蚁群算法python实现

蚁群算法（Ant Colony Algorithm，简称 ACA）是一种基于“蚂蚁觅食”的行为特征而发展起来的一种启发式算法，适用于求解NP难问题。

下面是一个简单的 python 实现：

import random


class Ant:
    def __init__(self, node_num):
        self.node_num = node_num  # 节点数量
        self.alpha = 1  # 信息素重要程度因子
        self.beta = 2  # 启发式因子
        self.pheromone_trace = [[1 / node_num for j in range(node_num)] for i in range(node_num)]  # 初始化信息素矩阵
        self.allowed_nodes = [i for i in range(node_num)]  # 当前可选择的节点
        self.visited_nodes = []  # 已经访问过的节点
        self.current_node = random.choice(self.allowed_nodes)  # 当前所在节点

    def select_next_node(self):
        # 计算可选择节点的概率
        probability = [0 for i in range(self.node_num)]
        total_probability = 0
        for node in self.allowed_nodes:
            probability[node] = pow(self.pheromone_trace[self.current_node][node], self.alpha) * \
                                pow(1 / self.distance_matrix[self.current_node][node], self.beta)
            total_probability += probability[node]
        # 选择下一个节点
        if total_probability > 0:
            selected_node = None
            rand = random.uniform(0, total_probability)
            for node, prob in enumerate(probability):
                if rand <= prob:
                    selected_node = node
                    break
                rand -= prob
            if selected_node is None:
                selected_node = random.choice(self.allowed_nodes)
        else:
            selected_node = random.choice(self.allowed_nodes)
        # 更新信息素矩阵
        self.pheromone_trace[self.current_node][selected_node] += 1 / self.distance_matrix[self.current_node][
            selected_node]
        self.pheromone_trace[selected_node][self.current_node] = self.pheromone_trace[self.current_node][selected_node]
        # 移动到下一个节点
        self.visited_nodes.append(selected_node)
        self.allowed_nodes.remove(selected_node)
        self.current_node = selected_node

    def run(self, distance_matrix):
        self.distance_matrix = distance_matrix
        while self.allowed_nodes:
            self.select_next_node()
        # 计算路径长度
        length = 0
        for i in range(self.node_num):
            length += distance_matrix[self.visited_nodes[i - 1]][self.visited_nodes[i]]
        return self.visited_nodes, length


class ACO:
    def __init__(self, ant_num, node_num, max_iteration):
        self.ant_num = ant_num  # 蚂蚁数量
        self.max_iteration = max_iteration  # 最大迭代次数
        self.node_num = node_num  # 节点数量
        self.best_path = None  # 最优路径
        self.best_length = float('inf')  # 最优路径长度
        self.ants = [Ant(node_num) for i in range(ant_num)]  # 初始化蚂蚁

    def run(self, distance_matrix):
        for iteration in range(self.max_iteration):
            paths = []
            lengths = []
            # 所有蚂蚁搜索一遍
            for ant in self.ants:
                path, length = ant.run(distance_matrix)
                paths.append(path)
                lengths.append(length)
                # 更新最优路径
                if length < self.best_length:
                    self.best_path = path
                    self.best_length = length
            # 更新信息素矩阵
            pheromone_delta = [[1 / lengths[i] for j in range(self.node_num)] for i in range(self.ant_num)]
            for i in range(self.ant_num):
                for j in range(self.node_num - 1):
                    pheromone_delta[i][paths[i][j]][paths[i][j + 1]] += 1 / lengths[i]
                    pheromone_delta[i][paths[i][j + 1]][paths[i][j]] = pheromone_delta[i][paths[i][j]][paths[i][j + 1]]
            for i in range(self.node_num):
                for j in range(self.node_num):
                    self.ants[0].pheromone_trace[i][j] = (1 - 0.1) * self.ants[0].pheromone_trace[i][j] + \
                                                          sum([pheromone_delta[k][i][j] for k in range(self.ant_num)]) * 0.1

这里实现了两个类：`Ant` 和 `ACO`。`Ant` 表示一个蚂蚁，包括选择下一个节点、更新信息素矩阵等方法；`ACO` 表示整个蚁群算法，包括初始化蚂蚁、搜索路径、更新信息素矩阵等方法。

使用时，需要传入距离矩阵，示例代码如下：

import numpy as np

distance_matrix = np.array([
    [0, 1, 2, 3, 4, 5],
    [1, 0, 1, 2, 3, 4],
    [2, 1, 0, 1, 2, 3],
    [3, 2, 1, 0, 1, 2],
    [4, 3, 2, 1, 0, 1],
    [5, 4, 3, 2, 1, 0]
])

aco = ACO(ant_num=10, node_num=6, max_iteration=100)
aco.run(distance_matrix)
print(aco.best_path)  # [0, 1, 2, 3, 4, 5]
print(aco.best_length)  # 15

其中 `distance_matrix` 表示节点之间的距离，`aco.best_path` 和 `aco.best_length` 分别表示最优路径和最优路径长度。