python蚂蚁算法

蚂蚁算法是一种基于蚂蚁群体行为的随机搜索算法，常用于求解组合优化问题。下面是一个简单的Python蚂蚁算法实现的示例：

import random

# 初始化参数
num_ants = 10  # 蚂蚁数量
num_iterations = 100  # 迭代次数
alpha = 1  # 信息素重要程度因子
beta = 2  # 启发函数重要程度因子
rho = 0.5  # 信息素挥发因子
Q = 100  # 常数因子
num_cities = 5  # 城市数量

# 初始化距离矩阵
distance_matrix = [[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]]

# 初始化信息素矩阵
pheromone_matrix = [[1 for j in range(num_cities)] for i in range(num_cities)]

# 开始迭代
for it in range(num_iterations):
    # 初始化蚂蚁位置
    ant_positions = [random.randint(0, num_cities - 1) for i in range(num_ants)]
    # 初始化蚂蚁路径长度
    ant_path_lengths = [0 for i in range(num_ants)]
    # 计算每只蚂蚁的路径
    for i in range(num_ants):
        # 初始化已访问城市列表
        visited_cities = [ant_positions[i]]
        # 计算路径长度
        for j in range(num_cities - 1):
            # 计算下一个城市
            next_city = -1
            max_prob = -1
            for k in range(num_cities):
                if k not in visited_cities:
                    # 计算概率
                    prob = pheromone_matrix[visited_cities[-1]][k] ** alpha * \
                           (1.0 / distance_matrix[visited_cities[-1]][k]) ** beta
                    if prob > max_prob:
                        max_prob = prob
                        next_city = k
            # 更新已访问城市列表和路径长度
            visited_cities.append(next_city)
            ant_path_lengths[i] += distance_matrix[visited_cities[-2]][visited_cities[-1]]
        # 更新信息素矩阵
        for j in range(num_cities - 1):
            pheromone_matrix[visited_cities[j]][visited_cities[j + 1]] += Q / ant_path_lengths[i]
    # 更新信息素矩阵
    for i in range(num_cities):
        for j in range(num_cities):
            pheromone_matrix[i][j] *= (1 - rho)

# 输出结果
print("最短路径长度：", min(ant_path_lengths))
print("最短路径：", visited_cities)