蚁群算法旅行商问题Python

以下是使用Python实现蚁群算法解决旅行商问题的代码：

import random

class Ant:
    def __init__(self, n, alpha, beta, pheromone, distance):
        self.n = n
        self.alpha = alpha
        self.beta = beta
        self.pheromone = pheromone
        self.distance = distance
        self.visited = [False] * n
        self.path = []
        self.total_distance = 0

    def select_next_city(self, current_city):
        unvisited_cities = [i for i in range(self.n) if not self.visited[i]]
        if not unvisited_cities:
            return None
        probabilities = [self.pheromone[current_city][i] ** self.alpha *
                         (1.0 / self.distance[current_city][i]) ** self.beta for i in unvisited_cities]
        total = sum(probabilities)
        r = random.uniform(0, total)
        prob_sum = 0
        for i, city in enumerate(unvisited_cities):
            prob_sum += probabilities[i]
            if prob_sum >= r:
                return city

    def visit_city(self, city):
        self.visited[city] = True
        self.path.append(city)
        if len(self.path) == 1:
            self.total_distance = 0
        else:
            prev = self.path[-2]
            self.total_distance += self.distance[prev][city]

    def __str__(self):
        return f'{self.path} ({self.total_distance})'


class AntColony:
    def __init__(self, distances, n_ants, n_best, n_iterations, decay, alpha=1, beta=1):
        self.distances = distances
        self.pheromone = [[1.0 / (distances[i][j]) for j in range(n)] for i in range(n)]
        self.all_ants = []
        for i in range(n_ants):
            self.all_ants.append(Ant(n, alpha, beta, self.pheromone, distances))
        self.n_best = n_best
        self.n_iterations = n_iterations
        self.decay = decay
        self.best_ant = None
        self.best_distance = float('inf')
        self.average_distance = 0

    def run(self):
        for iteration in range(self.n_iterations):
            for ant in self.all_ants:
                start = random.randint(0, self.n - 1)
                ant.visited = [False] * self.n
                ant.path = []
                ant.total_distance = 0
                ant.visit_city(start)
                for i in range(self.n - 1):
                    current_city = ant.path[-1]
                    next_city = ant.select_next_city(current_city)
                    if next_city is None:
                        break
                    ant.visit_city(next_city)
                if ant.total_distance < self.best_distance:
                    self.best_distance = ant.total_distance
                    self.best_ant = ant
                for i in range(1, len(ant.path)):
                    prev = ant.path[i - 1]
                    current = ant.path[i]
                    self.pheromone[prev][current] += 1.0 / ant.total_distance
                    self.pheromone[current][prev] = self.pheromone[prev][current]
                self.average_distance += ant.total_distance
            self.average_distance /= len(self.all_ants)
            for i, row in enumerate(self.pheromone):
                for j, value in enumerate(row):
                    self.pheromone[i][j] *= self.decay
                    self.pheromone[i][j] = max(self.pheromone[i][j], 0.0001)
        return self.best_ant

这段代码实现了Ant和AntColony类，其中Ant类表示一只蚂蚁，AntColony类管理整个蚁群算法的运行。在Ant类中，我们实现了选择下一个城市和访问城市的方法。在AntColony类中，我们使用了蚁群算法的基本步骤：初始化信息素、移动蚂蚁并更新信息素、更新最优解和信息素浓度、重复执行多次以找到最优解。

使用这段代码解决旅行商问题的步骤如下：

1. 创建一个n×n的距离矩阵，其中第i行第j列表示从城市i到城市j的距离。
2. 创建一个AntColony对象，并传入距离矩阵、蚂蚁数量、最优解数量、迭代次数、信息素挥发率等参数。
3. 调用AntColony的run()方法，得到最优解Ant对象。
4. 从Ant对象中获取路径和距离，即可得到最优解。

以下是一个简单的示例：

n = 5
distances = [[0, 2, 3, 4, 5],
             [2, 0, 4, 5, 6],
             [3, 4, 0, 6, 7],
             [4, 5, 6, 0, 8],
             [5, 6, 7, 8, 0]]
colony = AntColony(distances, n_ants=10, n_best=2, n_iterations=10, decay=0.1)
best_ant = colony.run()
print(best_ant)

这个示例中，我们创建了一个5个城市的旅行商问题，距离矩阵为distances。我们创建了一个AntColony对象，设置蚂蚁数量为10，最优解数量为2，迭代次数为10，信息素挥发率为0.1。最后，我们调用run()方法得到最优解，并打印出来。