Table 2 The multimodal benchmark functions.

F₅

\(\sum\nolimits_{i = 1}^{n} { - x_{i} \sin \left( {\sqrt {\left| {x_{i} } \right|} } \right)}\)

30

[− 500, 500]

− 418.98 × D

F₆

\(\mathop \sum \limits_{i = 1}^{n} \left[ {x_{i}^{2} - 10\cos \left( {2\pi x_{i} } \right) + 10} \right]\)

30

[− 5.12, 5.12]

0

F₇

\(- 20exp\left( { - 0.2\sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {x_{i}^{2} } } } \right) - exp\left( {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {\cos \left( {2\pi x_{i} } \right)} } \right) + 20 + e\)

30

[− 32, 32]

0

F₈

\(\frac{1}{4000}\sum\nolimits_{i = 1}^{n} {x_{i}^{2} } - \prod\nolimits_{i = 1}^{n} {\cos \left( {\frac{{x_{i} }}{\sqrt i }} \right) + 1}\)

30

[− 600, 600]

0