用蚁群算法求旅行商问题的最优解的python代码

以下是一个用蚁群算法求解旅行商问题的 Python 代码：

import numpy as np
from scipy.spatial import distance_matrix

# 蚂蚁类
class Ant:
    def __init__(self, num_cities):
        self.route = np.zeros(num_cities, dtype=np.int) # 记录路线
        self.visited_cities = np.zeros(num_cities, dtype=bool) # 记录已访问城市
        self.index = 0 # 当前所在城市的下标

    # 移动蚂蚁到下一个城市
    def move_to_next_city(self, tau, eta, alpha, beta):
        q0 = 0.9
        probabilities = self.compute_probabilities(tau, eta, alpha, beta)
        if np.random.random() < q0:
            next_city = np.argmax(probabilities)
        else:
            next_city = np.random.choice(range(len(probabilities)), p=probabilities)
        self.route[self.index] = next_city
        self.visited_cities[next_city] = True
        self.index = next_city

    # 计算下一个城市的概率
    def compute_probabilities(self, tau, eta, alpha, beta):
        pheromones = tau[self.index] ** alpha
        heuristic = (eta[self.index] ** beta) * (tau[self.index] ** alpha)
        probabilities = pheromones * heuristic
        probabilities[self.visited_cities] = 0
        probabilities = probabilities / np.sum(probabilities)
        return probabilities

# 蚁群算法求解旅行商问题
class AntColonyOptimization:
    def __init__(self, num_ants, num_iterations, decay, alpha, beta, q):
        self.num_ants = num_ants # 蚂蚁数量
        self.num_iterations = num_iterations # 迭代次数
        self.decay = decay # 信息素挥发因子
        self.alpha = alpha # alpha参数
        self.beta = beta # beta参数
        self.q = q # 信息素增量常数

    # 求解旅行商问题
    def solve_tsp(self, distance_matrix):
        num_cities = distance_matrix.shape[0]
        tau = np.ones((num_cities, num_cities)) # 信息素矩阵
        eta = 1 / distance_matrix # 启发值矩阵
        best_route = None
        best_cost = float('inf')
        for i in range(self.num_iterations):
            ants = [Ant(num_cities) for _ in range(self.num_ants)] # 创建蚂蚁
            for ant in ants:
                while not np.all(ant.visited_cities):
                    ant.move_to_next_city(tau, eta, self.alpha, self.beta) # 蚂蚁走一步
                distance = distance_matrix[ant.route[-1], ant.route[0]] # 回到起点
                for j in range(num_cities - 1):
                    distance += distance_matrix[ant.route[j], ant.route[j+1]]
                if distance < best_cost: # 更新最优解
                    best_route = ant.route
                    best_cost = distance
                # 更新信息素
                for j in range(num_cities - 1):
                    tau[ant.route[j], ant.route[j+1]] = (1 - self.decay) * tau[ant.route[j], ant.route[j+1]] + self.q / distance
                tau[ant.route[-1], ant.route[0]] = (1 - self.decay) * tau[ant.route[-1], ant.route[0]] + self.q / distance
                ant.route = np.zeros(num_cities, dtype=np.int)
                ant.visited_cities = np.zeros(num_cities, dtype=bool)
                ant.index = 0
            tau = (1 - self.decay) * tau # 信息素挥发
            if i % 10 == 0:
                print("Iteration {:2d}, Best Cost {:.2f}".format(i, best_cost))
        return best_route, best_cost

# 测试
if __name__ == '__main__':
    # 构造测试数据
    num_cities = 10
    np.random.seed(0)
    cities = np.random.rand(num_cities, 2)
    distance_matrix = distance_matrix(cities, cities)

    # 求解旅行商问题
    aco = AntColonyOptimization(num_ants=100, num_iterations=500, decay=0.5, alpha=1, beta=5, q=10)
    best_route, best_cost = aco.solve_tsp(distance_matrix)

    # 输出结果
    print("Best Route: {}".format(best_route))
    print("Best Cost: {:.2f}".format(best_cost))

以上是一个用蚁群算法求解旅行商问题的 Python 代码。