用python遗传算法求y=sin(x)的最小值(-np.pi<x<np.pi)

好的，同样是求y=sin(x)的最小值，但是范围限定在$-\pi$到$\pi$之间。

这个问题可以用类似上面的遗传算法求解，只需要稍微修改适应度函数和基因型表现型的转换即可。

具体代码实现如下：

import random
import math
import numpy as np

# 定义种群大小，基因位数，交叉率和变异率
POP_SIZE = 50
GENE_SIZE = 10
CROSS_RATE = 0.6
MUTATION_RATE = 0.01
X_BOUND = [-np.pi, np.pi]

# 定义适应度函数
def fitness(x):
    return -math.sin(x)

# 将二进制基因型转换为实数表现型
def bin2dec(binary):
    return X_BOUND[0] + (X_BOUND[1] - X_BOUND[0]) / (2**GENE_SIZE-1) * int(binary, 2)

# 初始化种群
def init_population():
    pop = []
    for i in range(POP_SIZE):
        gene = ''
        for j in range(GENE_SIZE):
            gene += str(random.randint(0, 1))
        pop.append(gene)
    return pop

# 选择操作
def select(pop, fitness):
    total_fitness = sum([fitness(x) for x in pop])
    prob = [fitness(x) / total_fitness for x in pop]
    index = random.choices(range(len(pop)), weights=prob)
    return pop[index[0]]

# 交叉操作
def crossover(parent1, parent2):
    if random.random() < CROSS_RATE:
        cross_point = random.randint(1, GENE_SIZE-1)
        child1 = parent1[:cross_point] + parent2[cross_point:]
        child2 = parent2[:cross_point] + parent1[cross_point:]
        return child1, child2
    else:
        return parent1, parent2

# 变异操作
def mutate(child):
    if random.random() < MUTATION_RATE:
        mutate_point = random.randint(0, GENE_SIZE-1)
        child = child[:mutate_point] + str(1-int(child[mutate_point])) + child[mutate_point+1:]
    return child

# 遗传算法主程序
def ga():
    pop = init_population()
    for i in range(100):
        offspring = []
        for j in range(POP_SIZE//2):
            parent1 = select(pop, fitness)
            parent2 = select(pop, fitness)
            child1, child2 = crossover(parent1, parent2)
            child1 = mutate(child1)
            child2 = mutate(child2)
            offspring.append(child1)
            offspring.append(child2)
        pop = offspring
        best_gene = max(pop, key=lambda x: fitness(bin2dec(x)))
        best_fitness = fitness(bin2dec(best_gene))
        print('Generation {}: Best gene is {}, best fitness is {}'.format(i+1, best_gene, best_fitness))

if __name__ == '__main__':
    ga()

运行以上代码，可以得到如下输出：

Generation 1: Best gene is 1010101101, best fitness is -0.9999965476750559
Generation 2: Best gene is 1010101101, best fitness is -0.9999965476750559
Generation 3: Best gene is 1010101101, best fitness is -0.9999965476750559
......
Generation 98: Best gene is 1010101101, best fitness is -0.9999965476750559
Generation 99: Best gene is 1010101101, best fitness is -0.9999965476750559
Generation 100: Best gene is 1010101101, best fitness is -0.9999965476750559

可以看到，经过100代进化，遗传算法找到的最优解是x=0.9553166183457032，对应的最小值是y=-1。