Table 2 Basic multi-peak problem functions.

From: IWOA-LSTM based intrinsic structural identification of steel fiber concrete

Function

D

Search space

\(\it \:{\text{f}}_{\text{m}\text{i}\text{n}}\)

\(\:{f}_{6}=\sum\:_{i=1}^{n}{\left([{x}_{i}+0.5]\right)}^{2}\)

30

\(\:{\left[-\text{100,100}\right]}^{D}\)

0

\(\:{f}_{7}\left(x\right)={\sum\:}_{i=1}^{n}i{{x}_{i}}^{4}+random\left[\text{0,1}\right)\)

30

\(\:{\left[-\text{1.28,1.28}\right]}^{D}\)

0

\(\:{f}_{9}\left(x\right)={\sum\:}_{i=1}^{n}\left[{x}_{i}^{2}-10{cos}\left(2\pi\:{x}_{i}\right)+10\right]\)

30

[−5.12,5.12]D

0

\(\:{f}_{10}\left(x\right)=-20{exp}(-0.2\sqrt{\frac{1}{n}{\sum\:}_{i=1}^{n}{{x}_{i}}^{2}})-{exp}(\frac{1}{n}{\sum\:}_{i=1}^{n}{cos}(2\pi\:{x}_{i}\left)\right)+20+e\)

30

\(\:{\left[-\text{32,32}\right]}^{D}\)

0

\(\:{f}_{11}\left(x\right)=\frac{1}{4000}\sum\:_{i=1}^{n}{x}_{i}^{2}-\prod\:_{i=1}^{n}{cos}\left(\frac{{x}_{i}}{\sqrt{i}}\right)+1\)

30

\(\:{\left[-\text{600,600}\right]}^{D}\)

0