Python遗传算法求三角函数最小值

Python遗传算法是一种模拟自然选择过程的优化方法，它通常用于解决复杂优化问题，包括求解数学函数的最小值。对于三角函数如正弦、余弦等的最小值，可以设计成一个问题实例：

首先，你需要定义适应度函数，这里我们可以用三角函数的绝对值作为目标，因为你想找到其取最小值的地方。例如，假设我们想找`f(x) = |sin(x)|`的最小值，那么适应度函数可以设置为`fitness(x) = abs(sin(x))`。

import numpy as np
from scipy.optimize import minimize
from deap import base, creator, tools

# 创建遗传算法基础结构
creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)

def eval_fitness(individual):
    x = individual[0]
    return abs(np.sin(x)), 

toolbox = base.Toolbox()
toolbox.register("attr_float", np.random.uniform, -np.pi, np.pi)
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_float, n=1)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)

toolbox.register("evaluate", eval_fitness)
toolbox.register("mate", tools.cxTwoPoint)
toolbox.register("mutate", tools.mutGaussian, mu=0, sigma=0.1, indpb=0.05)
toolbox.register("select", tools.selTournament, tournsize=3)

# 遗传算法核心部分
def main():
    pop = toolbox.population(n=50)
    hof = tools.HallOfFame(1)
    stats = tools.Statistics(lambda ind: ind.fitness.values)
    stats.register("avg", np.mean)
    stats.register("min", np.min)
    
    for gen in range(100):  # 迭代次数
        offspring = toolbox.select(pop, len(pop))
        offspring = [toolbox.clone(ind) for ind in offspring]

        for child1, child2 in zip(offspring[::2], offspring[1::2]):
            if np.random.rand() < 0.7:
                toolbox.mate(child1, child2)
                del child1.fitness.values
                del child2.fitness.values

        for mutant in offspring:
            if np.random.rand() < 0.2:
                toolbox.mutate(mutant)
                del mutant.fitness.values

        invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
        fitnesses = map(toolbox.evaluate, invalid_ind)
        for ind, fit in zip(invalid_ind, fitnesses):
            ind.fitness.values = fit

        pop[:] = offspring
        hof.update(pop)

    best_solution = hof[0][0]  # 返回当前最优解x值
    min_value = abs(np.sin(best_solution))  # 最小值

    print(f"Best solution after {gen} generations: {best_solution}, with minimum value: {min_value}")

if __name__ == "__main__":
    main()

运行这段代码后，你会得到`|sin(x)|`的一个近似最小值。注意这只是一个简化示例，实际应用可能需要调整参数、种群大小和其他细节。