给出SADE的python实现

SADE算法是DE算法的一种改进，通过策略自适应技术来提高DE算法的性能。下面是一个简单的SADE算法的Python实现：

import random
import numpy as np

def sade(popsize, bounds, maxiter, func, strategy=1, p=0.5, F=None):
    # 初始化参数
    num_params = len(bounds)
    pop = np.random.rand(popsize, num_params)
    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]

    # 迭代优化
    for i in range(maxiter):
        # 选择两个不同的个体作为parent
        p1, p2 = random.sample(range(popsize), 2)
        # 选择三个不同的个体作为mutation vectors
        idxs = [idx for idx in range(popsize) if idx not in (p1, p2)]
        a, b, c = pop[np.random.choice(idxs, 3, replace=False)]
        if strategy == 1:
            # DE/rand/1/bin策略
            mutant = a + F * (b - c)
        elif strategy == 2:
            # DE/current-to-best/1/bin策略
            mutant = pop[p1] + F * (best - pop[p1]) + F * (b - c)
        else:
            # DE/rand-to-best/1/bin策略
            mutant = a + F * (best - a) + F * (b - c)
        # 随机选择交叉点
        cross_points = np.random.rand(num_params) < p
        if not np.any(cross_points):
            cross_points[np.random.randint(0, num_params)] = True
        # 生成trial vector
        trial = np.where(cross_points, mutant, pop[p1])
        trial_denorm = min_b + trial * diff
        f = func(trial_denorm)
        # 选择个体替换
        if f < fitness[p1]:
            pop[p1] = trial
            fitness[p1] = f
            if f < fitness[best_idx]:
                best_idx = p1
                best = trial_denorm
        # 更新F
        if strategy == 1:
            F = np.clip(F + 0.001, 0.0, 1.0)
        elif strategy == 2:
            F = np.clip(F * 0.95, 0.0, 1.0)
        else:
            F = np.clip(F + 0.001, 0.0, 1.0)
            if random.random() < 0.1:
                strategy = random.choice([1, 2, 3])
        yield best, fitness[best_idx]

# 测试函数
def sphere(x):
    return sum(x**2)

# 运行SADE算法
popsize = 10
bounds = [(-5, 5)] * 10
maxiter = 1000
strategy = 1
p = 0.5
F = 0.5
for best, fitness in sade(popsize, bounds, maxiter, sphere, strategy, p, F):
    print("best: ", best, " fitness: ", fitness)

请注意，上面的代码只是一个简单的SADE算法示例，可能不是完全符合论文中描述的算法。如果你需要更多的参考资料，请参阅相关的文献或者开源科学计算库中的实现。