用遗传算法写一个TSP问题

TSP问题是指旅行商问题，即给定一系列城市和每对城市之间的距离，求解访问每一座城市恰好一次并回到起始城市的最短回路。

遗传算法是一种启发式优化算法，可用于解决TSP问题。下面是一个用遗传算法求解TSP问题的示例代码：

import random

# 定义城市坐标
city_locations = [(60, 200), (180, 200), (80, 180), (140, 180), (20, 160),
                  (100, 160), (200, 160), (140, 140), (40, 120), (100, 120),
                  (180, 100), (60, 80), (120, 80), (180, 60), (20, 40),
                  (100, 40), (200, 40), (20, 20), (60, 20), (160, 20)]

# 计算两个城市之间的距离
def distance(city1, city2):
    x1, y1 = city1
    x2, y2 = city2
    return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5

# 计算一个路径的总距离
def path_distance(path):
    distance_sum = 0
    for i in range(len(path)):
        distance_sum += distance(city_locations[path[i-1]], city_locations[path[i]])
    return distance_sum

# 初始化种群
def init_population(pop_size, gene_length):
    population = []
    for i in range(pop_size):
        individual = list(range(gene_length))
        random.shuffle(individual)
        population.append(individual)
    return population

# 交叉操作
def crossover(parent1, parent2):
    child = [-1] * len(parent1)
    start_pos = random.randint(0, len(parent1) - 1)
    end_pos = random.randint(0, len(parent1) - 1)
    if start_pos > end_pos:
        start_pos, end_pos = end_pos, start_pos
    for i in range(start_pos, end_pos + 1):
        child[i] = parent1[i]
    j = 0
    for i in range(len(parent2)):
        if parent2[i] not in child:
            while child[j] != -1:
                j += 1
            child[j] = parent2[i]
    return child

# 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

# 选择操作
def selection(population, fitness, num_parents):
    parents = []
    for i in range(num_parents):
        max_fitness_index = fitness.index(max(fitness))
        parents.append(population[max_fitness_index])
        population.pop(max_fitness_index)
        fitness.pop(max_fitness_index)
    return parents

# 遗传算法求解TSP问题
def tsp_ga(pop_size, num_generations, mutation_rate):
    gene_length = len(city_locations)
    population = init_population(pop_size, gene_length)
    for i in range(num_generations):
        fitness = [1.0 / path_distance(individual) for individual in population]
        parents = selection(population, fitness, 2)
        offspring = crossover(parents[0], parents[1])
        offspring = mutation(offspring, mutation_rate)
        population.append(offspring)
    fitness = [1.0 / path_distance(individual) for individual in population]
    best_index = fitness.index(max(fitness))
    best_individual = population[best_index]
    return best_individual, path_distance(best_individual)

# 测试
best_individual, shortest_distance = tsp_ga(100, 500, 0.01)
print("最短路径：", best_individual)
print("最短距离：", shortest_distance)

在上面的代码中，我们定义了一个`distance()`函数来计算两个城市之间的距离，一个`path_distance()`函数来计算一个路径的总距离，一个`init_population()`函数来初始化种群，一个`crossover()`函数来进行交叉操作，一个`mutation()`函数来进行变异操作，一个`selection()`函数来进行选择操作，一个`tsp_ga()`函数来执行遗传算法求解TSP问题。

我们将初始化种群大小设置为100，迭代次数设置为500次，变异率设置为0.01，运行代码后可以得到最短路径和最短距离的输出结果。需要注意的是，由于遗传算法是一种启发式算法，无法保证得到全局最优解，因此每一次运行的结果可能会有所不同。