定位坐标

[(456, 320), # location 0
(228, 0), # location 1
(912, 0), # location 2
(0, 80), # location 3
(114, 80), # location 4
(570, 160), # location 5
(798, 160), # location 6
(342, 240), # location 7
(684, 240), # location 8
(570, 400), # location 9
(912, 400), # location 10
(114, 480), # location 11
(228, 480), # location 12
(342, 560), # location 13
(684, 560), # location 14
(0, 640), # location 15
(798, 640)] # location 16

在这里我们根据上面的坐标算出不同位置之间的距离，距离函数使用曼哈顿距离:|x1 - x2| + |y1 - y2|.

好，基本问题都解释清楚了，我们还是直接看代码吧：

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

# 定义这个VRP问题的数据，使用字典结构存储
def create_data_model():
"""Creates the data for the example."""
data = {}
# Array of distances between locations.
_distances =
[
[0, 548, 776, 696, 582, 274, 502, 194, 308, 194, 536, 502, 388, 354, 468, 776, 662],
[548, 0, 684, 308, 194, 502, 730, 354, 696, 742, 1084, 594, 480, 674, 1016, 868, 1210],
[776, 684, 0, 992, 878, 502, 274, 810, 468, 742, 400, 1278, 1164, 1130, 788, 1552, 754],
[696, 308, 992, 0, 114, 650, 878, 502, 844, 890, 1232, 514, 628, 822, 1164, 560, 1358],
[582, 194, 878, 114, 0, 536, 764, 388, 730, 776, 1118, 400, 514, 708, 1050, 674, 1244],
[274, 502, 502, 650, 536, 0, 228, 308, 194, 240, 582, 776, 662, 628, 514, 1050, 708],
[502, 730, 274, 878, 764, 228, 0, 536, 194, 468, 354, 1004, 890, 856, 514, 1278, 480],
[194, 354, 810, 502, 388, 308, 536, 0, 342, 388, 730, 468, 354, 320, 662, 742, 856],
[308, 696, 468, 844, 730, 194, 194, 342, 0, 274, 388, 810, 696, 662, 320, 1084, 514],
[194, 742, 742, 890, 776, 240, 468, 388, 274, 0, 342, 536, 422, 388, 274, 810, 468],
[536, 1084, 400, 1232, 1118, 582, 354, 730, 388, 342, 0, 878, 764, 730, 388, 1152, 354],
[502, 594, 1278, 514, 400, 776, 1004, 468, 810, 536, 878, 0, 114, 308, 650, 274, 844],
[388, 480, 1164, 628, 514, 662, 890, 354, 696, 422, 764, 114, 0, 194, 536, 388, 730],
[354, 674, 1130, 822, 708, 628, 856, 320, 662, 388, 730, 308, 194, 0, 342, 422, 536],
[468, 1016, 788, 1164, 1050, 514, 514, 662, 320, 274, 388, 650, 536, 342, 0, 764, 194],
[776, 868, 1552, 560, 674, 1050, 1278, 742, 1084, 810, 1152, 274, 388, 422, 764, 0, 798],
[662, 1210, 754, 1358, 1244, 708, 480, 856, 514, 468, 354, 844, 730, 536, 194, 798, 0]
]
data["distances"] = _distances
data["num_locations"] = len(_distances) # 有几个节点
data["num_vehicles"] = 4 # 有几辆车
data["depot"] = 0 # 仓库索引，我们假设所有的车辆都从同一地点出发，也就是车场。
# 或者，你可以允许车辆在任何位置启动和结束。
return data

# 计算距离的回调函数，和之前的routing问题一样的
def create_distance_callback(data):
"""Creates callback to return distance between points."""
distances = data["distances"]

def distance_callback(from_node, to_node):
"""Returns the manhattan distance between the two nodes"""
return distances[from_node][to_node]

return distance_callback

def add_distance_dimension(routing, distance_callback):
"""Add Global Span constraint"""
distance = Distance
maximum_distance = 3000 # 每辆车能形式的最大距离
routing.AddDimension(
distance_callback,
0, # null slack
maximum_distance,
True, # 从累积到零，意思应该和「走了这么久还剩多少汽油」差不多吧
distance)
distance_dimension = routing.GetDimensionOrDie(distance)
# Try to minimize the max distance among vehicles.
# 尽量减少车辆之间的最大距离。
distance_dimension.SetGlobalSpanCostCoefficient(100)

# 列印每辆车的路线(访问的位置)，以及路线的距离。
# 请注意，这些距离包括从仓库到路线中第一个位置的距离以及从最后一个位置返回到仓库的距离。
# IndexToNode, NextVar 函数和前面的tsp问题是相同的意思
def print_solution(data, routing, assignment):
"""Print routes on console."""
total_distance = 0
for vehicle_id in range(data["num_vehicles"]):
index = routing.Start(vehicle_id)
plan_output = Route for vehicle {}:
.format(vehicle_id)
route_dist = 0
while not routing.IsEnd(index):
node_index = routing.IndexToNode(index)
next_node_index = routing.IndexToNode(
assignment.Value(routing.NextVar(index)))
route_dist += routing.GetArcCostForVehicle(node_index, next_node_index, vehicle_id)
plan_output += {0} ->.format(node_index)
index = assignment.Value(routing.NextVar(index))
plan_output += {}
.format(routing.IndexToNode(index))
plan_output += Distance of route: {}m
.format(route_dist)
print(plan_output)
total_distance += route_dist
print(Total distance of all routes: {}m.format(total_distance))

# 主函数
def main():
# 创建数据集
data = create_data_model()

# Create Routing Model
# 创建路由模型
routing = pywrapcp.RoutingModel(
data["num_locations"],
data["num_vehicles"],
data["depot"])

# 提供距离回调，以便解决程序可以计算位置之间的距离。
distance_callback = create_distance_callback(data)
routing.SetArcCostEvaluatorOfAllVehicles(distance_callback)

# 添加距离维度
add_distance_dimension(routing, distance_callback)

# Setting first solution heuristic (cheapest addition).
# 必须指定启发式方法来找到第一个解决方案
search_parameters = pywrapcp.RoutingModel.DefaultSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC) # pylint: disable=no-member

# 求解问题
assignment = routing.SolveWithParameters(search_parameters)
if assignment:
print_solution(data, routing, assignment)

if __name__ == __main__:
main()

# 结果
Route for vehicle 0:
0 -> 8 -> 6 -> 2 -> 5 -> 0
Distance of route: 1552m

Route for vehicle 1:
0 -> 7 -> 1 -> 4 -> 3 -> 0
Distance of route: 1552m

Route for vehicle 2:
0 -> 9 -> 10 -> 16 -> 14 -> 0
Distance of route: 1552m

Route for vehicle 3:
0 -> 12 -> 11 -> 15 -> 13 -> 0
Distance of route: 1552m

Total distance of all routes: 6208m

注意函数添加距离维度(Add a distance dimension)，

要解决这个VRP，需要创建一个距离维度，它计算每辆车沿其路线行驶的累计距离。然后，将成本设置为每条路线总距离的最大值。关于距离信息可以参考vrp_dimension_details.

若要添加距离维度，请使用求解器的AddDimension方法。下面的代码为距离创建一个维度，并设置累计距离成本。

def add_distance_dimension(routing, distance_callback):
"""Add Global Span constraint"""
distance = Distance
maximum_distance = 3000 # 每辆车能形式的最大距离
routing.AddDimension(
distance_callback,
0, # null slack
maximum_distance,
True, # 从累积到零，意思应该和「走了这么久还剩多少汽油」差不多吧
distance)
distance_dimension = routing.GetDimensionOrDie(distance)
# Try to minimize the max distance among vehicles.
# 尽量减少车辆之间的最大距离。
distance_dimension.SetGlobalSpanCostCoefficient(100)

下面是求解的结果：

看起来也不难呢，但是我想说的是，如果有1000个节点会怎样？欢迎大家讨论讨论。

参考

• allow-vehicles-to-start-and-end-any-location
• google_ortools_guide

大家看完记得关注点赞.

master苏.

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