给出遗传算法求解函数f(x,y)=x^2+y^2的最大值的代码

遗传算法是一种模拟自然选择和遗传机制的优化搜索算法，它通常用于解决复杂问题的全局最优解。下面是一个简单的Python代码示例，使用DEAP库（Distributed Evolutionary Algorithms in Python）实现遗传算法来寻找函数f(x, y) = x^2 + y^2的最大值。在这个例子中，我们将假设个体是由两个实数组成的列表，并且通过变异和交叉操作生成新一代。

from deap import base, creator, tools

# 定义函数和种群
creator.create("FitnessMax", base.Fitness, weights=(1.0,))
creator.create("Individual", list, fitness=creator.FitnessMax)

def eval_fitness(individual):
    x, y = individual
    return -abs(x**2 + y**2),  # 因为我们要找最大值，所以取负值

toolbox = base.Toolbox()

# 初始化参数
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", eval_fitness)
toolbox.register("mate", tools.cxTwoPoint)
toolbox.register("mutate", tools.mutGaussian, mu=0, sigma=1, indpb=0.1)
toolbox.register("select", tools.selTournament, tournsize=3)

def main():
    pop = toolbox.population(n=50)
    hof = tools.HallOfFame(1)
    stats = tools.Statistics(lambda ind: ind.fitness.values)
    stats.register("avg", numpy.mean)
    stats.register("std", numpy.std)
    stats.register("min", numpy.min)
    stats.register("max", numpy.max)

    for gen in range(100):  # 运行一定代数
        offspring = toolbox.select(pop, len(pop))
        offspring = [toolbox.clone(ind) for ind in offspring]

        # 变异和交叉操作
        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

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

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

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

        print(f"Generation {gen+1}: Best individual {hof[0]}, Fitness: {-hof[0].fitness.values[0]:.4f}")

if __name__ == "__main__":
    main()