在三维空间中利用蚁群算法求解TSP模型的python代码

以下是利用蚁群算法求解TSP模型的Python代码：

import numpy as np

# TSP模型的距离矩阵
distance = np.array([
    [0, 30, 84, 56, 70, 60, 20, 65, 30, 10],
    [30, 0, 65, 40, 52, 50, 30, 45, 50, 63],
    [84, 65, 0, 18, 20, 30, 90, 70, 80, 81],
    [56, 40, 18, 0, 12, 23, 58, 40, 41, 32],
    [70, 52, 20, 12, 0, 15, 50, 30, 45, 50],
    [60, 50, 30, 23, 15, 0, 30, 20, 30, 22],
    [20, 30, 90, 58, 50, 30, 0, 45, 50, 52],
    [65, 45, 70, 40, 30, 20, 45, 0, 15, 21],
    [30, 50, 80, 41, 45, 30, 50, 15, 0, 11],
    [10, 63, 81, 32, 50, 22, 52, 21, 11, 0]
])

# 蚂蚁类
class Ant:
    def __init__(self, alpha, beta, cities_num):
        self.alpha = alpha  # 信息素重要程度因子
        self.beta = beta  # 启发函数重要程度因子
        self.cities_num = cities_num  # 城市数量
        self.path = []  # 蚂蚁走过的路径
        self.visited = np.zeros(cities_num)  # 标记城市是否遍历过
        self.current_city = -1  # 当前所在城市
        self.total_distance = 0.0  # 蚂蚁走过的总距离

        # 启发函数，计算城市间的信息素和距离的倒数
        def calculate_probabilities(city):
            probabilities = np.zeros(self.cities_num)
            total = 0.0
            for i in range(self.cities_num):
                if self.visited[i] == 0:
                    probabilities[i] = pow(distance[city][i], self.beta) * pow(pheromone[city][i], self.alpha)
                    total += probabilities[i]
            if total == 0.0:
                return probabilities
            probabilities = probabilities / total
            return probabilities

        # 选择下一个城市
        def choose_next_city():
            probabilities = calculate_probabilities(self.current_city)
            next_city = np.random.choice(range(self.cities_num), p=probabilities)
            return next_city

        # 蚂蚁开始走路
        def travel():
            start_city = np.random.randint(self.cities_num)
            self.current_city = start_city
            self.visited[start_city] = 1
            self.path.append(start_city)
            while len(self.path) < self.cities_num:
                next_city = choose_next_city()
                self.visited[next_city] = 1
                self.path.append(next_city)
                self.total_distance += distance[self.current_city][next_city]
                self.current_city = next_city
            self.total_distance += distance[self.path[-1]][self.path[0]]

        travel()

# 更新信息素
def update_pheromone(ants):
    pheromone_new = np.zeros((10, 10))
    for ant in ants:
        for i in range(1, ant.cities_num):
            pheromone_new[ant.path[i - 1]][ant.path[i]] += 1.0 / ant.total_distance
        pheromone_new[ant.path[-1]][ant.path[0]] += 1.0 / ant.total_distance
    pheromone_new = (1 - rho) * pheromone + pheromone_new
    return pheromone_new

# 主程序
if __name__ == "__main__":
    # 初始化信息素矩阵
    pheromone = np.ones((10, 10)) / 10
    # 迭代次数
    max_iter = 50
    # 蚂蚁数量
    ant_num = 10
    # 每次迭代后信息素的挥发速度
    rho = 0.1
    # 信息素重要程度因子
    alpha = 1.0
    # 启发函数重要程度因子
    beta = 5.0

    for i in range(max_iter):
        ants = [Ant(alpha, beta, 10) for _ in range(ant_num)]
        pheromone = update_pheromone(ants)
        print("Iteration %d: %f" % (i + 1, ants[0].total_distance))

其中，`distance`为TSP模型的距离矩阵，`Ant`为蚂蚁类，`update_pheromone`为更新信息素的函数，主程序中利用循环迭代，不断更新信息素并输出每次迭代后蚂蚁走过的总距离。