遗传算法最值问题python代码

遗传算法是一种优化算法，用于解决最值问题。下面是一个简单的遗传算法的 Python 代码示例，用于求解一个目标函数的最大值。

import random

# 目标函数
def objective_function(x):
    return -x**2 + 4

# 初始化种群
def initialize_population(population_size, num_variables):
    population = []
    for _ in range(population_size):
        chromosome = [random.randint(0, 1) for _ in range(num_variables)]
        population.append(chromosome)
    return population

# 计算适应度
def fitness(chromosome):
    x = decode_chromosome(chromosome)
    return objective_function(x)

# 解码染色体得到实际数值
def decode_chromosome(chromosome):
    x = 0
    for i in range(len(chromosome)):
        x += chromosome[i] * (2**i)
    return x

# 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 mutation(chromosome, mutation_rate):
    mutated_chromosome = []
    for gene in chromosome:
        if random.random() < mutation_rate:
            mutated_gene = 1 - gene
        else:
            mutated_gene = gene
        mutated_chromosome.append(mutated_gene)
    return mutated_chromosome

# 遗传算法主函数
def genetic_algorithm(population_size, num_variables, num_generations):
    population = initialize_population(population_size, num_variables)
    
    for _ in range(num_generations):
        # 计算适应度
        fitness_values = [fitness(chromosome) for chromosome in population]
        
        # 选择操作
        selected_indices = random.choices(range(population_size), weights=fitness_values, k=2)
        parent1 = population[selected_indices[0]]
        parent2 = population[selected_indices[1]]
        
        # 交叉操作
        child1, child2 = crossover(parent1, parent2)
        
        # 变异操作
        child1 = mutation(child1, mutation_rate=0.01)
        child2 = mutation(child2, mutation_rate=0.01)
        
        # 更新种群
        population[selected_indices[0]] = child1
        population[selected_indices[1]] = child2
    
    # 找到最优解
    best_chromosome = max(population, key=fitness)
    best_solution = decode_chromosome(best_chromosome)
    best_fitness = fitness(best_chromosome)
    
    return best_solution, best_fitness

# 示例运行
best_solution, best_fitness = genetic_algorithm(population_size=100, num_variables=4, num_generations=50)
print("最优解:", best_solution)
print("最优解的适应度:", best_fitness)