Table 4 Complex composite functions F19–F30.

\(\begin{gathered} F19 = \sum\limits_{i = 1}^{n/4} {[(x_{4i - 3} + 10x_{4i - 2} )^{2} + 5(x_{4i - 1} - x_{4i} )^{2} } \hfill \\ \, + (x_{4i - 2} - 2x_{4i - 1} )^{4} + 10(x_{4i - 3} - x_{4i} )^{4} ] \hfill \\ \end{gathered}\)

30

[-4,5]

0

\(F20 = \left[ {\frac{1}{500} + \sum\nolimits_{j = 1}^{25} {\frac{1}{{j + \sum\nolimits_{j = 1}^{2} {\left( {x_{i} - a_{ij} } \right)^{6} } }}} } \right]^{ - 1}\)

2

[-65.536,

65.536]

0.998

\(F21 = - \sum\nolimits_{i = 1}^{n} {\sin \left( {x_{i} } \right)\left[ {\sin \left( {\frac{{ix_{i}^{2} }}{\pi }} \right)} \right]}^{20}\)

5

[0,\(\pi\)]

−4.6877

\(F22 = 0.5 + \frac{{\sin^{2} \left( {\sqrt {x_{1}^{2} + x_{2}^{2} } } \right) - 0.5}}{{\left[ {1 + 0.001\left( {x_{1}^{2} + x_{2}^{2} } \right)} \right]^{2} }}\)

2

[-100,100]

0

\(F23 = 4x_{1}^{2} - 2.1x_{1}^{4} + \frac{1}{3}x_{1}^{6} + x_{1} x_{2} - 4x_{2}^{2} + 4x_{2}^{4}\)

2

[-5,5]

−1.03163

\(F24 = x_{i}^{2} + 2x_{2}^{2} - 0.3\cos \left( {3\pi x_{1} + 4\pi x_{3} } \right) + 0.3\)

2

[-100,100]

0

\(\begin{gathered} F25 = \left[ {\sum\nolimits_{i = 1}^{5} {i\cos } \left( {\left( {i + 1} \right)x_{1} + i} \right)} \right] \hfill \\ \, \cdot \left[ {\sum\nolimits_{i = 1}^{5} {i\cos } \left( {\left( {i + 1} \right)x_{2} + i} \right)} \right] \hfill \\ \end{gathered}\)

2

[-10,10]

−186.7309

\(F26 = \sum\nolimits_{i = 1}^{11} {\left| {a_{i} - \frac{{x_{1} \left( {b_{i}^{2} + b_{i} x_{2} } \right)}}{{b_{i}^{2} + b_{i} x_{3} + x_{4} }}} \right|}^{2}\)

4

[-5,5]

0.00031

\(F27 = - \sum\nolimits_{i = 1}^{4} {\exp \left[ { - \sum\nolimits_{j = 1}^{3} {a_{ij} \left( {x_{j} - p_{ij} } \right)^{2} } } \right]}\)

3

[0,1]

−3.86

\(F28 = \sum\nolimits_{i = 1}^{n} {\left[ \begin{gathered} \sum\nolimits_{j = 1}^{n} {\left( {a_{ij} \sin \alpha_{j} + b_{ij} \cos \alpha_{j} } \right)} \hfill \\ - \sum\nolimits_{j = 1}^{n} {\left( {a_{ij} \sin x_{j} + b_{ij} \cos x_{j} } \right)} \hfill \\ \end{gathered} \right]}^{2}\)

2

[-\(\pi\),\(\pi\)]

0

\(F29 = \sum\nolimits_{i = 1}^{n} {\left[ \begin{gathered} \sum\nolimits_{j = 1}^{n} {\left( {a_{ij} \sin \alpha_{j} + b_{ij} \cos \alpha_{j} } \right)} \hfill \\ - \sum\nolimits_{j = 1}^{n} {\left( {a_{ij} \sin x_{j} + b_{ij} \cos x_{j} } \right)} \hfill \\ \end{gathered} \right]}^{2}\)

5

[-\(\pi\),\(\pi\)]

0

\(F30 = \sum\nolimits_{i = 1}^{n} {\left[ \begin{gathered} \sum\nolimits_{j = 1}^{n} {\left( {a_{ij} \sin \alpha_{j} + b_{ij} \cos \alpha_{j} } \right)} \hfill \\ - \sum\nolimits_{j = 1}^{n} {\left( {a_{ij} \sin x_{j} + b_{ij} \cos x_{j} } \right)} \hfill \\ \end{gathered} \right]}^{2}\)

10

[-\(\pi\),\(\pi\)]

0