写一个使用混合蛙跳算法解决TSP问题的Python程序

以下是一个使用混合蛙跳算法（Hybrid Genetic Algorithm and Particle Swarm Optimization，HGPSO）解决TSP问题的Python程序：

import numpy as np
import random
import math

# 定义TSP问题中的城市坐标
city_cords = 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]])

# 定义使用HGPSO算法解决TSP问题的类
class HGPSO_TSP:
    def __init__(self, n_pop, n_city, n_iter, w=0.7, c1=1.5, c2=1.5, p_crossover=0.9, p_mutation=0.1):
        self.n_pop = n_pop # 种群大小
        self.n_city = n_city # 城市数量
        self.n_iter = n_iter # 迭代次数
        self.w = w # 惯性权重
        self.c1 = c1 # 个体学习因子
        self.c2 = c2 # 群体学习因子
        self.p_crossover = p_crossover # 交叉概率
        self.p_mutation = p_mutation # 变异概率
        self.population = np.zeros((self.n_pop, self.n_city), dtype=int) # 种群中每个个体的基因型
        self.fitness = np.zeros(self.n_pop) # 种群中每个个体的适应度值
        self.global_best = np.zeros(self.n_city, dtype=int) # 全局最优解的基因型
        self.global_best_fitness = np.inf # 全局最优解的适应度值

    # 计算两个城市之间的欧氏距离
    def distance(self, city1, city2):
        return math.sqrt((city1[0]-city2[0])**2 + (city1[1]-city2[1])**2)

    # 计算一个个体的适应度值
    def evaluate(self, individual):
        distance_sum = 0
        for i in range(self.n_city-1):
            distance_sum += self.distance(city_cords[individual[i]], city_cords[individual[i+1]])
        distance_sum += self.distance(city_cords[individual[-1]], city_cords[individual[0]])
        return distance_sum

    # 初始化种群
    def initialize_population(self):
        for i in range(self.n_pop):
            self.population[i] = np.random.permutation(self.n_city)
            self.fitness[i] = self.evaluate(self.population[i])

    # 更新全局最优解
    def update_global_best(self):
        for i in range(self.n_pop):
            if self.fitness[i] < self.global_best_fitness:
                self.global_best_fitness = self.fitness[i]
                self.global_best = self.population[i]

    # 选择操作
    def selection(self):
        fitness_sum = np.sum(1/self.fitness)
        probs = (1/self.fitness) / fitness_sum
        selected_indices = np.random.choice(self.n_pop, self.n_pop, p=probs)
        selected_population = self.population[selected_indices]
        return selected_population

    # 交叉操作
    def crossover(self, parent1, parent2):
        child = np.zeros(self.n_city, dtype=int)
        start = random.randint(0, self.n_city-1)
        end = random.randint(start, self.n_city-1)
        child[start:end] = parent1[start:end]
        for i in range(self.n_city):
            if parent2[i] not in child:
                for j in range(self.n_city):
                    if child[j] == 0:
                        child[j] = parent2[i]
                        break
        return child

    # 变异操作
    def mutation(self, individual):
        index1 = random.randint(0, self.n_city-1)
        index2 = random.randint(0, self.n_city-1)
        individual[index1], individual[index2] = individual[index2], individual[index1]
        return individual

    # 更新种群
    def update_population(self):
        selected_population = self.selection()
        new_population = np.zeros((self.n_pop, self.n_city), dtype=int)
        for i in range(self.n_pop):
            parent1 = selected_population[i]
            if random.random() < self.p_crossover:
                parent2 = selected_population[random.randint(0, self.n_pop-1)]
                child = self.crossover(parent1, parent2)
                if random.random() < self.p_mutation:
                    child = self.mutation(child)
                new_population[i] = child
            else:
                new_population[i] = parent1
        self.population = new_population
        self.fitness = np.zeros(self.n_pop)
        for i in range(self.n_pop):
            self.fitness[i] = self.evaluate(self.population[i])

    # 更新速度
    def update_velocity(self, velocity, individual, local_best):
        r1 = np.random.rand(self.n_city)
        r2 = np.random.rand(self.n_city)
        personal_best = individual
        global_best = self.global_best
        for i in range(self.n_city):
            velocity[i] = self.w * velocity[i] + self.c1 * r1[i] * (personal_best[i] - individual[i]) + self.c2 * r2[i] * (global_best[i] - individual[i])
            if velocity[i] > self.n_city/2:
                velocity[i] = self.n_city/2
            elif velocity[i] < -self.n_city/2:
                velocity[i] = -self.n_city/2
        return velocity

    # 更新位置
    def update_position(self, individual, velocity):
        position = np.zeros(self.n_city, dtype=int)
        temp = individual + velocity
        for i in range(self.n_city):
            if temp[i] > self.n_city-1:
                temp[i] = self.n_city-1
            elif temp[i] < 0:
                temp[i] = 0
        for i in range(self.n_city):
            if temp[i] not in position:
                position[i] = temp[i]
            else:
                for j in range(self.n_city):
                    if position[j] == 0:
                        position[j] = temp[i]
                        break
        return position

    # 更新局部最优解
    def update_local_best(self, position, fitness):
        local_best = np.zeros(self.n_city, dtype=int)
        local_best_fitness = np.inf
        for i in range(self.n_pop):
            if fitness[i] < local_best_fitness and np.array_equal(position, self.population[i]):
                local_best_fitness = fitness[i]
                local_best = self.population[i]
        return local_best

    # HGPSO算法
    def run(self):
        self.initialize_population()
        self.update_global_best()
        velocity = np.zeros((self.n_pop, self.n_city), dtype=int)
        for i in range(self.n_iter):
            for j in range(self.n_pop):
                velocity[j] = self.update_velocity(velocity[j], self.population[j], self.update_local_best(self.population[j], self.fitness))
                self.population[j] = self.update_position(self.population[j], velocity[j])
                self.fitness[j] = self.evaluate(self.population[j])
            self.update_global_best()
        return self.global_best, self.global_best_fitness

# 测试
n_pop = 50 # 种群大小
n_city = 20 # 城市数量
n_iter = 100 # 迭代次数
hgpso_tsp = HGPSO_TSP(n_pop, n_city, n_iter)
best_path, best_dist = hgpso_tsp.run()
print("最短路径：", best_path)
print("最短距离：", best_dist)

在该程序中，我们首先定义了TSP问题中的城市坐标，然后定义了一个使用HGPSO算法解决TSP问题的类`HGPSO_TSP`。在该类中，我们先定义了一个`distance`函数，用于计算两个城市之间的欧氏距离。然后，我们定义了一系列方法来实现HGPSO算法中的各个操作，包括初始化种群、计算适应度值、选择操作、交叉操作、变异操作、更新种群、更新速度、更新位置、更新局部最优解和运行算法。最后，我们设置了一些参数，调用`HGPSO_TSP`类并运行算法，输出最短路径和最短距离。