### 优化参数算法的对比与实现 除了鲸鱼优化算法（WOA）外，还有多种元启发式优化算法可以用于参数优化。以下是几种常见的算法及其Python实现： #### 1. 遗传算法（Genetic Algorithm, GA） 遗传算法是一种基于自然选择和遗传机制的搜索优化方法。它通过模拟生物进化过程中的选择、交叉和变异操作来寻找最优解。 ```python import numpy as np def genetic_algorithm(pop_size, fitness_func, bounds, generations, mutation_rate): population = np.random.uniform(bounds[0], bounds[1], (pop_size, len(bounds[0]))) for generation in range(generations): # 计算适应度 fitness = np.array([fitness_func(ind) for ind in population]) # 选择 parents = population[np.argsort(fitness)[-int(pop_size / 2):]] offspring = [] for _ in range(pop_size - len(parents)): parent1, parent2 = np.random.choice(parents, size=2) child = (parent1 + parent2) / 2 # 简单交叉 # 变异 if np.random.rand() < mutation_rate: child += np.random.normal(0, 0.1, size=len(child)) offspring.append(child) population = np.vstack((parents, offspring)) best_individual = population[np.argmax([fitness_func(ind) for ind in population])] return best_individual # 示例目标函数 def fitness_func(x): return -np.sum(np.power(x, 2)) # 最小化平方和 bounds = [np.array([-5, -5]), np.array([5, 5])] result = genetic_algorithm(pop_size=50, fitness_func=fitness_func, bounds=bounds, generations=100, mutation_rate=0.1) print("遗传算法结果:", result) ``` #### 2. 粒子群优化算法（Particle Swarm Optimization, PSO） 粒子群优化算法是一种基于群体智能的优化算法，其灵感来源于鸟群觅食行为。每个粒子在搜索空间中移动，并根据自身经验和群体经验调整位置。 ```python import numpy as np def pso(fitness_func, bounds, particles, iterations, w=0.8, c1=1.5, c2=1.5): n_vars = len(bounds[0]) positions = np.random.uniform(bounds[0], bounds[1], (particles, n_vars)) velocities = np.random.uniform(-1, 1, (particles, n_vars)) personal_best_positions = positions.copy() personal_best_fitness = np.array([fitness_func(pos) for pos in positions]) global_best_position = personal_best_positions[np.argmin(personal_best_fitness)] for _ in range(iterations): r1, r2 = np.random.rand(particles, n_vars), np.random.rand(particles, n_vars) velocities = w * velocities + c1 * r1 * (personal_best_positions - positions) + c2 * r2 * (global_best_position - positions) positions += velocities current_fitness = np.array([fitness_func(pos) for pos in positions]) better_indices = current_fitness < personal_best_fitness personal_best_positions[better_indices] = positions[better_indices] personal_best_fitness[better_indices] = current_fitness[better_indices] global_best_position = personal_best_positions[np.argmin(personal_best_fitness)] return global_best_position # 示例目标函数 def fitness_func(x): return np.sum(np.power(x, 2)) bounds = [np.array([-5, -5]), np.array([5, 5])] result = pso(fitness_func, bounds, particles=30, iterations=100) print("粒子群优化算法结果:", result) ``` #### 3. 差分进化算法（Differential Evolution, DE） 差分进化算法是一种基于种群的优化算法，通过种群个体之间的差异向量进行搜索，具有较强的全局搜索能力。 ```python import numpy as np def differential_evolution(fitness_func, bounds, pop_size, max_iter, F=0.8, CR=0.9): dimensions = len(bounds[0]) population = np.random.uniform(bounds[0], bounds[1], (pop_size, dimensions)) fitness = np.array([fitness_func(ind) for ind in population]) for _ in range(max_iter): for i in range(pop_size): indices = [idx for idx in range(pop_size) if idx != i] a, b, c = population[np.random.choice(indices, 3, replace=False)] mutant = a + F * (b - c) trial = population[i].copy() j_rand = np.random.randint(dimensions) for j in range(dimensions): if np.random.rand() < CR or j == j_rand: trial[j] = mutant[j] trial_fitness = fitness_func(trial) if trial_fitness < fitness[i]: population[i] = trial fitness[i] = trial_fitness best_idx = np.argmin(fitness) return population[best_idx] # 示例目标函数 def fitness_func(x): return np.sum(np.power(x, 2)) bounds = [np.array([-5, -5]), np.array([5, 5])] result = differential_evolution(fitness_func, bounds, pop_size=20, max_iter=100) print("差分进化算法结果:", result) ``` 上述三种算法均具有各自的特点和适用场景。遗传算法适合解决离散优化问题[^2]；粒子群优化算法在连续优化问题中表现优异[^3]；差分进化算法则在高维复杂优化问题中表现出色[^4]。