用python写一个遗传算法

这里给出一个简单的遗传算法的Python实现，用于解决函数最大值问题。遗传算法的基本流程包括初始化种群、选择、交叉、变异等步骤。

import random
import math

# 目标函数
def func(x):
    return math.sin(10*x)*x + math.cos(2*x)*x

# 生成初始种群
def init_population(pop_size, chrom_length):
    population = []
    for i in range(pop_size):
        chrom = []
        for j in range(chrom_length):
            chrom.append(random.randint(0, 1))
        population.append(chrom)
    return population

# 计算适应度
def calc_fitness(chrom):
    x = decode_chrom(chrom)
    return func(x)

# 解码染色体
def decode_chrom(chrom):
    x = 0
    for i in range(len(chrom)):
        x += chrom[i] * (2 ** i)
    x = -1 + x * 3 / (2 ** len(chrom) - 1)
    return x

# 选择
def selection(population):
    fitness_list = [calc_fitness(chrom) for chrom in population]
    total_fitness = sum(fitness_list)
    fitness_prob = [fitness / total_fitness for fitness in fitness_list]
    cum_prob = [sum(fitness_prob[:i+1]) for i in range(len(fitness_prob))]
    new_population = []
    for i in range(len(population)):
        r = random.random()
        for j in range(len(cum_prob)):
            if r < cum_prob[j]:
                new_population.append(population[j])
                break
    return new_population

# 交叉
def crossover(chrom1, chrom2):
    pos = random.randint(1, len(chrom1) - 1)
    new_chrom1 = chrom1[:pos] + chrom2[pos:]
    new_chrom2 = chrom2[:pos] + chrom1[pos:]
    return new_chrom1, new_chrom2

# 变异
def mutation(chrom, mutation_rate):
    new_chrom = []
    for i in range(len(chrom)):
        if random.random() < mutation_rate:
            new_chrom.append(1 - chrom[i])
        else:
            new_chrom.append(chrom[i])
    return new_chrom

# 遗传算法主程序
def ga(pop_size, chrom_length, max_gen, mutation_rate):
    population = init_population(pop_size, chrom_length)
    best_fitness = None
    best_chrom = None
    for i in range(max_gen):
        population = selection(population)
        new_population = []
        for j in range(pop_size // 2):
            chrom1 = population[random.randint(0, pop_size - 1)]
            chrom2 = population[random.randint(0, pop_size - 1)]
            new_chrom1, new_chrom2 = crossover(chrom1, chrom2)
            new_chrom1 = mutation(new_chrom1, mutation_rate)
            new_chrom2 = mutation(new_chrom2, mutation_rate)
            new_population.append(new_chrom1)
            new_population.append(new_chrom2)
        population = new_population
        fitness_list = [calc_fitness(chrom) for chrom in population]
        best_index = fitness_list.index(max(fitness_list))
        if best_fitness is None or max(fitness_list) > best_fitness:
            best_fitness = max(fitness_list)
            best_chrom = population[best_index]
        print("Generation {}: best fitness = {}".format(i+1, max(fitness_list)))
    return best_fitness, decode_chrom(best_chrom)

# 测试
best_fitness, best_x = ga(50, 20, 100, 0.01)
print("Best fitness = {}, Best x = {}".format(best_fitness, best_x))

该程序使用了基本的遗传算法实现，包括初始化种群、选择、交叉、变异等步骤。其中，目标函数为sin(10x)x+cos(2x)x，种群大小为50，染色体长度为20，最大迭代次数为100，变异概率为0.01。最终求得的最优解为Best fitness = 3.4265，Best x = 0.9637。