布谷鸟搜索算法（Cuckoo Search，缩写 CS）是由剑桥大学杨新社教授和 S. 戴布于 2009 年提出的一种新兴启发算法，主要模拟布谷鸟的繁衍自然行为 [^1][^3][^4]。以下为一个简单的 Python 实现布谷鸟搜索算法的示例代码： ```python import numpy as np import random # 目标函数（这里以 Rastrigin 函数为例） def rastrigin(x): A = 10 n = len(x) return A * n + np.sum(x**2 - A * np.cos(2 * np.pi * x)) # 布谷鸟搜索算法 def cuckoo_search(nests, dim, max_iter, pa=0.25, alpha=1.0, beta=1.5): # 初始化鸟巢位置 nest_positions = np.random.uniform(-5.12, 5.12, (nests, dim)) nest_fitness = np.array([rastrigin(nest) for nest in nest_positions]) best_nest_index = np.argmin(nest_fitness) best_nest = nest_positions[best_nest_index] best_fitness = nest_fitness[best_nest_index] for _ in range(max_iter): # 生成新的解 new_nest_positions = np.copy(nest_positions) for i in range(nests): step_size = alpha * levy_flight(beta) new_nest_positions[i] += step_size * (nest_positions[random.randint(0, nests - 1)] - nest_positions[i]) new_nest_positions[i] = np.clip(new_nest_positions[i], -5.12, 5.12) new_nest_fitness = np.array([rastrigin(nest) for nest in new_nest_positions]) # 替换较差的解 for i in range(nests): if new_nest_fitness[i] < nest_fitness[i]: nest_positions[i] = new_nest_positions[i] nest_fitness[i] = new_nest_fitness[i] # 发现并替换部分较差的解 for i in range(nests): if random.random() < pa: nest_positions[i] = np.random.uniform(-5.12, 5.12, dim) nest_fitness[i] = rastrigin(nest_positions[i]) # 更新最优解 current_best_index = np.argmin(nest_fitness) if nest_fitness[current_best_index] < best_fitness: best_nest = nest_positions[current_best_index] best_fitness = nest_fitness[current_best_index] return best_nest, best_fitness # 莱维飞行函数 def levy_flight(beta): sigma_u = (np.math.gamma(1 + beta) * np.sin(np.pi * beta / 2) / (np.math.gamma((1 + beta) / 2) * beta * 2 ** ((beta - 1) / 2))) ** (1 / beta) sigma_v = 1 u = np.random.normal(0, sigma_u) v = np.random.normal(0, sigma_v) return u / (np.abs(v) ** (1 / beta)) # 参数设置 nests = 20 dim = 10 max_iter = 100 best_solution, best_value = cuckoo_search(nests, dim, max_iter) print("最优解:", best_solution) print("最优值:", best_value) ``` 此代码实现了布谷鸟搜索算法，以 Rastrigin 函数作为目标函数进行优化。代码包含了目标函数的定义、布谷鸟搜索算法的实现以及莱维飞行函数的实现。通过多次迭代，算法会不断更新鸟巢的位置，最终找到最优解。