遗传算法求解函数最小值的python实现

遗传算法是一种模拟自然选择和遗传机制的优化搜索技术，用于解决复杂优化问题。在Python中，我们可以使用`deap`库来实现遗传算法，它提供了一个高级API来处理这个问题。

以下是一个简单的遗传算法求解函数最小值的Python示例，假设我们有一个需要最小化的函数`f(x)`：

import random
from deap import base, creator, tools

# 定义问题函数和适应度函数
def fitness_function(solution):
    # 这里替换为你要优化的实际函数，比如 f = x**2 + y**2
    return - solution[1]**2  # 假设我们要最小化x和y的平方和

# 创建遗传算法的环境
creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)

toolbox = base.Toolbox()
toolbox.register("attr_float", random.uniform, -10.0, 10.0)
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_float, n=2)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)

toolbox.register("evaluate", fitness_function)
toolbox.register("mate", tools.cxTwoPoint)  # 随机交叉操作
toolbox.register("mutate", tools.mutGaussian, mu=0, sigma=1, indpb=0.1)  # 高斯变异
toolbox.register("select", tools.selTournament, tournsize=3)  # 择优竞赛

def main(population_size, generations):
    pop = toolbox.population(n=population_size)
    hof = tools.HallOfFame(1)  # 保存最佳解决方案

    for gen in range(generations):
        offspring = toolbox.select(pop, len(pop))
        offspring = [toolbox.clone(ind) for ind in offspring]

        # 交叉和变异
        for child1, child2 in zip(offspring[::2], offspring[1::2]):
            if random.random() < 0.5:
                toolbox.mate(child1, child2)
                del child1.fitness.values
                del child2.fitness.values

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

        # 评估新个体的适应度
        invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
        fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
        for ind, fit in zip(invalid_ind, fitnesses):
            ind.fitness.values = fit

        pop[:] = offspring

        # 保存当前最佳解
        best_ind = tools.selBest(pop, 1)[0]
        hof.update([best_ind])

    return hof[0]  # 返回最终找到的最佳解

# 调用主函数并设置参数
best_solution = main(population_size=100, generations=100)
print(f"最优解：{best_solution} (fitness={fitness_function(best_solution)})")