如何利用车辆路径问题中的每辆车

如何解决如何利用车辆路径问题中的每辆车

我正在尝试使用 ortools 解决无能力的取货和送货问题。每辆车的容量为 1，如果交付/作业的数量 > 车辆数量，必须至少使用一次。当然，必须有一个解决方案，但我无法找到它。我已经尝试了 here 描述的方法，如下所示：

# Set Minimum Number of nodes
  count_dimension_name = 'count'
  # assume some variable num_nodes holds the total number of nodes
  routing.AddConstantDimension(
      1,# increment by one every time
      len(data['demands']),# number of nodes incl depot
      True,# set count to zero
      count_dimension_name)
  count_dimension = routing.GetDimensionorDie(count_dimension_name)
  for veh in range(0,data['num_vehicles']):
      index_end = routing.End(veh)
      count_dimension.SetCumulVarSoftLowerBound(index_end,2,100000)

但是，对于可重现的示例（下面的完整代码），总是有一种车辆根本没有被使用（其他示例则有更多车辆）。如何强制使用每辆车并仍然能够找到至少一个可行的解决方案？也许通过改变搜索方法？

可重现的代码：

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'] = [[0,641,331,360,3,920,342,1],[641,505,663,643,504,639,1556,638,397,644,641],[331,623,334,1,329,1188,110,333,111,1187,330],[360,358,1007,359,575,574,1006,361],[3,335,6,917,5,345,4],330,[2,923,340,922,2],[920,1242,921],3],[342,341],920],[1,361,4,921,341,0]]
    data['pickups_deliveries'] = [[ 1,8],[ 2,9],[ 3,10],[ 4,11],[ 5,12],[ 6,13],[ 7,14]]
    data['num_vehicles'] = 4
    data['depot'] = 0
    data['vehicle_capacities'] = [1,1]
    data['demands'] = [0,-1,-1]

    return data

def print_solution(data,manager,routing,assignment):
    """Prints assignment on console."""
    total_distance = 0
    total_load = 0
    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} Load({1}) -> '.format(node_index,route_load)
            prevIoUs_index = index
            index = assignment.Value(routing.Nextvar(index))
            route_distance += routing.GetArcCostForVehicle(
                prevIoUs_index,index,vehicle_id)
        plan_output += ' {0} Load({1})\n'.format(manager.IndexToNode(index),route_load)
        plan_output += 'distance of the route: {}m\n'.format(route_distance)
        plan_output += 'Load of the route: {}\n'.format(route_load)
        print(plan_output)
        total_distance += route_distance
        total_load += route_load
    print('Total distance of all routes: {}m'.format(total_distance))
    print('Total load of all routes: {}'.format(total_load))
   
def main():    
  """Entry point of the program."""
  
  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)
  
  # Define cost of each arc.
  def distance_callback(from_index,to_index):
      """Returns the manhattan 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)
  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,# null capacity slack
      data['vehicle_capacities'],# vehicle maximum capacities
      True,# start cumul to zero
      'Capacity')
  
  # Add distance constraint.
  dimension_name = 'distance'
  routing.AddDimension(
      transit_callback_index,# no slack
      1000000,# vehicle maximum travel distance
      True,# start cumul to zero
      dimension_name)
  distance_dimension = routing.GetDimensionorDie(dimension_name)
  distance_dimension.SetGlobalSpanCostCoefficient(100)
  
  # Set Minimum Number of nodes
  count_dimension_name = 'count'
  # assume some variable num_nodes holds the total number of nodes
  routing.AddConstantDimension(
      1,100000)
   
  # Define Transportation Requests.
  for request in data['pickups_deliveries']:
      pickup_index = manager.NodetoIndex(request[0])
      delivery_index = manager.NodetoIndex(request[1])
      routing.AddPickupAndDelivery (pickup_index,delivery_index)
      routing.solver().Add(routing.VehicleVar(pickup_index) == routing.VehicleVar(delivery_index))
      routing.solver().Add(distance_dimension.CumulVar(pickup_index) <= distance_dimension.CumulVar(delivery_index))
  
  # Define Search Approach
  search_parameters = pywrapcp.DefaultRoutingSearchParameters()
  search_parameters.first_solution_strategy = (routing_enums_pb2.FirstSolutionStrategy.AUTOMATIC)
  search_parameters.local_search_Metaheuristic = (routing_enums_pb2.LocalSearchMetaheuristic.AUTOMATIC)
  search_parameters.time_limit.FromSeconds(10)
  
  
  # Solve the problem.
  assignment = routing.solveWithParameters(search_parameters)
  
  # Print solution on console.
  if assignment:
      print_solution(data,assignment)


if __name__ == '__main__':
    main()