用混合遗传模拟退火算法求解TSP问题并给出实现代码

TSP问题是一个经典的组合优化问题，它的目标是找到一条经过所有给定城市并回到起点的最短路径。混合遗传模拟退火算法（Hybrid Genetic Simulated Annealing Algorithm，HGSA）是一种结合了遗传算法和模拟退火算法的优化算法，可以用于求解TSP问题。

以下是使用Python实现HGSA算法求解TSP问题的示例代码：

import numpy as np
import random

# TSP问题中的城市坐标
cities = np.array([[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):
    return np.sqrt(np.sum((city1 - city2) ** 2))

# 计算路径的总长度
def path_length(path):
    length = 0
    for i in range(len(path) - 1):
        length += distance(cities[path[i]], cities[path[i+1]])
    length += distance(cities[path[-1]], cities[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, end = sorted([random.randint(0, len(parent1)-1) for _ in range(2)])
    for i in range(start, end+1):
        child[i] = parent1[i]
    j = 0
    for i in range(len(parent2)):
        if parent2[i] not in child:
            if child[j] == -1:
                child[j] = parent2[i]
            j += 1
    return child

# 变异操作
def mutation(path):
    path = path.copy()
    start, end = sorted([random.randint(0, len(path)-1) for _ in range(2)])
    path[start:end+1] = reversed(path[start:end+1])
    return path

# 模拟退火操作
def simulated_annealing(path, temperature):
    old_length = path_length(path)
    new_path = mutation(path)
    new_length = path_length(new_path)
    if new_length < old_length:
        return new_path
    else:
        delta = new_length - old_length
        probability = np.exp(-delta / temperature)
        if random.random() < probability:
            return new_path
        else:
            return path

# 适应度函数
def fitness(path):
    return 1 / path_length(path)

# 选择操作
def selection(population, fitness_values):
    idx = np.random.choice(len(population), size=2, p=fitness_values/fitness_values.sum(), replace=False)
    return population[idx[0]], population[idx[1]]

# HGSA算法
def hgsa(pop_size, num_cities, max_iter):
    population = init_population(pop_size, num_cities)
    for i in range(max_iter):
        # 交叉操作
        new_population = []
        fitness_values = np.array([fitness(path) for path in population])
        for j in range(pop_size // 2):
            parent1, parent2 = selection(population, fitness_values)
            child1 = crossover(parent1, parent2)
            child2 = crossover(parent2, parent1)
            new_population.append(child1)
            new_population.append(child2)
        # 模拟退火操作
        for j in range(pop_size):
            temperature = (max_iter - i) / max_iter
            new_population[j] = simulated_annealing(new_population[j], temperature)
        population = new_population
    # 返回最优解
    fitness_values = np.array([fitness(path) for path in population])
    idx = np.argmax(fitness_values)
    return population[idx], path_length(population[idx])

# 测试代码
path, length = hgsa(100, len(cities), 1000)
print("最短路径：", path)
print("路径长度：", length)

在上面的代码中，我们首先定义了TSP问题中的城市坐标，然后实现了计算两个城市之间距离、计算路径总长度、初始化种群、交叉操作、变异操作、模拟退火操作、适应度函数和选择操作等函数。最后，我们使用HGSA算法求解TSP问题，并输出最优解的路径和长度。

需要注意的是，上面的代码只是一个示例，实际应用中需要根据具体问题进行调整和优化。