scikit-opt是一个一个封装了7种启发式算法的 Python 代码库（差分进化算法、遗传算法、粒子群算法、模拟退火算法、蚁群算法、鱼群算法、免疫优化算法）。源码具有很大的学习价值。这篇文章主要是根据差分进化(DE)算法的原理解读一下源码。
DE算法及源码解读设函数，有三个未知解
def obj_func(p):
x1, x2, x3 = p
return x1 ** 2 + x2 ** 2 + x3 ** 2
初始解形状
self.X = None # shape = (size_pop, n_dim)
生成初始解 （种群）（DE继承类GeneticAlgorithmbase）lb, ub为x的上下限，新解为约束条件上下界内均匀分布的向量
class DE(GeneticAlgorithmbase):
def __init__(self, func, n_dim, F=0.5,
size_pop=50, max_iter=200, prob_mut=0.3,
lb=-1, ub=1,
constraint_eq=tuple(), constraint_ueq=tuple()):
super().__init__(func, n_dim, size_pop, max_iter, prob_mut,
constraint_eq=constraint_eq, constraint_ueq=constraint_ueq)
self.F = F
self.V, self.U = None, None
self.lb, self.ub = np.array(lb) * np.ones(self.n_dim), np.array(ub) * np.ones(self.n_dim)
self.crtbp()
def crtbp(self):
# create the population
self.X = np.random.uniform(low=self.lb, high=self.ub, size=(self.size_pop, self.n_dim))
return self.X
变异，产生新解向量V，如果V超出解的边界，保留原初始解。这里采用了最经典的变异方法，可以改进。
def mutation(self):
'''
V[i]=X[r1]+F(X[r2]-X[r3]),
where i, r1, r2, r3 are randomly generated
'''
X = self.X
# i is not needed,
# and TODO: r1, r2, r3 should not be equal
random_idx = np.random.randint(0, self.size_pop, size=(self.size_pop, 3))
r1, r2, r3 = random_idx[:, 0], random_idx[:, 1], random_idx[:, 2]
# 这里F用固定值，为了防止早熟，可以换成自适应值
self.V = X[r1, :] + self.F * (X[r2, :] - X[r3, :])
# the lower & upper bound still works in mutation
mask = np.random.uniform(low=self.lb, high=self.ub, size=(self.size_pop, self.n_dim))
self.V = np.where(self.V < self.lb, mask, self.V)
self.V = np.where(self.V > self.ub, mask, self.V)
return self.V
交叉操作，对初始解X和变异解V进行概率交叉，生成解向量U，这里的self.prob_mut为CR
def crossover(self):
'''
if rand < prob_crossover, use V, else use X
'''
mask = np.random.rand(self.size_pop, self.n_dim) < self.prob_mut
self.U = np.where(mask, self.V, self.X)
return self.U
选择操作，根据函数值大小选择是否保留U
def selection(self):
'''
greedy selection
'''
X = self.X.copy()
f_X = self.x2y().copy()
self.X = U = self.U
f_U = self.x2y()
self.X = np.where((f_X < f_U).reshape(-1, 1), X, U)
return self.X
迭代，继续变异，选择
def run(self, max_iter=None):
self.max_iter = max_iter or self.max_iter
for i in range(self.max_iter):
self.mutation()
self.crossover()
self.selection()
# record the best ones
generation_best_index = self.Y.argmin()
self.generation_best_X.append(self.X[generation_best_index, :].copy())
self.generation_best_Y.append(self.Y[generation_best_index])
self.all_history_Y.append(self.Y)
global_best_index = np.array(self.generation_best_Y).argmin()
self.best_x = self.generation_best_X[global_best_index]
self.best_y = self.func(np.array([self.best_x]))
return self.best_x, self.best_y
