用差分进化算法求解香蕉函数最小值的Python代码

以下是使用差分进化算法求解香蕉函数最小值的Python代码：

import numpy as np

# 定义香蕉函数
def banana(x):
    return (1-x[0])**2 + 100*(x[1]-x[0]**2)**2

# 定义差分进化算法
def differential_evolution(func, bounds, popsize=20, mutation=0.8, recombination=0.7, maxiter=1000):
    # 随机生成初始种群
    dimensions = len(bounds)
    pop = np.random.rand(popsize, dimensions)
    min_b, max_b = np.asarray(bounds).T
    diff = np.fabs(min_b - max_b)
    pop_denorm = min_b + pop * diff
    # 迭代优化
    for i in range(maxiter):
        # 变异操作
        mutant = pop[np.random.randint(0, popsize, popsize), :]
        for j in range(popsize):
            idxs = np.arange(popsize) != j
            a, b, c = mutant[np.random.choice(idxs, 3, replace=False)]
            mutant[j] = np.clip(a + mutation * (b - c), 0, 1)
        # 交叉操作
        cross_points = np.random.rand(popsize, dimensions) < recombination
        if not np.any(cross_points):
            cross_points[np.random.randint(0, popsize), np.random.randint(0, dimensions)] = True
        pop_new = np.where(cross_points, mutant, pop)
        # 选择操作
        pop_denorm_new = min_b + pop_new * diff
        scores = np.asarray([func(ind) for ind in pop_denorm])
        scores_new = np.asarray([func(ind) for ind in pop_denorm_new])
        idx = scores_new < scores
        pop[idx] = pop_new[idx]
    # 返回最优解和最优值
    return min_b + pop[np.argmin(scores)]

# 定义搜索范围
bounds = [(-10, 10), (-10, 10)]

# 调用差分进化算法求解最小值
result = differential_evolution(banana, bounds)

# 输出结果
print("最小值点：", result)
print("最小值：", banana(result))

在上述代码中，首先定义了香蕉函数 `banana(x)`，然后定义了差分进化算法 `differential_evolution()`，其中包括随机生成初始种群、变异操作、交叉操作和选择操作等步骤。最后定义了搜索范围并调用差分进化算法求解最小值，输出结果为最小值点和最小值。