使用遗传算法 - 函数最优解计算相关代码，求解f(x)在区间 [0,5] 上的最大值:f(x)=xsin(10x)+xcos(2x)

遗传算法是一种基于自然选择原理的优化搜索算法，通常用于解决复杂函数的全局优化问题。在Python中，可以使用`deap`库来实现遗传算法寻找函数`f(x)`= `x * sin(10*x) + x * cos(2*x)`在区间[0, 5]上的最大值。以下是一个简化的示例：

import numpy as np
from deap import base, creator, tools

# 定义函数 f(x)
def fitness_function(solution):
    x = solution[0]
    return -solution[0] * np.sin(10 * x) - solution[0] * np.cos(2 * x)

# 初始化遗传算法参数
creator.create("FitnessMax", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMax)

toolbox = base.Toolbox()
toolbox.register("attr_float", lambda: np.random.uniform(0, 5))
toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attr_float, n=1)
toolbox.register("population", tools.initRepeat, list, toolbox.individual)

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

# 设置其他算法参数，如种群大小、代数等
POPULATION_SIZE = 100
MAX_GENERATIONS = 1000

pop = toolbox.population(n=POPULATION_SIZE)
hof = tools.HallOfFame(1) # 保存最佳个体

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

    # 遗传操作
    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() < 0.1:
            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
    best_solution = hof.items[0] if hof else None

print(f"经过{gen+1}代迭代，找到的最大值约为 {best_solution[0]:.4f}")