### CVRP问题的Python源代码实现 车辆路径问题（Vehicle Routing Problem, VRP）是一类经典的组合优化问题，其中最常见的是带容量约束的车辆路径问题（Capacitated Vehicle Routing Problem, CVRP）。以下是基于遗传算法的一种简单实现方式来解决CVRP问题。 #### 遗传算法求解CVRP的核心思路 遗传算法是一种启发式全局优化方法，通过模拟自然界的进化过程来寻找最优解。对于CVRP问题，可以将其转化为一组染色体表示可能的解决方案，并利用交叉、变异等操作逐步逼近最佳路径方案[^1]。 下面是具体的Python代码实现： ```python import numpy as np import random from deap import base, creator, tools, algorithms # 参数设置 NUM_CITIES = 20 # 城市数量 CAPACITY = 30 # 车辆最大装载量 DEMANDS = [random.randint(1, 10) for _ in range(NUM_CITIES)] # 各城市需求 DISTANCE_MATRIX = [[np.linalg.norm(np.array([random.random(), random.random()]) - np.array([random.random(), random.random()])) for i in range(NUM_CITIES)] for j in range(i+1, NUM_CITIES)] creator.create("FitnessMin", base.Fitness, weights=(-1.0,)) creator.create("Individual", list, fitness=creator.FitnessMin) toolbox = base.Toolbox() toolbox.register("indices", random.sample, range(NUM_CITIES), NUM_CITIES) toolbox.register("individual", tools.initIterate, creator.Individual, toolbox.indices) toolbox.register("population", tools.initRepeat, list, toolbox.individual) def eval_vrp(individual): total_distance = 0 current_load = 0 num_vehicles = 1 for i in range(len(individual)): city_index = individual[i] if current_load + DEMANDS[city_index] > CAPACITY: total_distance += DISTANCE_MATRIX[individual[i-1]][0] # 返回仓库 current_load = 0 num_vehicles += 1 current_load += DEMANDS[city_index] if i < len(individual)-1: next_city = individual[i+1] total_distance += DISTANCE_MATRIX[city_index][next_city] return (total_distance, ) toolbox.register("evaluate", eval_vrp) toolbox.register("mate", tools.cxOrdered) toolbox.register("mutate", tools.mutShuffleIndexes, indpb=0.05) toolbox.register("select", tools.selTournament, tournsize=3) pop = toolbox.population(n=50) hof = tools.HallOfFame(1) stats = tools.Statistics(lambda ind: ind.fitness.values) stats.register("avg", np.mean) stats.register("min", np.min) stats.register("max", np.max) algorithms.eaSimple(pop, toolbox, cxpb=0.7, mutpb=0.2, ngen=40, stats=stats, halloffame=hof, verbose=True) print(f"Best Individual: {hof[0]}") ``` 此代码片段展示了如何使用遗传算法框架`DEAP`库构建一个简单的CVRP求解器。它定义了一个适应度函数用于评估个体性能，并实现了基本的选择、交叉和变异机制[^3]。 --- ###