灰狼优化 (GWO) 算法的实现

什么是灰狼优化算法？

灰狼优化算法是一种新兴的优化算法，基于狼群的社会行为进行优化搜索。

GWO算法流程

1. 初始化灰狼群，包括灰狼数量、检索空间边界等;
2. 每个灰狼根据目标函数值在检索空间内随机移动;
3. 灰狼进行适应度排序;
4. 更新灰狼猎物之间的位置，使每个灰狼向最优解移动。
5. 重复2-4步骤, 直到达到预定的迭代次数或者满足停止条件。

GWO算法Python实现

import numpy as np

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

# 初始化灰狼群
def init_wolves(num_wolves, x_min, x_max, dim):
    wolves = []
    for i in range(num_wolves):
        wolf_pos = np.random.uniform(x_min, x_max, dim)
        wolves.append({'position': wolf_pos, 'cost': f(wolf_pos)})
    return wolves

# 获取最优解
def get_best_wolf(wolves):
    sorted_wolves = sorted(wolves, key=lambda k: k['cost'])
    best_wolf = sorted_wolves[0]
    return best_wolf

# 更新猎物位置
def update_prey_position(wolf, best_wolf, a):
    x_pre = wolf['position']
    r1 = np.random.rand(len(x_pre))
    r2 = np.random.rand(len(x_pre))
    A = 2 * a * r1 - a
    C = 2 * r2
    D = np.abs(C * best_wolf['position'] - x_pre)
    x_new = np.clip(best_wolf['position'] - A*D, -1, 1)
    return x_new

# 更新猎人位置
def update_hunter_position(wolf, wolves, A, alpha):
    x_hunter = wolf['position']
    idx_wolves = [i for i in range(len(wolves))]
    idx_wolves.remove(wolves.index(wolf))
    leader_wolf = wolves[np.argmin([w['cost'] for w in wolves])]
    x_leader = leader_wolf['position']
    D_alpha = np.abs(alpha * x_leader - x_hunter)
    A_ = 2 * A * np.random.rand(len(x_hunter)) - A
    x_new = np.clip(x_leader - A_ * D_alpha, -1, 1)
    return x_new

# 灰狼优化算法
def GWO(num_iter, num_wolves, x_min, x_max, dim):
    alpha = 1
    a = 2 * alpha
    wolves = init_wolves(num_wolves, x_min, x_max, dim)
    best_wolf = get_best_wolf(wolves)
    for i in range(num_iter):
        for wolf in wolves:
            x_pre = wolf['position']
            if wolf == best_wolf:
                x_new = update_prey_position(wolf, best_wolf, a)
            else:
                x_new = update_hunter_position(wolf, wolves, a, alpha)
            cost_new = f(x_new)
            if cost_new < wolf['cost']:
                wolf['position'] = x_new.copy()
                wolf['cost'] = cost_new
        best_wolf = get_best_wolf(wolves)
    return best_wolf['position'], best_wolf['cost']

# Test GWO function
x_min, x_max, dim = -1, 1, 10
num_iter = 200
num_wolves = 30
best_pos, best_cost = GWO(num_iter, num_wolves, x_min, x_max, dim)
print(f"Best position: {best_pos}")
print(f"Best cost: {best_cost}")

结论

灰狼优化算法是一种新兴的优化算法，它是基于狼群的社会行为进行优化搜索。本文实现了灰狼优化算法，并使用一个简单的测试函数进行测试。该算法的性能表现表明它可以在多元函数优化问题中发挥作用。