使用python编写帝王蝶优化算法

帝王蝶优化算法（Monarch Butterfly Optimization Algorithm, MBO）是一种基于群体智能的优化算法，其灵感来源于帝王蝶的觅食行为。下面是使用Python编写的帝王蝶优化算法的代码实现：

import random
import numpy as np

# 定义目标函数
def objective_function(x):
    return x**2

# 定义帝王蝶优化算法
def monarch_butterfly_optimization(n_iterations, n_butterflies, search_range):
    # 初始化种群
    butterflies = np.zeros((n_butterflies, search_range.shape[0]))
    for i in range(n_butterflies):
        butterflies[i] = search_range[:, 0] + np.random.rand(search_range.shape[0]) * (search_range[:, 1] - search_range[:, 0])
    
    # 初始化目标函数值
    objective_values = np.zeros(n_butterflies)
    for i in range(n_butterflies):
        objective_values[i] = objective_function(butterflies[i])
    
    # 寻找最优解
    best_objective_value = np.min(objective_values)
    best_solution = butterflies[np.argmin(objective_values)]
    
    # 迭代寻优
    for iteration in range(n_iterations):
        # 更新每只蝴蝶的位置
        for i in range(n_butterflies):
            # 计算蝴蝶的速度
            velocity = np.zeros(search_range.shape[0])
            for j in range(search_range.shape[0]):
                velocity[j] = random.uniform(-1, 1) * (best_solution[j] - butterflies[i][j])
            
            # 更新蝴蝶的位置
            new_position = butterflies[i] + velocity
            
            # 限制位置在搜索范围内
            for j in range(search_range.shape[0]):
                if new_position[j] < search_range[j][0]:
                    new_position[j] = search_range[j][0]
                if new_position[j] > search_range[j][1]:
                    new_position[j] = search_range[j][1]
            
            # 更新目标函数值
            new_objective_value = objective_function(new_position)
            if new_objective_value < objective_values[i]:
                butterflies[i] = new_position
                objective_values[i] = new_objective_value
            
            # 更新最优解
            if new_objective_value < best_objective_value:
                best_solution = new_position
                best_objective_value = new_objective_value
    
    return best_solution, best_objective_value

参数说明：

- n_iterations：迭代次数
- n_butterflies：蝴蝶数量
- search_range：搜索范围

使用示例：

search_range = np.array([[-5, 5]])  # 搜索范围
best_solution, best_objective_value = monarch_butterfly_optimization(n_iterations=100, n_butterflies=50, search_range=search_range)
print("最优解：", best_solution)
print("最优目标函数值：", best_objective_value)