# 給定要訪問的地點的旅行商問題

here中有一個很好的例子，說明瞭如何解決旅行商的問題：

``````"""Simple travelling salesman problem between cities."""

from __future__ import print_function
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, 2451, 713, 1018, 1631, 1374, 2408, 213, 2571, 875, 1420, 2145, 1972],
[2451, 0, 1745, 1524, 831, 1240, 959, 2596, 403, 1589, 1374, 357, 579],
[713, 1745, 0, 355, 920, 803, 1737, 851, 1858, 262, 940, 1453, 1260],
[1018, 1524, 355, 0, 700, 862, 1395, 1123, 1584, 466, 1056, 1280, 987],
[1631, 831, 920, 700, 0, 663, 1021, 1769, 949, 796, 879, 586, 371],
[1374, 1240, 803, 862, 663, 0, 1681, 1551, 1765, 547, 225, 887, 999],
[2408, 959, 1737, 1395, 1021, 1681, 0, 2493, 678, 1724, 1891, 1114, 701],
[213, 2596, 851, 1123, 1769, 1551, 2493, 0, 2699, 1038, 1605, 2300, 2099],
[2571, 403, 1858, 1584, 949, 1765, 678, 2699, 0, 1744, 1645, 653, 600],
[875, 1589, 262, 466, 796, 547, 1724, 1038, 1744, 0, 679, 1272, 1162],
[1420, 1374, 940, 1056, 879, 225, 1891, 1605, 1645, 679, 0, 1017, 1200],
[2145, 357, 1453, 1280, 586, 887, 1114, 2300, 653, 1272, 1017, 0, 504],
[1972, 579, 1260, 987, 371, 999, 701, 2099, 600, 1162, 1200, 504, 0],
]  # yapf: disable
data['num_vehicles'] = 1
data['depot'] = 0
return data

def print_solution(manager, routing, assignment):
"""Prints assignment on console."""
print('Objective: {} miles'.format(assignment.ObjectiveValue()))
index = routing.Start(0)
plan_output = 'Route for vehicle 0:\n'
route_distance = 0
while not routing.IsEnd(index):
plan_output += ' {} ->'.format(manager.IndexToNode(index))
previous_index = index
index = assignment.Value(routing.NextVar(index))
route_distance += routing.GetArcCostForVehicle(previous_index, index, 0)
plan_output += ' {}\n'.format(manager.IndexToNode(index))
print(plan_output)
plan_output += 'Route distance: {}miles\n'.format(route_distance)

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)

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

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

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

if __name__ == '__main__':
main()
``````

``````Objective: 7293 miles
Route for vehicle 0:
0 -> 7 -> 2 -> 3 -> 4 -> 12 -> 6 -> 8 -> 1 -> 11 -> 10 -> 5 -> 9 -> 0
``````

``````    manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),
data['num_vehicles'], data['depot'])
``````

``````    manager = pywrapcp.RoutingIndexManager(5,
data['num_vehicles'], data['depot'])
``````

Thanks to @Laurent Perron for their answer - I've tried modifying the code as follows, and it appears to work fine:

``````from __future__ import print_function
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, 2451, 713, 1018, 1631, 1374, 2408, 213, 2571, 875, 1420, 2145, 1972],
[2451, 0, 1745, 1524, 831, 1240, 959, 2596, 403, 1589, 1374, 357, 579],
[713, 1745, 0, 355, 920, 803, 1737, 851, 1858, 262, 940, 1453, 1260],
[1018, 1524, 355, 0, 700, 862, 1395, 1123, 1584, 466, 1056, 1280, 987],
[1631, 831, 920, 700, 0, 663, 1021, 1769, 949, 796, 879, 586, 371],
[1374, 1240, 803, 862, 663, 0, 1681, 1551, 1765, 547, 225, 887, 999],
[2408, 959, 1737, 1395, 1021, 1681, 0, 2493, 678, 1724, 1891, 1114, 701],
[213, 2596, 851, 1123, 1769, 1551, 2493, 0, 2699, 1038, 1605, 2300, 2099],
[2571, 403, 1858, 1584, 949, 1765, 678, 2699, 0, 1744, 1645, 653, 600],
[875, 1589, 262, 466, 796, 547, 1724, 1038, 1744, 0, 679, 1272, 1162],
[1420, 1374, 940, 1056, 879, 225, 1891, 1605, 1645, 679, 0, 1017, 1200],
[2145, 357, 1453, 1280, 586, 887, 1114, 2300, 653, 1272, 1017, 0, 504],
[1972, 579, 1260, 987, 371, 999, 701, 2099, 600, 1162, 1200, 504, 0],
]  # yapf: disable
data['num_vehicles'] = 1
data['depot'] = 0
data['vehicle_capacities'] = [5]
data['demands'] = [1]*13
return data

def print_solution(data, manager, routing, assignment):
"""Prints assignment on console."""
total_distance = 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
while not routing.IsEnd(index):
node_index = manager.IndexToNode(index)
previous_index = index
index = assignment.Value(routing.NextVar(index))
route_distance += routing.GetArcCostForVehicle(
previous_index, index, vehicle_id)
plan_output += 'Distance of the route: {}m\n'.format(route_distance)
print(plan_output)
total_distance += route_distance
print('Total distance of all routes: {}m'.format(total_distance))

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)
demand_callback_index,
0,  # null capacity slack
data['vehicle_capacities'],  # vehicle maximum capacities
True,  # start cumul to zero
'Capacity')

penalty = 1000
for node in range(1, len(data['distance_matrix'])):

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

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

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

if __name__ == '__main__':
main()
$$```$$
``````