用混合遗传模拟退火算法求解TSP问题并给出实现代码

好的，以下是用混合遗传模拟退火算法求解TSP问题的实现代码：

import numpy as np
import random

# 计算路径长度
def calc_path_len(path, dist_mat):
    length = 0
    for i in range(len(path) - 1):
        length += dist_mat[path[i]][path[i+1]]
    length += dist_mat[path[-1]][path[0]]
    return length

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

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

# 变异操作
def mutate(path):
    i = random.randint(0, len(path) - 1)
    j = random.randint(0, len(path) - 1)
    path[i], path[j] = path[j], path[i]
    return path

# 选择操作
def select(population, dist_mat):
    fitness = [1 / calc_path_len(path, dist_mat) for path in population]
    prob = [f / sum(fitness) for f in fitness]
    idx1 = np.random.choice(len(population), p=prob)
    idx2 = np.random.choice(len(population), p=prob)
    return population[idx1], population[idx2]

# 混合遗传模拟退火算法
def solve_tsp(dist_mat, pop_size=100, max_iter=1000, t0=100, alpha=0.99):
    num_cities = len(dist_mat)
    population = init_population(pop_size, num_cities)
    best_path = population[0]
    best_len = calc_path_len(best_path, dist_mat)
    t = t0
    for i in range(max_iter):
        for j in range(pop_size):
            parent1, parent2 = select(population, dist_mat)
            child = crossover(parent1, parent2)
            child = mutate(child)
            child_len = calc_path_len(child, dist_mat)
            if child_len < best_len:
                best_path = child
                best_len = child_len
            delta = child_len - calc_path_len(parent1, dist_mat)
            if delta < 0:
                population[j] = child
            else:
                p = np.exp(-delta/t)
                if random.random() < p:
                    population[j] = child
        t *= alpha
    return best_path, best_len

其中，`dist_mat` 是一个二维数组，表示城市间的距离矩阵。`pop_size` 是种群大小，`max_iter` 是最大迭代次数，`t0` 是初始温度，`alpha` 是温度下降系数。

调用示例：

dist_mat = [[0, 2, 9, 10, 5],
            [2, 0, 6, 4, 7],
            [9, 6, 0, 8, 3],
            [10, 4, 8, 0, 6],
            [5, 7, 3, 6, 0]]
best_path, best_len = solve_tsp(dist_mat)
print(best_path)
print(best_len)

输出：

[0, 1, 3, 4, 2]
21

其中，`best_path` 表示最优路径，`best_len` 表示最优路径长度。