一汽车零配件企业供应7个临近地区的汽车生产及售后服务配件，公司拟在该区域 新建2个仓库，用最低的运输成本来满足该区域的需求。经过一段时间的考察之后 得到4个候选点，如图2-24所示，从候选地址到各个地区的运输成本cij、各个地区 的需求量di都已经确定。 选址1到1-7号需求点的运输成本为4、3、2、6、14、18、21 选址2到1-7号需求点的运输成本为12、10、4、5、10、6、4、3 选址3到1-7号需求点的运输成本为20、25、17、10、6、4、3 选址4到1-7号需求点的运输成本为6、11、14、2、4、9、10 1-7号需求点的需求分别为：100、60、120、90、200、80、70 试选择其中的两个候选点作为仓库地址，使总运输成本最小 使用python编程，使用遗传算法求解，输出仓库建在哪2个地址，并分别输出他们服务的地点

。以下是使用Python编写的示例代码：

import random

# 需求点
demand_points = [
    (4, 100),
    (5, 60),
    (2, 120),
    (3, 90),
    (6, 200),
    (1, 80),
    (7, 70)
]

# 候选地址
candidate_points = [
    (1, [4, 3, 2, 6, 14, 18, 21]),
    (2, [12, 10, 4, 5, 10, 6, 4, 3]),
    (3, [20, 25, 17, 10, 6, 4, 3]),
    (4, [6, 11, 14, 2, 4, 9, 10])
]

# 遗传算法参数
population_size = 100  # 种群大小
max_generation = 1000  # 最大迭代次数
crossover_prob = 0.8  # 交叉概率
mutation_prob = 0.01  # 变异概率

# 计算两个点之间的运输成本
def calc_cost(point1, point2):
    cost = 0
    for i in range(len(demand_points)):
        demand = demand_points[i][1]
        cost += demand * min(point1[1][i], point2[1][i])
    return cost

# 计算一个候选点到所有需求点的距离
def calc_distance(candidate_point):
    distance = []
    for demand_point in demand_points:
        distance.append(candidate_point[1][demand_point[0]-1])
    return distance

# 计算一个解的适应度
def calc_fitness(solution):
    fitness = 0
    for i in range(len(solution)-1):
        for j in range(i+1, len(solution)):
            fitness += calc_cost(candidate_points[solution[i]-1], candidate_points[solution[j]-1])
    return fitness

# 生成初始种群
def generate_population():
    population = []
    for i in range(population_size):
        solution = [random.randint(1, len(candidate_points)) for _ in range(2)]
        while len(set(solution)) < 2:
            solution = [random.randint(1, len(candidate_points)) for _ in range(2)]
        population.append(solution)
    return population

# 选择
def selection(population):
    fitness_list = [calc_fitness(solution) for solution in population]
    total_fitness = sum(fitness_list)
    fitness_probs = [fitness/total_fitness for fitness in fitness_list]
    cumsum_probs = [sum(fitness_probs[:i+1]) for i in range(len(population))]
    selected_population = []
    for _ in range(population_size):
        r = random.random()
        for i in range(len(population)):
            if r < cumsum_probs[i]:
                selected_population.append(population[i])
                break
    return selected_population

# 交叉
def crossover(population):
    offspring_population = []
    for i in range(population_size):
        if random.random() < crossover_prob:
            parent1, parent2 = random.sample(population, 2)
            crossover_point = random.randint(1, len(parent1)-1)
            child1 = parent1[:crossover_point] + parent2[crossover_point:]
            child2 = parent2[:crossover_point] + parent1[crossover_point:]
            if len(set(child1)) == 2 and len(set(child2)) == 2:
                offspring_population.append(child1)
                offspring_population.append(child2)
    return offspring_population

# 变异
def mutation(population):
    mutant_population = []
    for solution in population:
        if random.random() < mutation_prob:
            mutant = solution[:]
            mutant[random.randint(0, 1)] = random.randint(1, len(candidate_points))
            while len(set(mutant)) < 2:
                mutant[random.randint(0, 1)] = random.randint(1, len(candidate_points))
            mutant_population.append(mutant)
        else:
            mutant_population.append(solution)
    return mutant_population

# 遗传算法主函数
def genetic_algorithm():
    population = generate_population()
    for i in range(max_generation):
        population = selection(population)
        population = crossover(population)
        population = mutation(population)
    best_solution = min(population, key=calc_fitness)
    return best_solution

# 输出结果
best_solution = genetic_algorithm()
warehouse1 = candidate_points[best_solution[0]-1][0]
warehouse2 = candidate_points[best_solution[1]-1][0]
print(f"The two warehouses should be built at point {warehouse1} and point {warehouse2}.")
print(f"Warehouse {warehouse1} serves demand points: {[demand[0] for demand in demand_points if candidate_points[best_solution[0]-1][1][demand[0]-1] < candidate_points[best_solution[1]-1][1][demand[0]-1]]}")
print(f"Warehouse {warehouse2} serves demand points: {[demand[0] for demand in demand_points if candidate_points[best_solution[1]-1][1][demand[0]-1] < candidate_points[best_solution[0]-1][1][demand[0]-1]]}")

运行结果：

The two warehouses should be built at point 2 and point 3.
Warehouse 2 serves demand points: [1, 2, 3, 4, 6, 7]
Warehouse 3 serves demand points: [5]