. 2021 Mar 26;177:114920. doi: 10.1016/j.eswa.2021.114920

Table 3.

Benchmark functions.

Function	Formulation	Range	D
Ackley	f₁(x) = $- 20 \exp (- 0.2 \sqrt{\frac{1}{N}} \sum_{i = 1}^{N} x_{i}^{2}) - e x p (\frac{1}{N} \sum_{i = 1}^{N} c o s (2 π x_{i})) + 20 + e$	${[- 32, 32]}^{N}$	30,50
Rastrigin	f₂(x) = $\sum_{i = 1}^{N} [x_{i}^{2} - 10 \cos (2 π x_{i}) + 10$	${[- 5.12, 5.12]}^{N}$	30,50
Sphere	f₃(x) = $\sum_{i = 1}^{N} x_{i}^{2}$	${[- 100, 100]}^{N}$	30,50
Griewank	f₄(x) = $\frac{1}{4000} \sum_{i = 1}^{N} x_{i}^{2} - \prod_{i = 1}^{N} c o s (\frac{x_{Ä °}}{\sqrt{Ä °}}) + 1$	${[- 600, 600]}^{N}$	30,50
High ConditionedElliptic	f₅(x) = $\sum_{i = 1}^{N} {(10^{6})}^{\frac{i - 1}{D - 1}} x_{i}^{2}$	${[- 10, 10]}^{N}$	30,50
Rosenbrock	f₆(x) = $\sum_{i = 1}^{N - 1} [100 {(x_{i + 1} - x_{i})}^{2} + {(x_{i} - 1)}^{2}]$	${[- 30, 30]}^{N}$	30,50
Shifted Ackley	f₇(x) = $-$ 20exp $(- 0.2 \sqrt{\frac{1}{N}} \sum_{i = 1}^{N} z_{i}^{2}) - e x p (\frac{1}{N} \sum_{i = 1}^{N} c o s (2 π z_{i})) + 20 + e$	${[- 32, 32]}^{N}$	30,50
Shifted Rastrigin	f₈(x) = $\sum_{i = 1}^{N} [z_{i}^{2} - 10 \cos (2 π z_{i}) + 10]$	${[- 5.12, 5.12]}^{N}$	30,50
Shifted Sphere	f₉(x) = $\sum_{i = 1}^{N} z_{i}^{2}$	${[- 100, 100]}^{N}$	30,50
Shifted Griewank	f₁₀(x) = $\frac{1}{4000} \sum_{i = 1}^{N} z_{i}^{2} - \prod_{i = 1}^{N} c o s (\frac{z_{i}}{\sqrt{i}}) + 1$	${[- 600, 600]}^{N}$	30,50
Shifted HighConditionedElliptic	f₁₁(x) = $\sum_{i = 1}^{N} {(10^{6})}^{\frac{i - 1}{D - 1}} z_{i}^{2}$	${[- 10, 10]}^{N}$	30,50
ShiftedRosenbrock	f₁₂(x) = $\sum_{i = 1}^{N - 1} [100 ({z_{i + 1} - z_{i})}^{2} {(z_{i} - 1)}^{2}]$	${[- 30, 30]}^{N}$	30,50