以下是一个解决“不访问每个节点的CVRP”的示例代码:
import numpy as np
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp
def solve_cvrp_without_visiting_all_nodes(num_vehicles, num_nodes, vehicle_capacities, demands, distances):
# 创建求解器
routing = pywrapcp.RoutingModel(num_nodes, num_vehicles, 0)
# 设置车辆容量限制
def vehicle_capacity_callback(from_index):
# 获取节点索引
node_index = routing.IndexToNode(from_index)
return vehicle_capacities[node_index]
capacity_callback_index = routing.RegisterUnaryTransitCallback(vehicle_capacity_callback)
routing.AddDimensionWithVehicleCapacity(capacity_callback_index, 0, vehicle_capacities, True, "Capacity")
# 设置节点需求
def demand_callback(from_index):
# 获取节点索引
node_index = routing.IndexToNode(from_index)
return demands[node_index]
demand_callback_index = routing.RegisterUnaryTransitCallback(demand_callback)
routing.AddDimensionWithVehicleCapacity(demand_callback_index, 0, demands, True, "Demand")
# 设置距离回调函数
def distance_callback(from_index, to_index):
# 获取节点索引
from_node = routing.IndexToNode(from_index)
to_node = routing.IndexToNode(to_index)
return distances[from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(distance_callback)
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
# 设置每个车辆的起始节点
for vehicle_id in range(num_vehicles):
start_node = 0 # 起始节点为0
routing.SetArcCostEvaluatorOfVehicle(transit_callback_index, vehicle_id, distance_callback)
routing.AddDisjunction([start_node], 0) # 不访问其他节点
# 设置搜索参数
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC
# 解决问题
solution = routing.SolveWithParameters(search_parameters)
# 输出解决方案
if solution:
total_distance = 0
total_demand = 0
for vehicle_id in range(num_vehicles):
index = routing.Start(vehicle_id)
plan_output = f"Vehicle {vehicle_id}:\n"
route_distance = 0
route_demand = 0
while not routing.IsEnd(index):
node_index = routing.IndexToNode(index)
next_node_index = routing.IndexToNode(solution.Value(routing.NextVar(index)))
route_distance += routing.GetArcCostForVehicle(node_index, next_node_index, vehicle_id)
route_demand += demands[node_index]
plan_output += f" -> {node_index}"
index = solution.Value(routing.NextVar(index))
plan_output += f" -> {routing.IndexToNode(index)}\n"
plan_output += f"Distance of the route: {route_distance}m\n"
plan_output += f"Demand of the route: {route_demand}\n"
print(plan_output)
total_distance += route_distance
total_demand += route_demand
print(f"\nTotal distance of all routes: {total_distance}m")
print(f"Total demand of all routes: {total_demand}")
else:
print("No solution found!")
# 示例数据
num_vehicles = 2
num_nodes = 6
vehicle_capacities = [10, 10]
demands = [0, 1, 2, 3, 4, 5]
distances = [[0, 1, 2, 3, 4, 5],
[1, 0, 1, 2, 3, 4],
[2, 1, 0, 1, 2, 3],
[3, 2, 1, 0, 1, 2],
[4, 3, 2, 1, 0, 1],
[5, 4, 3, 2, 1, 0]]
# 解决问题
solve_cvrp_without_visiting_all_nodes(num_vehicles, num_nodes, vehicle_capacities, demands, distances)
请注意,这个示例使用Google OR-Tools库来解决CVRP问题。在这个示例中,我们通过设置