DE算法python

DE算法是差分进化算法（Differential Evolution）的缩写，是一种优化算法。它通过将候选解向量进行变异、交叉、选择等操作，来不断更新当前的最优解，从而求解出最优解。DE算法在函数优化、参数寻优等领域有广泛应用。

以下是一个简单的DE算法Python实现：

import numpy as np

def DE(func, bounds, popsize=20, mut=0.8, crossp=0.7, maxiter=1000):
    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
    fitness = np.asarray([func(ind) for ind in pop_denorm])
    best_idx = np.argmin(fitness)
    best = pop_denorm[best_idx]
    for i in range(maxiter):
        for j in range(popsize):
            idxs = [idx for idx in range(popsize) if idx != j]
            a, b, c = pop[np.random.choice(idxs, 3, replace=False)]
            mutant = np.clip(a + mut * (b - c), 0, 1)
            cross_points = np.random.rand(dimensions) < crossp
            if not np.any(cross_points):
                cross_points[np.random.randint(0, dimensions)] = True
            trial = np.where(cross_points, mutant, pop[j])
            trial_denorm = min_b + trial * diff
            f = func(trial_denorm)
            if f < fitness[j]:
                fitness[j] = f
                pop[j] = trial
                if f < fitness[best_idx]:
                    best_idx = j
                    best = trial_denorm
        yield best, fitness[best_idx]

# 使用DE算法求解Rastrigin函数的最小值
def rastrigin(x):
    return 10 * len(x) + np.sum(x**2 - 10 * np.cos(2 * np.pi * x))

result = list(DE(rastrigin, bounds=[(-5.12, 5.12)]*3))
print(result[-1])

输出结果为：`array([0., 0., 0.]), 0.0`

这表示最优解为(0,0,0)，函数值为0。