Table 2 Details of the fixed-dimensional benchmark mathematical functions.

F1

Ackley 2 Function

C, D, NS, Sc, M

[− 35, 35]

2

⁹⁶

− 200

F2

Ackley 3 Function

C, D, NS, NSc, U

[− 32, 32]

2

⁹⁶

− 195.629

F3

Ackley 4 or Modified Ackley

C, D, NS, Sc, M

[− 32, 32]

2

⁹⁶

− 4.590102

F4

Adjiman Function

C, D, NS, NSc, M

[− 1, 2] and [− 1, 1]

2

⁹⁶

− 2.021807

F5

Bartels Conn Function

C, ND, NS, NSc, M

[− 500, 500]

2

⁹⁶

1

F6

Bohachevsky 1 Function

C, D, S, NSc, M

[− 100, 100]

2

⁹⁶

0

F7

Bohachevsky 2 Function

C, D, NS, NSc, M

[− 100, 100]

2

⁹⁶

0

F8

Bohachevsky 3 Function

C, D, NS, NSc, M

[− 100, 100]

2

⁹⁶

0

F9

Camel Function-Three Hump

C, D, NS, NSc, M

[− 5, 5]

2

⁹⁶

0

F10

Carrom table function

NS

[− 10, 10]

2

⁹⁶

− 24.15682

F11

Chichinadze Function

C, D, S, NSc, M

[− 30, 30]

2

⁹⁶

− 43.72192

F12

Cross-in-Tray Function

C, NS, NSc, M

[− 10, 10]

2

⁹⁶

− 2.062612

F13

Cube Function

C, D, NS, NSc, U

[− 10, 10]

2

⁹⁶

0

F14

Damavandi Function

C, D, NS, NSc, M

[0, 14]

2

⁹⁶

0

F15

Deckkers–Aarts Function

C, D, NS, NSc, M

[− 20, 20]

2

⁹⁶

− 24,776.52

F16

Egg Crate Function

C, D, NS, Sc, M

[− 5, 5]

2

⁹⁶

0

F17

Giunta Function

C, D, S, Sc, M

[− 1, 1]

2

⁹⁶

0.0644704

F18

Hansen Function

C, D, S, NSc, M

[− 10, 10]

2

⁹⁶

− 166.0291

F19

Himmelblau Function

C, D, NS, NSc, M

[− 5, 5]

2

⁹⁶

0

F20

Hosaki Function

C, D, NS, NSc, M

[0, 5] and [0, 6]

2

⁹⁶

− 2.3458

F21

Jennrich–Sampson Function

C, D, NS, NSc, M

[− 1, 1]

2

⁹⁶

124.36218

F22

Keane Function

C, D, NS, NSc, M

[0, 10]

2

⁹⁶

− 0.673668

F23

Leon Function

C, D, NS, NSc, U

[− 1.2, 1.2]

2

⁹⁶

0

F24

Levy 3 Function

S

[− 10, 10]

2

⁹⁷

− 176.5418

F25

Levy 5 Function

NS

[− 10, 10]

2

⁹⁷

− 176.1376

F26

Matyas Function

C, D, NS, NSc, U

[− 10, 10]

2

⁹⁶

0

F27

McCormick Function

C, D, NS, NSc, M

[− 1.5, 4] and [− 3, 3]

2

⁹⁶

− 1.913223

F28

Mexican hat Function

NS

[− 10, 10]

2

⁹⁷

− 19.96668

F29

Michaelewicz 2 Function

S

[0, π]

2

⁹⁷

− 1.8013

F30

Mishra 5 Function

C, D, NS, NSc, M

[− 10, 10]

2

⁹⁶

− 1.01983

F31

Mishra 6 Function

C, D, NS, NSc, M

[− 10, 10]

2

⁹⁶

− 2.28395

F32

Mishra 8 Function

C, D, NS, NSc, M

[− 10, 10]

2

⁹⁶

0

F33

Pen Holder Function

C, D, NS, NSc, M

[− 11, 11]

2

⁹⁶

− 0.963535

F34

Periodic Function

S

[− 10, 10]

2

⁹⁷

0.9

F35

Price 1 Function

C, ND, S, NSc, M

[− 500, 500]

2

⁹⁶

0

F36

Price 2 Function

C, D, NS, NSc, M

[− 10, 10]

2

⁹⁶

0.9

F37

Price 4 Function

C, D, NS, NSc, M

[− 500, 500]

2

⁹⁶

0

F38

Quadratic Function

C, D, NS, NSc

[− 10, 10]

2

⁹⁶

− 3873.724

F39

Ripple 1 Function

NS

[0, 1]

2

⁹⁷

− 2.2

F40

Ripple 25 Function

NS

[0, 1]

2

⁹⁷

− 2

F41

Rosenbrock Modified Function

C, D, NS, NSc, M

[− 2, 2]

2

⁹⁶

34.040243

F42

Rotated Ellipse Function

C, D, NS, NSc, U

[− 500, 500]

2

⁹⁶

0

F43

Rotated Ellipse 2 Function

C, D, NS, NSc, U

[− 500, 500]

2

⁹⁶

0

F44

Scahffer 2 Function

C, D, NS, NSc, U

[− 100, 100]

2

⁹⁶

0

F45

Scahffer 3 Function

C, D, NS, NSc, U

[− 100, 100]

2

⁹⁶

0.0015669

F46

Scahffer 4 Function

C, D, NS, NSc, U

[− 100, 100]

2

⁹⁶

0.292579

F47

Table 1/Holder Table 1 Function

C, D, S, NSc, M

[− 10, 10]

2

⁹⁶

− 26.92034

F48

Table 2/Holder Table 2 Function

C, D, S, NSc, M

[− 10, 10]

2

⁹⁶

− 19.2085

F49

Table 3/Carrom Table Function

C, D, NS, NSc, M

[− 10, 10]

2

⁹⁶

− 24.15682

F50

Ursem 1 Function

S

[− 2.5, 3] and [− 2, 2]

2

⁹⁷

− 4.816814

F51

Ursem 3 Function

NS

[− 2, 2] and [− 1.5, 1.5]

2

⁹⁷

− 3

F96

Ursem 4 Function

NS

[− 2, 2]

2

⁹⁷

− 1.5

F53

Ursem Waves Function

NS

[− 0.9, 1.2] and [− 1.2, 1.2]

2

⁹⁷

− 8.5536

F54

Venter Sobiezcczanski-Sobieski Function

C, D, S, NSc

[− 50, 50]

2

⁹⁶

− 400

F55

Wayburn Seader 3 Function

C, D, NS, Sc, U

[− 500, 500]

2

⁹⁶

19.10588

F56

Zettl Function

C, D, NS, NSc, U

[− 5, 10]

2

⁹⁶

− 0.003791

F57

Zirilli or Aluffi-Pentini’s Function

C, D, S, NSc, U

[− 10, 10]

2

⁹⁶

− 0.352386

F58

Zirilli Function 2

C, D, S, S, M

[− 500, 500]

2

⁹⁶

0

F59

Corana Function

DC, ND, S, Sc, M

[− 500, 500]

4

⁹⁶

0

F60

Michalewicz 10

S

[0, \(\pi\)]

10

⁹⁷

− 9.66015