Scipy BFGS求解30维CEC2013函数时精度损失问题求助

我正在使用Scipy的BFGS算法求解自行实现的CEC2013基准函数，但在30维情况下，Rotated Bent Cigar函数和Rotated Schaffers F7函数的求解效果极差，均出现精度损失问题。作为优化领域新手，已查阅大量资料仍无法解决，恳请帮助🙏

重现Rotated Bent Cigar问题 #

从Scipy导入BFGS后，使用np.ones(30)作为初始点(x0)，为避免结果出现nan，将gtol设置为1e-9：

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

fmin_bfgs(f3, np.ones(30), fprime=None, args=(), gtol=1e-9, norm=float('inf'), epsilon=math.sqrt(np.finfo(float).eps), maxiter=None, full_output=0, disp=1, retall=0, callback=None)

得到的输出 #

RuntimeWarning: overflow encountered in double_scalars
Y = Z[0]**2 + 1e6 * np.sum(Z[1:]**2) - 1200

RuntimeWarning: overflow encountered in square
Y = Z[0]**2 + 1e6 * np.sum(Z[1:]**2) - 1200

RuntimeWarning: invalid value encountered in subtract 
df = fun(x) - f0

Warning: Desired error not necessarily achieved due to precision loss.
     Current function value: 77457993654581510275072.000000
     Iterations: 28
     Function evaluations: 3524
     Gradient evaluations: 113

重现Rotated Schaffers F7问题 #

对于Rotated Schaffers F7，使用默认的gtol=1e-5：

fmin_bfgs(f7, np.ones(30), fprime=None, args=(), gtol=1e-5, norm=float('inf'), epsilon=math.sqrt(np.finfo(float).eps), maxiter=None, full_output=0, disp=1, retall=0, callback=None)

得到的输出 #

Warning: Desired error not necessarily achieved due to precision loss. Current function value: 2406912647990380032.000000 Iterations: 1 Function evaluations: 1531 Gradient evaluations: 49

基准函数代码 #

def read_M(self, dim, m):
    return self.rotate_data[m * dim : (m + 1) * dim]

def shift_data(self, dim, m):
    return np.array(self.sd[m * dim : (m + 1) * dim])

def carat(self, dim, alpha):    # 不确定这个实现是否正确！！！
    return alpha ** (np.arange(dim)/(2*(dim-1)))

def T_asy(self, X, Y, beta):
    D = len(X)
    for i in range(D):
        if X[i] > 0:
            Y[i] = X[i] ** (1 + beta * (i/(D-1)) * np.sqrt(X[i])  ) 
    pass

# Rotated Bent Cigar Function
# 函数编号3
def f3(self,X):
    X_shift = X - self.O
    X_rotate = self.M1 @ X_shift
    self.T_asy(X_rotate, X_shift, 0.5)
    Z = self.M2 @ X_shift

    Y = Z[0]**2 + 1e6 * np.sum(Z[1:]**2) - 1200
    return Y

# Rotated Schaffers F7 Function
# 函数编号7
def f7(self,X):
    d = len(X)
    X_shift = X - self.O
    X_rotate = self.M1 @ X_shift
    self.T_asy(X_rotate, X_shift, 0.5)
    Z = self.M2 @ (self.carat(d, 10) * X_shift)

    Z = np.sqrt(Z[:-1]**2 + Z[1:]**2)
    Y = (np.sum(np.sqrt(Z) + np.sqrt(Z) * np.sin(50 * Z**0.2)**2 ) / (d-1))**2 - 800
    return Y

已尝试的方法 #

• 调小epsilon的值，但无效果

内容的提问来源于stack exchange，提问作者Vicky