GWO多目标算法程序

以下是GWO多目标算法的Python代码示例：

import numpy as np
import math
import copy

def GWO_multi_obj_search(objective_func, lb, ub, dim, search_agents_no, max_iter):
    # 初始化灰狼种群
    alpha_pos = np.zeros(dim)
    beta_pos = np.zeros(dim)
    delta_pos = np.zeros(dim)
    alpha_score = float("inf")
    beta_score = float("inf")
    delta_score = float("inf")
    pos_list = np.zeros((search_agents_no, dim))
    for i in range(search_agents_no):
        pos_list[i, :] = lb + (ub - lb) * np.random.rand(dim)

    # 开始迭代
    for iter_count in range(max_iter):
        for i in range(search_agents_no):
            # 计算适应值
            current_pos = pos_list[i, :]
            fitness = objective_func(current_pos)
            obj_len = len(fitness)
            if obj_len != 2:
                print("Error: Objective function should return two values!")
                return None, None
            # 更新alpha、beta、delta
            if fitness[0] < alpha_score and fitness[1] < alpha_score:
                delta_pos = copy.copy(beta_pos)
                delta_score = copy.copy(beta_score)
                beta_pos = copy.copy(alpha_pos)
                beta_score = copy.copy(alpha_score)
                alpha_pos = copy.copy(current_pos)
                alpha_score = copy.copy(fitness[0])
            elif fitness[0] < beta_score and fitness[1] < beta_score:
                delta_pos = copy.copy(beta_pos)
                delta_score = copy.copy(beta_score)
                beta_pos = copy.copy(current_pos)
                beta_score = copy.copy(fitness[0])
            elif fitness[0] < delta_score and fitness[1] < delta_score:
                delta_pos = copy.copy(current_pos)
                delta_score = copy.copy(fitness[0])
        # 更新灰狼位置
        a = 2 - iter_count * (2 / max_iter)  # 匀速下降参数
        for i in range(search_agents_no):
            r1 = np.random.rand(dim)
            r2 = np.random.rand(dim)
            A1 = 2 * a * r1 - a  # 计算系数A1
            C1 = 2 * r2  # 计算系数C1
            D_alpha = abs(C1 * alpha_pos - pos_list[i, :])  # 计算向量D_alpha
            X1 = alpha_pos - A1 * D_alpha  # 计算新位置X1

            r1 = np.random.rand(dim)
            r2 = np.random.rand(dim)
            A2 = 2 * a * r1 - a  # 计算系数A2
            C2 = 2 * r2  # 计算系数C2
            D_beta = abs(C2 * beta_pos - pos_list[i, :])  # 计算向量D_beta
            X2 = beta_pos - A2 * D_beta  # 计算新位置X2

            r1 = np.random.rand(dim)
            r2 = np.random.rand(dim)
            A3 = 2 * a * r1 - a  # 计算系数A3
            C3 = 2 * r2  # 计算系数C3
            D_delta = abs(C3 * delta_pos - pos_list[i, :])  # 计算向量D_delta
            X3 = delta_pos - A3 * D_delta  # 计算新位置X3

            pos_list[i, :] = (X1 + X2 + X3) / 3  # 更新位置
            # 边界处理
            pos_list[i, :] = np.clip(pos_list[i, :], lb, ub)

    return alpha_pos, alpha_score

# 测试函数
def test_func(x):
    y1 = x[0]**2 + x[1]**2
    y2 = (x[0]-1)**2 + x[1]**2
    return [y1, y2]

# 测试
lb = [-5, -5]
ub = [5, 5]
dim = 2
search_agents_no = 30
max_iter = 200
alpha_pos, alpha_score = GWO_multi_obj_search(test_func, lb, ub, dim, search_agents_no, max_iter)
print("优化结果：")
print("最优位置：", alpha_pos)
print("最优目标值：", alpha_score)

在这个示例中，我们定义了一个测试函数 `test_func`，它有两个目标值。然后我们使用 GWO 多目标算法寻找该函数的 Pareto 前沿。在 `GWO_multi_obj_search` 函数中，我们先初始化灰狼种群，并按照算法的迭代方式进行更新。最后返回 Pareto 前沿上的最优解和对应的目标值。