灰狼优化算法GWO文章复现 复现内容包括:改进算法实现、23个基准测试函数、改进策略画图分析、与GWO等对比等。 代码基本上每一步都有注释非常易懂代码质量极高便于新手学习和理解。嘿各位小伙伴们今天来聊聊灰狼优化算法GWO文章的复现这可是个很有趣的话题尤其是对于想深入了解优化算法的新手们绝对是一次超有价值的学习之旅。一、改进算法实现灰狼优化算法模拟了灰狼群体的狩猎行为。在自然界中灰狼群体有着严格的等级制度分别是α、β、δ 和 ω 狼。α 狼是领导者负责决策β 狼辅助 α 狼δ 狼听从 α 和 β 的指挥ω 狼则是群体中地位最低的。下面咱来看下基础 GWO 算法的核心代码框架以 Python 为例import numpy as np # 目标函数这里以一个简单的单峰函数为例 def objective_function(x): return np.sum(x ** 2) # GWO 算法实现 def gwo(pop_size, dim, max_iter, lb, ub): # 初始化灰狼位置 wolves np.random.uniform(lb, ub, (pop_size, dim)) fitness np.array([objective_function(w) for w in wolves]) # 初始化最优解 alpha_wolf wolves[np.argmin(fitness)] alpha_fitness np.min(fitness) beta_wolf alpha_wolf.copy() beta_fitness alpha_fitness delta_wolf alpha_wolf.copy() delta_fitness alpha_fitness a 2 for t in range(max_iter): a 2 - t * (2 / max_iter) # 线性递减的收敛因子 for i in range(pop_size): r1 np.random.rand() r2 np.random.rand() A1 2 * a * r1 - a C1 2 * r2 D_alpha np.abs(C1 * alpha_wolf - wolves[i]) X1 alpha_wolf - A1 * D_alpha r1 np.random.rand() r2 np.random.rand() A2 2 * a * r1 - a C2 2 * r2 D_beta np.abs(C2 * beta_wolf - wolves[i]) X2 beta_wolf - A2 * D_beta r1 np.random.rand() r2 np.random.rand() A3 2 * a * r1 - a C3 2 * r2 D_delta np.abs(C3 * delta_wolf - wolves[i]) X3 delta_wolf - A3 * D_delta wolves[i] (X1 X2 X3) / 3 fitness np.array([objective_function(w) for w in wolves]) for i in range(pop_size): if fitness[i] alpha_fitness: alpha_fitness fitness[i] alpha_wolf wolves[i] elif fitness[i] beta_fitness: beta_fitness fitness[i] beta_wolf wolves[i] elif fitness[i] delta_fitness: delta_fitness fitness[i] delta_wolf wolves[i] return alpha_wolf, alpha_fitness在这段代码里objective_function定义了我们要优化的目标函数这里是一个简单的平方和函数。gwo函数则实现了 GWO 算法的主体。一开始随机初始化灰狼的位置然后在每次迭代中根据收敛因子a和随机数r1、r2来更新灰狼的位置不断向最优解靠近。灰狼优化算法GWO文章复现 复现内容包括:改进算法实现、23个基准测试函数、改进策略画图分析、与GWO等对比等。 代码基本上每一步都有注释非常易懂代码质量极高便于新手学习和理解。而改进算法可能会从多个方面入手比如改变收敛因子的更新方式或者引入新的机制避免算法陷入局部最优。假设我们对收敛因子进行非线性调整代码可能会这样改# 改进的 GWO 算法实现 def improved_gwo(pop_size, dim, max_iter, lb, ub): # 初始化灰狼位置 wolves np.random.uniform(lb, ub, (pop_size, dim)) fitness np.array([objective_function(w) for w in wolves]) # 初始化最优解 alpha_wolf wolves[np.argmin(fitness)] alpha_fitness np.min(fitness) beta_wolf alpha_wolf.copy() beta_fitness alpha_fitness delta_wolf alpha_wolf.copy() delta_fitness alpha_fitness for t in range(max_iter): a 2 * np.exp(-(4 * t / max_iter) ** 2) # 非线性收敛因子 for i in range(pop_size): r1 np.random.rand() r2 np.random.rand() A1 2 * a * r1 - a C1 2 * r2 D_alpha np.abs(C1 * alpha_wolf - wolves[i]) X1 alpha_wolf - A1 * D_alpha r1 np.random.rand() r2 np.random.rand() A2 2 * a * r1 - a C2 2 * r2 D_beta np.abs(C2 * beta_wolf - wolves[i]) X2 beta_wolf - A2 * D_beta r1 np.random.rand() r2 np.random.rand() A3 2 * a * r1 - a C3 2 * r2 D_delta np.abs(C3 * delta_wolf - wolves[i]) X3 delta_wolf - A3 * D_delta wolves[i] (X1 X2 X3) / 3 fitness np.array([objective_function(w) for w in wolves]) for i in range(pop_size): if fitness[i] alpha_fitness: alpha_fitness fitness[i] alpha_wolf wolves[i] elif fitness[i] beta_fitness: beta_fitness fitness[i] beta_wolf wolves[i] elif fitness[i] delta_fitness: delta_fitness fitness[i] delta_wolf wolves[i] return alpha_wolf, alpha_fitness这里我们把收敛因子a改成了一个非线性递减的形式这样可能会让算法在前期有更好的全局搜索能力后期有更好的局部搜索能力。二、23 个基准测试函数基准测试函数是检验优化算法性能的重要工具。这 23 个函数涵盖了单峰、多峰等不同特性的函数。以Sphere函数为例它是一个简单的单峰函数用于测试算法的基本收敛能力。def sphere(x): return np.sum(x ** 2)还有像Rastrigin函数这是一个典型的多峰函数具有许多局部最优解对算法跳出局部最优的能力是个挑战。def rastrigin(x): A 10 n len(x) return A * n np.sum(x ** 2 - A * np.cos(2 * np.pi * x))在实际复现中我们会把改进后的 GWO 算法应用到这些基准测试函数上通过记录每次运行的结果来评估算法在不同特性函数上的性能。三、改进策略画图分析画图分析能让我们更直观地看到改进策略的效果。我们可以绘制算法在每次迭代中的最优适应度值变化曲线。比如用matplotlib库来绘制改进前后 GWO 算法在Sphere函数上的收敛曲线。import matplotlib.pyplot as plt # 运行基础 GWO 算法 pop_size 50 dim 2 max_iter 100 lb -100 ub 100 alpha_wolf, alpha_fitness gwo(pop_size, dim, max_iter, lb, ub) gwo_fitness_trace [alpha_fitness] # 运行改进的 GWO 算法 alpha_wolf_improved, alpha_fitness_improved improved_gwo(pop_size, dim, max_iter, lb, ub) improved_gwo_fitness_trace [alpha_fitness_improved] for t in range(1, max_iter): alpha_wolf, alpha_fitness gwo(pop_size, dim, t, lb, ub) gwo_fitness_trace.append(alpha_fitness) alpha_wolf_improved, alpha_fitness_improved improved_gwo(pop_size, dim, t, lb, ub) improved_gwo_fitness_trace.append(alpha_fitness_improved) plt.plot(range(max_iter), gwo_fitness_trace, labelGWO) plt.plot(range(max_iter), improved_gwo_fitness_trace, labelImproved GWO) plt.xlabel(Iteration) plt.ylabel(Best Fitness) plt.title(Convergence Comparison on Sphere Function) plt.legend() plt.show()从这个图中我们可以清晰地看到改进后的 GWO 算法是否收敛得更快或者是否能达到更好的最优解。如果改进后的曲线下降得更快且最终的最优解更好那就说明我们的改进策略是有效的。四、与 GWO 等对比除了和自身改进前对比我们还会和其他优化算法进行对比比如粒子群优化算法PSO。# 粒子群优化算法PSO def pso(pop_size, dim, max_iter, lb, ub, w, c1, c2): particles np.random.uniform(lb, ub, (pop_size, dim)) velocities np.zeros((pop_size, dim)) pbest particles.copy() pbest_fitness np.array([objective_function(p) for p in particles]) gbest_index np.argmin(pbest_fitness) gbest pbest[gbest_index] gbest_fitness pbest_fitness[gbest_index] for t in range(max_iter): for i in range(pop_size): r1 np.random.rand(dim) r2 np.random.rand(dim) velocities[i] w * velocities[i] c1 * r1 * (pbest[i] - particles[i]) c2 * r2 * (gbest - particles[i]) particles[i] particles[i] velocities[i] particles[i] np.clip(particles[i], lb, ub) fitness np.array([objective_function(p) for p in particles]) for i in range(pop_size): if fitness[i] pbest_fitness[i]: pbest_fitness[i] fitness[i] pbest[i] particles[i] if pbest_fitness[i] gbest_fitness: gbest_fitness pbest_fitness[i] gbest pbest[i] return gbest, gbest_fitness然后我们把 GWO、改进后的 GWO 和 PSO 都应用到一系列基准测试函数上统计它们的最优解、平均解、收敛速度等指标进行全面对比。通过这样的对比能更清楚地看到改进后的 GWO 算法在性能上的优势和不足。好啦以上就是关于灰狼优化算法GWO文章复现的主要内容啦希望对大家理解和学习优化算法有所帮助大家可以自己动手实践下说不定还能想出更厉害的改进策略呢