Table 1 Algorithm test function.

From: Multi-fault diagnosis and damage assessment of rolling bearings based on IDBO-VMD and CNN-BiLSTM

Test function

Dimension

Scope

Optimal value

\(\:{F}_{1}\left(X\right)=\sum\:_{i=1}^{n}\:i{x}_{i}^{4}+\text{r}5\:\text{a}\text{n}\text{d}\text{o}\text{m}\left[\text{0,1}\right)\)

30, 50, 100

[-128, 128]

0

\(\:{F}_{2}\left(X\right)=\sum\:_{i=1}^{n}\:\left[{x}_{i}^{2}-10\text{c}\text{o}\text{s}\left(2\pi\:{x}_{i}\right)+10\right]\)

30, 50, 100

[-5.12, 5.12]

0

\(\:{\text{F}}_{3}\left(X\right)=-\sum\:_{i=1}^{4}\:{c}_{i}\text{e}\text{x}\text{p}\left(-\sum\:_{j=1}^{6}\:{a}_{ij}{\left({x}_{j}-{p}_{ij}\right)}^{2}\right)\)

3

[0,1]

-3.86