灰狼优化算法python程序

灰狼优化算法（Grey Wolf Optimizer，GWO）是一种基于群体智能的优化算法，受到灰狼群行为的启发而提出。下面是一个用 Python 实现的简单的灰狼优化算法程序：

import numpy as np

# 目标函数
def f(x):
    return np.sum(np.square(x))

# 灰狼优化算法
def GWO(f, lb, ub, dim, SearchAgents_no, Max_iter):
    # 初始化灰狼群
    Positions = np.zeros((SearchAgents_no, dim))
    for i in range(dim):
        Positions[:, i] = np.random.uniform(lb[i], ub[i], SearchAgents_no)
    # 初始化 alpha、beta、delta 灰狼
    Alpha_pos = np.zeros(dim)
    Alpha_score = float("inf")
    Beta_pos = np.zeros(dim)
    Beta_score = float("inf")
    Delta_pos = np.zeros(dim)
    Delta_score = float("inf")
    # 迭代寻优
    for l in range(0, Max_iter):
        for i in range(0, SearchAgents_no):
            # 计算适应度值
            fitness = f(Positions[i, :])
            # 更新 alpha、beta、delta 灰狼
            if fitness < Alpha_score:
                Alpha_score = fitness
                Alpha_pos = Positions[i, :].copy()
            if fitness > Alpha_score and fitness < Beta_score:
                Beta_score = fitness
                Beta_pos = Positions[i, :].copy()
            if fitness > Alpha_score and fitness > Beta_score and fitness < Delta_score:
                Delta_score = fitness
                Delta_pos = Positions[i, :].copy()
        # 调整灰狼群的位置
        a = 2 - l * (2 / Max_iter)  # a 衰减
        for i in range(0, SearchAgents_no):
            r1 = np.random.rand(dim)
            r2 = np.random.rand(dim)
            A = 2 * a * r1 - a
            C = 2 * r2
            D_alpha = np.abs(C * Alpha_pos - Positions[i, :])
            X1 = Alpha_pos - A * D_alpha
            r1 = np.random.rand(dim)
            r2 = np.random.rand(dim)
            A = 2 * a * r1 - a
            C = 2 * r2
            D_beta = np.abs(C * Beta_pos - Positions[i, :])
            X2 = Beta_pos - A * D_beta
            r1 = np.random.rand(dim)
            r2 = np.random.rand(dim)
            A = 2 * a * r1 - a
            C = 2 * r2
            D_delta = np.abs(C * Delta_pos - Positions[i, :])
            X3 = Delta_pos - A * D_delta
            Positions[i, :] = (X1 + X2 + X3) / 3
    # 返回最优解和最优值
    Best_pos = Alpha_pos
    Best_score = Alpha_score
    return Best_pos, Best_score

# 测试
if __name__ == "__main__":
    lb = [-10, -10, -10]  # 搜索区间下界
    ub = [10, 10, 10]  # 搜索区间上界
    dim = 3  # 变量维数
    SearchAgents_no = 30  # 灰狼数量
    Max_iter = 100  # 最大迭代次数
    Best_pos, Best_score = GWO(f, lb, ub, dim, SearchAgents_no, Max_iter)
    print("Best position: ", Best_pos)
    print("Best score: ", Best_score)

上面的程序中，目标函数为 $f(x) = \sum_{i=1}^{dim}x_i^2$，搜索区间为 $[-10, 10]$，变量维数为 3，灰狼数量为 30，最大迭代次数为 100。程序输出搜索到的最优解和最优值。你可以根据需要修改这些参数和目标函数，来解决不同的优化问题。