A Sequential Optimization Sampling Method for Metamodels with Radial Basis Functions

Table 3

Numerical function and global minimum.

Number	Function	Design domain	Global minimum
1	𝑓(𝑥)=−10sin𝑐𝑥1⋅sin𝑐𝑥2	−2≤𝑥≤2	𝑥=(0,0),𝑓min=−10
2	𝑓(𝑥)=4𝑥1⋅𝑒^−𝑥21−𝑥22	−2≤𝑥≤2	𝑥=(−√2/2,0),𝑓min=−1.72
3	𝑓(𝑥)=𝑥^21+𝑥^22−10∗cos2𝜋𝑥1+cos2𝜋𝑥1+20	−0.8≤𝑥≤0.8	𝑥=(0,0),𝑓min=0
4	𝑓(𝑥)=3(1−𝑥1)^2⋅𝑒^−𝑥21−(𝑥2+1)2𝑥−10^15−𝑥^31−𝑥^52⋅𝑒^−𝑥21−𝑥22−13𝑒^−(𝑥1+1)2−𝑥22	−3≤𝑥≤3	𝑥=(0.228,−1.63),𝑓min=−6.55
5	𝑓(𝑥)=−60/[1+𝑥1+1^2+𝑥2−3^2]−20/[1+𝑥1−1^2+𝑥2−3^2]−30/[1+𝑥^21+𝑥2+4^2]+30	−6≤𝑥≤6	𝑥=(−0.97,3),𝑓min=−34.63
6	𝑓(𝑥)=−10(sin𝑥^21+𝑥^22+eps/𝑥^21+𝑥^22+eps)+10,eps=10^−15	−3𝜋≤𝑥≤3𝜋	𝑥=(0,0),𝑓min=0