Table 1 Test functions.

Kowalik

\(f\left( x \right)={\sum\limits_{{i=1}}^{{11}} {\left[ {{a_i} - \frac{{{x_1}\left( {b_{i}^{2}+{b_i}{x_2}} \right)}}{{b_{i}^{2}+{b_i}{x_3}+{x_4}}}} \right]} ^2}\)

\(\left[ { - 5,5} \right]\)

Schwefel

\(f\left( x \right)=418.9829D - \sum\limits_{{i=1}}^{D} {{x_i}} \sin \left( {\sqrt {\left| {{x_i}} \right|} } \right)\)

\(\left[ { - 500,500} \right]\)

Griewank

\(f(x)=1+\frac{1}{{400}}\sum\limits_{{i=1}}^{D} {x_{i}^{2}} - \prod\limits_{{i=1}}^{D} {\cos \left( {\frac{{{x_i}}}{{\sqrt i }}} \right)}\)

\(\left[ { - 600,600} \right]\)

Rastrigin

\(f(x)=\sum\limits_{{i=1}}^{D} {\left[ {x_{i}^{2} - 10\cos \left( {2\pi {x_i}} \right)+10} \right]}\)

\(\left[ { - 5.12,5.12} \right]\)