Table 2 Test functions description.

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

0

\(F_{2} (x) = \sum\limits_{i = 1}^{n} {\left| {x_{i} } \right|} + \prod\limits_{i = 1}^{n} {\left| {x_{i} } \right|}\)

0

\(F_{3} (x) = \sum\limits_{i = 1}^{n} {(\sum\limits_{j - 1}^{i} {x_{j} } )^{2} }\)

0

\(F_{4} (x) = \mathop {\max }\limits_{i} \{ \left| {x_{i} } \right|,\,\,\,\,1 \le i \le n\}\)

0

\(F_{5} (x) = \sum\limits_{i = 1}^{n - 1} {[100(x_{i + 1} - x_{i}^{2} ) + (x_{i} - 1)^{2} ]}\)

0

\(F_{6} (x) = \frac{1}{4000}\sum\limits_{i = 1}^{n} {x_{i}^{2} } - \prod\limits_{i = 1}^{n} {\cos (\frac{{x_{i} }}{\sqrt i })} + 1\)

0

\(F_{7} (x) = \left( {\frac{1}{500} + \sum\limits_{j = 1}^{25} {\frac{1}{{j + \sum\limits_{i = 1}^{2} {\left( {x_{i} - a_{ij} } \right)^{6} } }}} } \right)^{ - 1}\)

1

\(F_{8} (x) = \sum\limits_{i = 1}^{11} {\left[ {a_{i} - \frac{{x_{1} \left( {b_{i}^{2} + b_{i} x_{2} } \right)}}{{b_{i}^{2} + b_{i} x_{3} + x_{4} }}} \right]^{2} }\)

0.0003

\(F_{9} (x) = 4x_{1}^{2} - 2.1x_{1}^{4} + \frac{1}{3}x_{1}^{6} + x_{1} x_{2} - 4x_{2}^{2} + 4x_{2}^{4}\)

− 1.0316

\(\begin{gathered} F_{10} (x) = \left[ {1 + \left( {x_{1} + x_{2} + 1} \right)^{2} \left( {19 - 14x_{1} + 3x_{1}^{2} - 14x_{2} + 6x_{1} x_{2} + 3x_{2}^{2} } \right)} \right] \hfill \\ \quad \quad \quad \times \left[ {30 + \left( {2x_{1} - 3x_{2} } \right)^{2} \times \left( {18 - 32x_{1} + 12x_{1}^{2} + 48x_{2} - 36x_{1} x_{2} + 27x_{2}^{2} } \right)} \right] \hfill \\ \end{gathered}\)

3