以下是两个使用Python实现遗传算法的简单示例： ### 示例一：解决简单整数优化问题 此示例用于解决找到使函数$f(x) = x^2$最小的整数$x$（$x$范围为0到7的整数）的问题，用于展示遗传算法的基本概念[^2]。 ```python import random # 目标函数 def fitness(x): return x**2 # 初始化种群 def initialize_population(pop_size): return [random.randint(0, 7) for _ in range(pop_size)] # 选择操作 def selection(population): fitness_scores = [fitness(x) for x in population] total_fitness = sum(fitness_scores) probabilities = [score / total_fitness for score in fitness_scores] selected_index = random.choices(range(len(population)), weights=probabilities)[0] return population[selected_index] # 交叉操作 def crossover(parent1, parent2): # 简单交叉，这里只是随机选择一个父代 return random.choice([parent1, parent2]) # 变异操作 def mutate(child, mutation_rate): if random.random() < mutation_rate: return random.randint(0, 7) return child # 遗传算法主函数 def genetic_algorithm(pop_size, generations, mutation_rate): population = initialize_population(pop_size) for _ in range(generations): new_population = [] for _ in range(pop_size): parent1 = selection(population) parent2 = selection(population) child = crossover(parent1, parent2) child = mutate(child, mutation_rate) new_population.append(child) population = new_population best_solution = min(population, key=fitness) return best_solution # 运行遗传算法 pop_size = 20 generations = 50 mutation_rate = 0.1 result = genetic_algorithm(pop_size, generations, mutation_rate) print(f"使函数 f(x) = x^2 最小的整数 x 是: {result}") ``` ### 示例二：求解函数$y = x^2$的最大值 此示例假设需要求解函数$y = x^2$的最大值，解决方案是一个长度为`chromosome_length`的一维数组，每个元素代表一个基因，取值范围为0到9。算法的参数包括种群大小、交叉率、变异率和迭代次数等[^3]。 ```python import random # 目标函数 def fitness(chromosome): x = int(''.join(map(str, chromosome))) return x ** 2 # 初始化种群 def initialize_population(pop_size, chromosome_length): return [[random.randint(0, 9) for _ in range(chromosome_length)] for _ in range(pop_size)] # 选择操作 def selection(population): fitness_scores = [fitness(chromosome) for chromosome in population] total_fitness = sum(fitness_scores) probabilities = [score / total_fitness for score in fitness_scores] selected_index = random.choices(range(len(population)), weights=probabilities)[0] return population[selected_index] # 交叉操作 def crossover(parent1, parent2): crossover_point = random.randint(1, len(parent1) - 1) child1 = parent1[:crossover_point] + parent2[crossover_point:] child2 = parent2[:crossover_point] + parent1[crossover_point:] return child1, child2 # 变异操作 def mutate(chromosome, mutation_rate): for i in range(len(chromosome)): if random.random() < mutation_rate: chromosome[i] = random.randint(0, 9) return chromosome # 遗传算法主函数 def genetic_algorithm(pop_size, generations, chromosome_length, crossover_rate, mutation_rate): population = initialize_population(pop_size, chromosome_length) for _ in range(generations): new_population = [] while len(new_population) < pop_size: if random.random() < crossover_rate: parent1 = selection(population) parent2 = selection(population) child1, child2 = crossover(parent1, parent2) child1 = mutate(child1, mutation_rate) child2 = mutate(child2, mutation_rate) new_population.extend([child1, child2]) else: individual = selection(population) individual = mutate(individual, mutation_rate) new_population.append(individual) population = new_population[:pop_size] best_solution = max(population, key=fitness) best_value = fitness(best_solution) print(f"最佳染色体: {best_solution}") print(f"最大值: {best_value}") # 运行遗传算法 pop_size = 50 generations = 100 chromosome_length = 3 crossover_rate = 0.8 mutation_rate = 0.1 genetic_algorithm(pop_size, generations, chromosome_length, crossover_rate, mutation_rate) ```