Table 3 51 benchmark functions, U: Uni-modal, M: Multi-modal, S: Separable, N: Non-separable.
From: Learning cooking algorithm for solving global optimization problems
\({\text {Name}}\) | \({\text {Function}}\) | \({\text {Characteristics}}\) | \({\text {Dimension}}\) | \({\text {Range}}\) | \({\text {f}}_{\text {optimal}}\) |
|---|---|---|---|---|---|
\({\text {F1}}\) | Sphere | US | 30 | [– 100, 100] | 0 |
\({\text {F2}}\) | Schwefel’problem2.22 | UN | 30 | [– 10, 10] | 0 |
\({\text {F3}}\) | Schwefel’problem1.2 | UN | 30 | [– 100, 100] | 0 |
\({\text {F4}}\) | Schwefel’problem2.21 | UN | 30 | [– 100, 100] | 0 |
\({\text {F5}}\) | Rosen brock | UN | 30 | [– 30, 30] | 0 |
\({\text {F6}}\) | Step | US | 30 | [– 100, 100] | 0 |
\({\text {F7}}\) | Noise | US | 30 | [– 1.28, 1.28] | 0 |
\({\text {F8}}\) | Generalized Schwefel’s problem | MS | 30 | [– 500, 500] | – 12569.5 |
\({\text {F9}}\) | Rastrigin | MS | 30 | [– 5.12, 5.12] | 0 |
\({\text {F10}}\) | Ackley | MN | 30 | [– 32, 32] | 0 |
\({\text {F11}}\) | Griewank | MN | 30 | [– 600, 600] | 0 |
\({\text {F12}}\) | Generalized penalized function1 | MN | 30 | [– 50, 50] | 0 |
\({\text {F13}}\) | Generalized penalized function2 | MN | 30 | [– 50, 50] | 0 |
\({\text {F14}}\) | Shekel’s foxholes function | MS | 2 | [– 65, 65] | 1 |
\({\text {F15}}\) | Kowalik’s function | MN | 4 | [– 5, 5] | 0.00030 |
\({\text {F16}}\) | Six-hump camelback | MN | 2 | [– 5, 5] | – 1.0316 |
\({\text {F17}}\) | Branin | MS | 2 | [– 5, 5] | 0.398 |
\({\text {F18}}\) | Goldstein-price function | MN | 2 | [– 2, 2] | 3 |
\({\text {F19}}\) | Hartmann1 | MN | 3 | [1, 3] | – 3.86 |
\({\text {F20}}\) | Hartmann2 | MN | 6 | [0, 1] | – 3.32 |
\({\text {F21}}\) | Shekel1 | MN | 4 | [0, 10] | – 10.1532 |
\({\text {F22}}\) | Shekel2 | MN | 4 | [0, 10] | – 10.4028 |
\({\text {F23}}\) | Shekel3 | MN | 4 | [0, 10] | – 10.5363 |
\({\text {F24}}\) | Stepint | US | 5 | [– 5.12, 5.12] | 0 |
\({\text {F25}}\) | SumSquares | US | 30 | [– 10, 10] | 0 |
\({\text {F26}}\) | Beale | UN | 5 | [– 4.5, 4.5] | 0 |
\({\text {F27}}\) | Easom | UN | 2 | [– 100, 100] | – 1 |
\({\text {F28}}\) | Matyas | UN | 2 | [– 10, 10] | 0 |
\({\text {F29}}\) | Colville | UN | 4 | [– 10, 10] | 0 |
\({\text {F30}}\) | Trid6 | UN | 6 | [\(-D^2\),\(D^2\)] | – 360 |
\({\text {F31}}\) | Trid10 | UN | 10 | [\(-D^2\),\(D^2\) ] | – 2600 |
\({\text {F32}}\) | Zakharov | UN | 10 | [– 5, 10] | 0 |
\({\text {F33}}\) | Powell | UN | 24 | [– 4, 5] | 0 |
\({\text {F34}}\) | Dixon– Price | UN | 30 | [– 10, 10] | 0 |
\({\text {F35}}\) | Bohachevsky1 | MS | 2 | [– 100, 100] | 0 |
\({\text {F36}}\) | Booth | MS | 2 | [– 10, 10] | 0 |
\({\text {F37}}\) | Michalewicz2 | MS | 2 | [0,\(\pi \)] | – 1.8013 |
\({\text {F38}}\) | Michalewicz5 | MS | 5 | [0,\(\pi \)] | – 4.6877 |
\({\text {F39}}\) | Michalewicz10 | MS | 10 | [0,\(\pi \)] | – 9.6602 |
\({\text {F40}}\) | Schaffer | MN | 2 | [– 100, 100] | 0 |
\({\text {F41}}\) | Bohachevshy2 | MN | 2 | [– 100, 100] | 0 |
\({\text {F42}}\) | Bohachevshy3 | MN | 2 | [– 100, 100] | 0 |
\({\text {F43}}\) | Shubert | MN | 2 | [– 100, 100] | – 25 |
\({\text {F44}}\) | Perm | MN | 4 | [\(- D\),D] | 0 |
\({\text {F45}}\) | PowerSum | MN | 4 | [0,D] | 0 |
\({\text {F46}}\) | Langerman2 | MN | 2 | [0, 10] | – 1.08 |
\({\text {F47}}\) | Langerman5 | MN | 5 | [0, 10] | – 4.825 |
\({\text {F48}}\) | Langerman10 | MN | 10 | [0, 10] | – 8.76 |
\({\text {F49}}\) | FletcherPowell2 | MN | 2 | [\(-\pi \),\(\pi \)] | 0 |
\({\text {F50}}\) | FletcherPowell5 | MN | 5 | [\(-\pi \),\(\pi \)] | 0 |
\({\text {F51}}\) | FletcherPowell10 | MN | 10 | [\(-\pi \),\(\pi \)] | 0 |
