Table 2 Test function settings.

\({F_1}(x)=\sum\limits_{{i=1}}^{n} {x_{i}^{2}}\)

0

\({F_2}(x)=\sum\limits_{{i=1}}^{n} {|x_{i}^{{}}|+\prod\nolimits_{{i=1}}^{n} {|{x_i}|} }\)

0

\({F_3}(x)=\sum\limits_{{i=1}}^{n} {{{(\sum\nolimits_{{j=1}}^{i} {x_{j}^{{}}} )}^2}}\)

0

\({F_4}(x)=\hbox{max} \{ |{x_i}|,1 \leqslant i \leqslant n\}\)

0

\({F_5}(x)= - 20\exp ( - 0.2\sqrt {\frac{1}{n}\sum\limits_{{i=1}}^{n} {x_{i}^{2}} } ) - \exp (\frac{1}{n}\sum\limits_{{i=1}}^{n} {\cos (2\pi {x_i})} )+20+e\)

0

\(\begin{gathered} {F_6}(x)=\frac{\pi }{n}\{ 10\sin (\pi {y_1})+\sum\nolimits_{{i=1}}^{{n - 1}} {{{({y_i} - 1)}^2}[1+10{{\sin }^2}(\pi {y_{i+1}})]+{{({y_n} - 1)}^2}} \} +\sum\nolimits_{{i=1}}^{n} {u({x_i},10,100,4)} , \\ {y_i}=1+\frac{{{x_i}+1}}{4} \\ \end{gathered}\)

0

\({F_7}(x)={\sum\limits_{{i=1}}^{{11}} {[{a_i} - \frac{{{x_1}(b_{i}^{2}+{b_i}{x_2})}}{{b_{i}^{2}+{b_i}{x_3}+{x_4}}}]} ^2}\)

0.0003075

\({F_8}(x)= - \sum\nolimits_{{i=1}}^{4} {{c_i}\exp ( - \sum\nolimits_{{j=1}}^{6} {{a_{ij}}{{({x_j} - {p_{ij}})}^2}} )}\)

− 3.32

\({F_9}(x)= - \sum\limits_{{i=1}}^{5} {{{[(x - {a_i}){{(x - {a_i})}^T}+{c_i}]}^{ - 1}}}\)

− 10