使用遗传算法实现上述问题建模求解，列出算法的python代码，结果需要体现出三辆车分别的运输路径，并将迭代过程已图表呈现

要使用遗传算法解决上述多车场车辆路径问题（VRP），可以按照以下步骤进行：

1. **建立数学模型**：定义问题的目标函数和约束条件。
2. **设计遗传算法**：包括初始化种群、选择、交叉、变异等操作。
3. **编写Python代码**：实现遗传算法并求解问题。

以下是完整的Python代码示例，包括遗传算法的实现和结果可视化：

### Python代码

import numpy as np
import matplotlib.pyplot as plt
import random

# 距离矩阵
distance_matrix = [
    [0, 15, 11, 13, 20, 7, 8, 5, 12, 15, 7, 19, 6, 11],
    [15, 0, 19, 7, 15, 19, 17, 13, 7, 14, 6, 7, 9, 20],
    [11, 19, 0, 18, 20, 8, 14, 17, 6, 8, 6, 13, 18, 9],
    [13, 7, 18, 0, 6, 11, 13, 14, 15, 13, 15, 11, 16, 6],
    [20, 15, 20, 6, 0, 17, 14, 6, 7, 19, 15, 14, 17, 16],
    [7, 19, 8, 11, 17, 0, 14, 6, 7, 19, 13, 9, 10, 12],
    [8, 17, 14, 13, 14, 14, 0, 8, 8, 15, 7, 15, 12, 5],
    [5, 13, 17, 14, 6, 6, 8, 0, 11, 16, 16, 13, 10, 20],
    [12, 7, 6, 15, 7, 7, 8, 11, 0, 16, 10, 19, 17, 17],
    [15, 14, 18, 13, 19, 19, 15, 16, 16, 0, 7, 16, 7, 19],
    [7, 6, 6, 15, 15, 13, 7, 16, 10, 7, 0, 10, 17, 7],
    [19, 7, 13, 11, 14, 9, 15, 13, 19, 16, 10, 0, 9, 14],
    [6, 9, 18, 16, 17, 10, 12, 10, 17, 7, 17, 9, 0, 13],
    [11, 20, 9, 6, 16, 12, 5, 20, 17, 19, 7, 14, 13, 0]
]

# 物品重量
weights = [564, 509, 503, 350, 297, 355, 595, 446, 292, 343, 443, 233, 227]

# 车辆载重量
capacity = 2000

# 初始化种群
def initialize_population(pop_size, num_customers):
    population = []
    for _ in range(pop_size):
        route = list(range(1, num_customers + 1))
        random.shuffle(route)
        population.append(route)
    return population

# 计算单条路线的距离
def calculate_route_distance(route):
    total_distance = 0
    current_position = 0
    for customer in route:
        total_distance += distance_matrix[current_position][customer]
        current_position = customer
    total_distance += distance_matrix[current_position][0]  # 返回配送中心
    return total_distance

# 计算总距离
def calculate_total_distance(routes):
    total_distance = 0
    for route in routes:
        total_distance += calculate_route_distance(route)
    return total_distance

# 检查是否满足容量限制
def is_feasible(routes):
    for route in routes:
        if sum(weights[customer - 1] for customer in route) > capacity:
            return False
    return True

# 生成初始解
def generate_initial_solution(population):
    feasible_solutions = []
    for route in population:
        current_routes = []
        current_route = []
        current_weight = 0
        for customer in route:
            if current_weight + weights[customer - 1] <= capacity:
                current_route.append(customer)
                current_weight += weights[customer - 1]
            else:
                current_routes.append(current_route)
                current_route = [customer]
                current_weight = weights[customer - 1]
        current_routes.append(current_route)
        if is_feasible(current_routes):
            feasible_solutions.append(current_routes)
    return feasible_solutions

# 选择操作
def selection(population, fitness_scores):
    selected_indices = np.random.choice(len(population), size=len(population), p=fitness_scores / np.sum(fitness_scores))
    return [population[i] for i in selected_indices]

# 交叉操作
def crossover(parent1, parent2):
    start, end = sorted(random.sample(range(len(parent1)), 2))
    child1 = [-1] * len(parent1)
    child2 = [-1] * len(parent2)
    
    child1[start:end+1] = parent1[start:end+1]
    child2[start:end+1] = parent2[start:end+1]
    
    set1 = set(child1)
    set2 = set(child2)
    
    for i in range(len(parent1)):
        if parent2[i] not in set1:
            child1[child1.index(-1)] = parent2[i]
        if parent1[i] not in set2:
            child2[child2.index(-1)] = parent1[i]
    
    return child1, child2

# 变异操作
def mutation(individual, mutation_rate):
    for i in range(len(individual)):
        if random.random() < mutation_rate:
            j = random.randint(0, len(individual) - 1)
            individual[i], individual[j] = individual[j], individual[i]
    return individual

# 主函数
def genetic_algorithm(pop_size, num_generations, mutation_rate):
    population = initialize_population(pop_size, len(weights))
    best_solution = None
    best_distance = float('inf')
    history = []

    for generation in range(num_generations):
        feasible_solutions = generate_initial_solution(population)
        distances = [calculate_total_distance(solution) for solution in feasible_solutions]
        
        if min(distances) < best_distance:
            best_distance = min(distances)
            best_solution = feasible_solutions[distances.index(min(distances))]
        
        fitness_scores = [1 / (d + 1) for d in distances]
        new_population = selection(feasible_solutions, fitness_scores)
        
        next_population = []
        while len(next_population) < pop_size:
            parent1, parent2 = random.sample(new_population, 2)
            child1, child2 = crossover(parent1, parent2)
            child1 = mutation(child1, mutation_rate)
            child2 = mutation(child2, mutation_rate)
            next_population.extend([child1, child2])
        
        population = next_population[:pop_size]
        history.append(best_distance)

    return best_solution, best_distance, history

# 参数设置
pop_size = 100
num_generations = 500
mutation_rate = 0.01

# 运行遗传算法
best_solution, best_distance, history = genetic_algorithm(pop_size, num_generations, mutation_rate)

# 打印结果
print("Best Solution:")
for i, route in enumerate(best_solution):
    print(f"Vehicle {i+1}: {route}")
print(f"Total Distance: {best_distance}")

# 绘制迭代过程图
plt.plot(history)
plt.xlabel('Generation')
plt.ylabel('Best Total Distance')
plt.title('Genetic Algorithm Convergence')
plt.show()

### 结果解释
1. **最佳解决方案**：输出每辆车的运输路径。
2. **总距离**：显示所有车辆的总行驶距离。
3. **迭代过程图**：绘制遗传算法在每次迭代中的最优解变化情况。

通过运行上述代码，你可以得到一个合理的车辆路径分配方案，并且可以看到算法的收敛过程。