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生物进化原理的全局优化搜索方法，常用于解决复杂的优化问题。对于给定的函数 f(x) = x*sin(10x) + x*cos(2x)，我们可以通过遗传算法模拟种群的演化过程来找到这个函数在区间 [0, 5] 内的最大值。

以下是使用 Python 和 `scipy` 库实现遗传算法的基本步骤：

import numpy as np
from scipy.optimize import differential_evolution
import math

# 定义目标函数
def fitness_function(x):
    return x * np.sin(10 * x) + x * np.cos(2 * x)

# 设置搜索范围、种群大小和迭代次数等参数
lower_bound = 0
upper_bound = 5
population_size = 100
generations = 1000

# 初始化随机种群
def generate_population(population_size, lower_bound, upper_bound):
    return np.random.uniform(lower_bound, upper_bound, population_size)

# 适应度函数评估
def evaluate_fitness(individual):
    return fitness_function(individual[0])

# 遗传操作（选择、交叉、变异）
def genetic_operators(population, offspring_size):
    # ... (这里可以添加选择、交叉和变异的具体实现)
    pass

# 主遗传算法循环
def genetic_algorithm():
    population = generate_population(population_size, lower_bound, upper_bound)
    best_solution = None
    for _ in range(generations):
        offspring = genetic_operators(population, int(population_size / 2))
        new_population = np.concatenate((population, offspring))

        # 更新最佳解
        if best_solution is None or evaluate_fitness(new_population[-1]) > evaluate_fitness(best_solution):
            best_solution = new_population[-1]

        # 更新种群
        population = new_population

    return best_solution, fitness_function(best_solution[0])

best_x, max_value = genetic_algorithm()
print(f"最大值：{max_value:.4f}，对应的 x 值：{best_x:.4f}")