全局优化算法

import numpy as np

# 目标函数
def objective_function(x):
    return x**2

# 遗传算法主函数
def genetic_algorithm(pop_size, num_generations, mutation_rate):
    population = np.random.uniform(-10, 10, pop_size)
    
    for generation in range(num_generations):
        # 计算适应度
        fitness = np.array([1 / (1 + objective_function(x)) for x in population])
        
        # 选择
        selected_indices = np.random.choice(range(pop_size), size=pop_size, p=fitness/fitness.sum())
        selected_population = population[selected_indices]
        
        # 交叉
        offspring = []
        for i in range(0, pop_size, 2):
            parent1, parent2 = selected_population[i], selected_population[i+1]
            crossover_point = np.random.randint(1, len(parent1))
            child1 = np.concatenate((parent1[:crossover_point], parent2[crossover_point:]))
            child2 = np.concatenate((parent2[:crossover_point], parent1[crossover_point:]))
            offspring.extend([child1, child2])
        
        # 变异
        for i in range(pop_size):
            if np.random.rand() < mutation_rate:
                offspring[i] += np.random.normal(0, 1)
        
        population = np.array(offspring)
    
    best_solution = population[np.argmax(fitness)]
    return best_solution

# 运行遗传算法
best_solution = genetic_algorithm(pop_size=100, num_generations=100, mutation_rate=0.01)
print("Best solution found:", best_solution)