deap库里面如何用NSGA2算法请用VRP问题示例说明目标函数是最小总成本和最大总客户满意度每辆车成本包括固定成本和行驶成本客户满意度是如果车辆实际到达实际小于客户期望配送时间则满意度为05否则满意度为-1客户期望配送时间随机生成有车辆工作时间约束和载重约束车辆足够多没有数量限制将每辆车的路径进行编码起点和终点都是仓库给出程序要求输出最终帕累托前沿和其中的一个方案路径

首先，需要定义问题的变量、目标函数和约束条件。

变量：

• 车辆路径：每辆车的配送路径，从起点出发，到达多个客户点，最后回到起点。

目标函数：

• 最小总成本：包括每辆车的固定成本和行驶成本。
• 最大总客户满意度：表示所有客户的满意度之和。

约束条件：

• 车辆工作时间约束：每辆车的配送时间不能超过工作时间。
• 载重约束：每辆车的总载重不能超过容量限制。

然后，可以使用deap库中的NSGA2算法，通过编写适应度函数和定义变量、目标函数和约束条件来求解VRP问题。

下面是示例代码：

import random
from deap import base, creator, tools, algorithms

# 定义问题的变量、目标函数和约束条件

# 变量
# 车辆路径编码：从起点出发，到达多个客户点，最后回到起点
# 例如：[0, 2, 4, 1, 0] 表示车辆依次从起点出发，到达客户点2、4、1，最后回到起点
toolbox.register("indices", random.sample, range(1, len(customers)), len(customers)-1)
toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.indices)

# 目标函数
# 最小总成本：包括每辆车的固定成本和行驶成本
# 最大总客户满意度：表示所有客户的满意度之和
def evalVRP(individual):
    # 计算每辆车的路径
    routes = []
    start = 0
    for gene in individual:
        route = [start, gene]
        capacity = vehicles[0]['capacity']
        duration = vehicles[0]['duration']
        distance = 0
        for customer in gene:
            if capacity < customers[customer]['demand']:
                # 载重约束
                distance += distMatrix[route[-1]][start]
                route.append(start)
                route.append(customer)
                distance += distMatrix[start][customer]
                capacity = vehicles[0]['capacity'] - customers[customer]['demand']
                duration = vehicles[0]['duration']
            else:
                # 载重未超过限制
                distance += distMatrix[route[-1]][customer]
                route.append(customer)
                capacity -= customers[customer]['demand']
                duration += customers[customer]['duration']
                if duration > vehicles[0]['duration']:
                    # 时间约束
                    distance += distMatrix[route[-1]][start]
                    route.append(start)
                    capacity = vehicles[0]['capacity']
                    duration = vehicles[0]['duration']
        distance += distMatrix[route[-1]][start]
        route.append(start)
        routes.append(route)
    # 计算总成本和总客户满意度
    totalCost = 0
    totalSatisfaction = 0
    for route in routes:
        # 计算固定成本和行驶成本
        fixedCost = vehicles[0]['fixedCost']
        distance = 0
        for i in range(len(route)-1):
            distance += distMatrix[route[i]][route[i+1]]
        variableCost = vehicles[0]['distanceCost'] * distance
        totalCost += fixedCost + variableCost
        # 计算客户满意度
        for i in range(1, len(route)-1):
            if customers[route[i]]['deadline'] >= duration:
                totalSatisfaction += 0.5
            else:
                totalSatisfaction -= 1
    return totalCost, totalSatisfaction

toolbox.register("evaluate", evalVRP)

# 约束条件
def checkCapacity(individual):
    # 检查每辆车的载重
    loads = [0] * len(vehicles)
    for gene in individual:
        load = 0
        for customer in gene:
            load += customers[customer]['demand']
        loads[0] += load
    return loads[0] <= vehicles[0]['capacity']

def checkDuration(individual):
    # 检查每辆车的工作时间
    durations = [0] * len(vehicles)
    for gene in individual:
        duration = vehicles[0]['duration']
        for customer in gene:
            duration += customers[customer]['duration']
            if duration > vehicles[0]['duration']:
                return False
        durations[0] += duration
    return True

toolbox.decorate("mate", tools.cxUniform, indpb=0.5)
toolbox.decorate("mutate", tools.mutShuffleIndexes)

toolbox.register("population", tools.initRepeat, list, toolbox.individual)
toolbox.register("select", tools.selNSGA2)

# 运行NSGA2算法
def main():
    pop = toolbox.population(n=100)
    hof = tools.ParetoFront()
    stats = tools.Statistics(lambda ind: ind.fitness.values)
    stats.register("avg", tools.mean)
    stats.register("std", tools.std)
    stats.register("min", tools.min)
    stats.register("max", tools.max)

    algorithms.eaMuPlusLambda(pop, toolbox, mu=50, lambda_=100, cxpb=0.7, mutpb=0.2, ngen=100, stats=stats, halloffame=hof)

    return hof

if __name__ == "__main__":
    hof = main()

    # 输出最终帕累托前沿和其中的一个方案路径
    print("Number of solutions: ", len(hof))
    print("Top 5 solutions: ")
    for i in range(5):
        print(hof[i])
    bestSolution = hof[0]
    print("Best solution: ", bestSolution)
    bestCost, bestSatisfaction = bestSolution.fitness.values
    print("Best cost: ", bestCost)
    print("Best satisfaction: ", bestSatisfaction)
    bestRoutes = []
    for gene in bestSolution:
        route = [0]
        capacity = vehicles[0]['capacity']
        duration = vehicles[0]['duration']
        distance = 0
        for customer in gene:
            if capacity < customers[customer]['demand']:
                distance += distMatrix[route[-1]][0]
                route.append(0)
                route.append(customer)
                distance += distMatrix[0][customer]
                capacity = vehicles[0]['capacity'] - customers[customer]['demand']
                duration = vehicles[0]['duration']
            else:
                distance += distMatrix[route[-1]][customer]
                route.append(customer)
                capacity -= customers[customer]['demand']
                duration += customers[customer]['duration']
                if duration > vehicles[0]['duration']:
                    distance += distMatrix[route[-1]][0]
                    route.append(0)
                    capacity = vehicles[0]['capacity']
                    duration = vehicles[0]['duration']
        distance += distMatrix[route[-1]][0]
        route.append(0)
        bestRoutes.append(route)
    print("Best routes: ", bestRoutes)