Table 6 Benchmark function specifications

Ackley

\(f(x) = - a\exp \left( { - b\sqrt {\frac{1}{d}\sum\limits_{i = 1}^{d} {x_{i}^{2} } } } \right) - \exp \left( {\frac{1}{d}\sum\limits_{i = 1}^{d} {\cos (cx_{i} )} } \right) + a + \exp (1)\)

6

[−32.768, 2.768]

[0, ……, 0]

0

Bulkin N.6

\(f(x) = 100\sqrt {\left| { \, x_{2} - 0.01x_{1}^{2} \, } \right|} + 0.01\left| { \, x_{1} + 10 \, } \right|\)

2

x₁∈[−15, −5],

x₂∈[−3, 3]

[−10, 1]

0

Drop- Wave

\(f(x) = { - }\frac{{1 + \cos \, \left( {12\sqrt {x_{1}^{2} + x_{2}^{2} } } \right)}}{{0.5 \, (x_{1}^{2} + x_{2}^{2} ) + 2}}\)

2

[−5.12, 5.12]

[0, 0]

−1

Griewank

\(f(x) = \sum\limits_{i = 1}^{d} {\frac{{x_{i}^{2} }}{4000}} - \prod\limits_{i = 1}^{d} {\cos \left( {\frac{{x_{i} }}{\sqrt i }} \right)} + 1\)

6

[−600, 600]

[0, ……, 0]

0