【机器学习|学习笔记】遗传算法（Genetic Algorithm, GA）的起源、发展、应用和未来前景！并附实现代码。（二）-优快云博客

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【机器学习|学习笔记】遗传算法（Genetic Algorithm, GA）的起源、发展、应用和未来前景！并附实现代码。（二）

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【机器学习|学习笔记】遗传算法（Genetic Algorithm, GA）的起源、发展、应用和未来前景！并附实现代码。（二）

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遗传算法的Python实现

下面是一个简单的遗传算法实现，用于求解一个简单的数学优化问题，目标是最大化 $f(x) = x^2$ ，在区间 $[0, 31]$ 内。

import random

# 目标函数：f(x) = x^2
def fitness(x):
    return x**2

# 二进制编码解码
def decode(binary):
    return int(binary, 2)

def encode(x, length=5):
    return format(x, f"0{length}b")

# 选择操作：轮盘赌选择
def selection(population):
    total_fitness = sum(fitness(decode(individual)) for individual in population)
    pick = random.uniform(0, total_fitness)
    current = 0
    for individual in population:
        current += fitness(decode(individual))
        if current > pick:
            return individual

# 交叉操作：单点交叉
def crossover(parent1, parent2):
    crossover_point = random.randint(1, len(parent1)-1)
    offspring1 = parent1[:crossover_point] + parent2[crossover_point:]
    offspring2 = parent2[:crossover_point] + parent1[crossover_point:]
    return offspring1, offspring2

# 变异操作：位翻转
def mutation(offspring, mutation_rate=0.01):
    mutated = list(offspring)
    for i in range(len(mutated)):
        if random.random() < mutation_rate:
            mutated[i] = '1' if mutated[i] == '0' else '0'
    return ''.join(mutated)

# 主遗传算法函数
def genetic_algorithm(population_size=10, generations=100, mutation_rate=0.01):
    population = [encode(random.randint(0, 31)) for _ in range(population_size)]
    
    for generation in range(generations):
        new_population = []
        for _ in range(population_size//2):
            parent1 = selection(population)
            parent2 = selection(population)
            offspring1, offspring2 = crossover(parent1, parent2)
            new_population.append(mutation(offspring1, mutation_rate))
            new_population.append(mutation(offspring2, mutation_rate))
        
        population = new_population
        best_individual = max(population, key=lambda ind: fitness(decode(ind)))
        print(f"Generation {generation+1}: Best fitness = {fitness(decode(best_individual))}, x = {decode(best_individual)}")

    return population

# 运行遗传算法
genetic_algorithm(population_size=20, generations=50, mutation_rate=0.05)