoint(38.917767, -77.0159, name='GC43T1F', description='DC Hidden Murals #22: How We Live by exmachina (2/1)'),
        GPXWaypoint(38.880617, -76.979417,  name='GC23GKB', description='SSB - Congressional Cemetery by Star-Spangled Banner (1,5/1,5)'),
        GPXWaypoint(38.879183, -76.979733, name='GC6RNVG', description="Bonaparte's Cache by puglisimclare (1,5/1,5)"),
        GPXWaypoint(38.905583, -77.007567,  name='GC89MWE', description='DC Hidden Murals #31: AVA NoMa by exmachina (1,5/1,5)'),
        GPXWaypoint(38.89367, -76.99609,  name='GC9XBFP', description='Hais Market by NatsGeo6 (1,5/1,5)'),
        GPXWaypoint(38.889717, -76.996217,  name='GC9RQEP', description='16th and 44th by DCSunshine11 (1,5/1,5)'),
        GPXWaypoint(38.918983, -77.028,  name='GC37CJT', description='DC Hidden Murals #7: Scout by exmachina (2/1)'),
        GPXWaypoint(38.924896, -77.034439,  name='GC8ZXCP', description='Olive’s pipe by CharlesGeo8, Olive (1,5/1)'),
        GPXWaypoint(38.917467, -77.026933,  name='GC3VVZF', description='DC Hidden Murals #18: Bohemian Caverns by exmachina (2/1,5)'),   
         ]
    waypoints.insert(0, START_LOCATION)
    return waypoints

def create2dDistanceMatrix(locations:List[GPXWaypoint]):
    """Creates a distance matrix for the locations"""
    distance_matrix = []
    for i, location in enumerate(locations):
        distance_matrix.append([])
        for j, location_2 in enumerate(locations):
            distance_matrix[i].append(location.distance_2d(location_2))
    return distance_matrix

def create_data_model():
    """Stores the data for the problem."""
    data = {}
    data['num_vehicles'] = 1
    data['depot'] = 0
    data['vehicle_capacities'] = [5]
    print("Using 2d distances.")
    locations = [point for point in readGpxData() if point.name[:2] == "GC"]
    data["distance_matrix"] = create2dDistanceMatrix(locations)
    # Convert all distances to integers
    data["distance_matrix"] = [[int(i) for i in row] for row in data["distance_matrix"]]
    data['demands'] = [1]*len(data["distance_matrix"])
    return data


def print_solution(data, manager, routing, assignment):
    """Prints assignment on console."""
    total_distance = 0
    total_load = 0
    locations = readGpxData()
    stations = []
    for vehicle_id in range(data['num_vehicles']):
        index = routing.Start(vehicle_id)
        plan_output = 'Route for vehicle {}:\n'.format(vehicle_id)
        route_distance = 0
        route_load = 0
        while not routing.IsEnd(index):
            node_index = manager.IndexToNode(index)
            route_load += data['demands'][node_index]
            plan_output += ' {0} -> '.format(locations[node_index].name)
            stations.append(locations[node_index])
            previous_index = index
            index = assignment.Value(routing.NextVar(index))
            route_distance += routing.GetArcCostForVehicle(
                previous_index, index, vehicle_id)
        plan_output += ' {0} \n'.format(readGpxData()[data["depot"]].name)
        stations.append(readGpxData()[data["depot"]])
        plan_output += 'Distance of the route: {}m\n'.format(route_distance)
        print(plan_output)
        total_distance += route_distance
        total_load += route_load
    print('Total distance of all routes: {}m'.format(total_distance))
    createOutputGpxRouteFile(stations)

def main():
    """Entry point of the program."""
    # 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)

    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)

    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')

    penalty = 999999999
    for node in range(1, len(data['distance_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.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    search_parameters.time_limit.FromSeconds(1)


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

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


if __name__ == '__main__':
    main()

Answer 1

In general heuristics can produce sub-optimal solutions (in your case tours), which might look "strange" when visualized, but which are perfectly valid.

However, you should check whether your visualization is representing the solution correctly, since your input data does not contain node coordiates but only the distances between them so that the positions are only relative to each other.

Your visualization should at least contain the node number / node coordinates of each node and the distance of each edge to aid you in inspecting your solution.

Answer 2

You should enable the guided local search please add:

    search_parameters.local_search_metaheuristic = (
        routing_enums_pb2.LocalSearchMetaheuristic.GUIDED_LOCAL_SEARCH)
    search_parameters.time_limit.FromSeconds(1)
    # search_parameters.log_search = True # enable solution log

Answer 3

This could be caused by the data. Your example does not provide enough information.

Please replace the code that queries OpenRouteService , also please provide a fixed vehicule capacity, and not rely on input() .