车辆路径问题python代码

车辆路径问题（Vehicle Routing Problem，VRP）指的是在配送过程中，如何合理地规划车辆的路径，以达到最大化效益、最小化成本的目的。解决VRP问题是优化配送业务的关键。在Python中，我们可以使用OR-Tools包来解决VRP问题。

首先，我们需要定义车辆的起始位置、终止位置、装载容量等信息，以及需要配送的点的位置、需要配送的数量等信息。然后，我们可以使用OR-Tools中的vrp_solver模块来解决VRP问题。它可以通过定义问题的约束条件和目标函数，自动求解最优解。

具体代码如下：

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

# 定义车辆信息
num_vehicles = 2
vehicle_capacity = [4, 5] # 每辆车的装载容量
starting_nodes = [0, 1] # 每辆车的起始点
ending_nodes = [6, 6] # 每辆车的终止点

# 定义需配送点信息
locations = [(4, 4), (2, 0), (8, 0), (0, 1), (1, 2), (5, 5), (7, 8)] # 需配送点的坐标
demands = [1, 1, 2, 1, 2, 4, 2] # 需配送点的需求量

def create_data_model():
    """创建数据模型"""
    data = {}
    data['num_vehicles'] = num_vehicles
    data['vehicle_capacity'] = vehicle_capacity
    data['starting_nodes'] = starting_nodes
    data['ending_nodes'] = ending_nodes
    data['depot'] = 0 # 公司的起始位置
    data['locations'] = locations
    data['demands'] = demands
    return data
    
def print_solution(manager, routing, solution):
    """输出解决方案"""
    max_route_distance = 0
    for vehicle_id in range(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)
            plan_output += ' {} -> '.format(node_index)
            previous_index = index
            index = solution.Value(routing.NextVar(index))
            route_distance += routing.GetArcCostForVehicle(previous_index, index, vehicle_id)
        plan_output += '{}\n'.format(manager.IndexToNode(index))
        plan_output += 'Distance of the route: {}m\n'.format(route_distance)
        print(plan_output)
        max_route_distance = max(route_distance, max_route_distance)
    print('Maximum Distance of the route: {}m'.format(max_route_distance))
        
def main():
    data = create_data_model()
    manager = pywrapcp.RoutingIndexManager(len(data['locations']), data['num_vehicles'], data['starting_nodes'], data['ending_nodes'])
    routing = pywrapcp.RoutingModel(manager)
    transit_callback_index = routing.RegisterTransitCallback(
        lambda from_index, to_index: 
            manhattan_distance(
                data['locations'][manager.IndexToNode(from_index)], 
                data['locations'][manager.IndexToNode(to_index)]
            )
    )
    routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
    demand_callback_index = routing.RegisterUnaryTransitCallback(
        lambda index: data['demands'][manager.IndexToNode(index)]
    )
    routing.AddDimension(
        demand_callback_index,
        0, 
        sum(data['demands']), 
        True, 
        'Demand'
    )
    for vehicle_id in range(data['num_vehicles']):
        routing.AddDimension(
            transit_callback_index,
            0, # no minimum transit time (driver just needs to finish within working time)
            300, # 5 hours (300 minutes) in seconds
            False, # add slack to vertex wait time
            'Time'
        )
        routing.SetDepotVehicle(data['depot'], vehicle_id)
    search_parameters = pywrapcp.DefaultRoutingSearchParameters()
    search_parameters.first_solution_strategy = (
        routing_enums_pb2.FirstSolutionStrategy.PARALLEL_CHEAPEST_INSERTION
    )
    solution = routing.SolveWithParameters(search_parameters)
    if solution:
        print_solution(manager, routing, solution)

def manhattan_distance(position_1, position_2):
    """曼哈顿距离"""
    return (
        abs(position_1[0] - position_2[0]) +
        abs(position_1[1] - position_2[1])
    )

if __name__ == '__main__':
    main()

以上是一个简单的VRP问题求解的Python代码实现。在代码中，我们定义了一些车辆和需配送点的信息，并调用OR-Tools中的vrp_solver模块求解该问题。输出代码解决方案后，可以看到每个车辆的行驶路径和该路径的距离，以及最远的路径。