用遗传算法对公式进行力更新

import random
import numpy as np

# 目标函数
def objective_function(x):
    return x**2 + 4*x + 5

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

# 计算适应度
def calculate_fitness(population):
    fitness = []
    for chromosome in population:
        x = decode_chromosome(chromosome)
        f = objective_function(x)
        fitness.append(f)
    return fitness

# 解码染色体
def decode_chromosome(chromosome):
    x = 0
    for bit in chromosome:
        x = (x << 1) | bit
    return x - 127  # 假设解空间为[-128, 127]

# 选择操作
def selection(population, fitness):
    total_fitness = sum(fitness)
    probabilities = [f / total_fitness for f in fitness]
    selected_indices = np.random.choice(len(population), size=len(population), p=probabilities)
    selected_population = [population[i] for i in selected_indices]
    return selected_population

# 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):
    for i in range(len(chromosome)):
        if random.random() < mutation_rate:
            chromosome[i] = 1 - chromosome[i]
    return chromosome

# 遗传算法主函数
def genetic_algorithm(pop_size, chromosome_length, max_generations, crossover_rate, mutation_rate):
    population = initialize_population(pop_size, chromosome_length)
    for generation in range(max_generations):
        fitness = calculate_fitness(population)
        selected_population = selection(population, fitness)
        new_population = []
        while len(new_population) < pop_size:
            parent1, parent2 = random.sample(selected_population, 2)
            if random.random() < crossover_rate:
                child1, child2 = crossover(parent1, parent2)
                new_population.extend([child1, child2])
        for i in range(len(new_population)):
            new_population[i] = mutation(new_population[i], mutation_rate)
        population = new_population[:pop_size]
    best_chromosome = population[np.argmin(fitness)]
    best_x = decode_chromosome(best_chromosome)
    best_f = objective_function(best_x)
    return best_x, best_f

# 参数设置
pop_size = 100
chromosome_length = 8
max_generations = 100
crossover_rate = 0.8
mutation_rate = 0.1

# 运行遗传算法
best_x, best_f = genetic_algorithm(pop_size, chromosome_length, max_generations, crossover_rate, mutation_rate)
print(f"最优解: x = {best_x}, f(x) = {best_f}")