Table 3 The applied test function.

Rastrigin

\({\text{f}}_{1}\left(\text{x}\right)=10\text{D}+\sum_{\text{i}=1}^{\text{D}}\left({\text{x}}_{\text{i}}^{2}-10\text{cos}\left(2\uppi {\text{x}}_{\text{i}}\right)\right)\)

(−517, 517)

Rosenbrock

\({\text{f}}_{2}\left(\text{x}\right)=\sum_{\text{i}=1}^{\text{D}-1}\left(100\left({\text{x}}_{\text{i}}^{2}-{\text{x}}_{\text{i}+1}\right)+{\left({\text{x}}_{\text{i}}-1\right)}^{2}\right)\)

(−3.055, 3.055)

Ackley

\({\text{f}}_{3}\left(\text{x}\right)=20+\text{e}-20\text{exp}\left(-0.2\sqrt{\frac{1}{\text{D}}\sum_{\text{i}=1}^{\text{D}}\left({\text{x}}_{\text{i}}^{2}\right)}\right)-\text{exp}\left(\frac{1}{\text{D}}\sum_{\text{i}=1}^{\text{D}}\left(\text{cos}\left(2\uppi {\text{x}}_{\text{i}}\right)\right)\right)\)

(−12, 12)

Sphere

\({\text{f}}_{4} \left( {\text{x}} \right) = \sum\limits_{{{\text{i}} = 1}}^{{\text{D}}} {{\text{x}}_{{\text{i}}}^{2} }\)

(−517, 517)