Test functions for optimization: Difference between revisions

Revision as of 13:41, 29 December 2023

Revision as of 13:48, 29 December 2023

Line 18:

==Test functions for single-objective optimization==

{| class="sortable wikitable" style="text-align:center"

! Name

|-

! Name !! Plot !
! Formula !
! Global minimum !
! Search ___domain

|-

| [[Rastrigin function]]

Line 107 ⟶ 110:

|-

| Three-hump camel function

| [[File:Three-hump-camel contour.svg|200px|Three Hump Camel function]]

| <math>f(x,y) = 2x^{2} - 1.05x^{4} + \frac{x^{6}}{6} + xy + y^{2}</math>

| <math>f(0,0) = 0</math>

| <math>-5\le x,y \le 5</math>

Line 119 ⟶ 122:

|-

| Cross-in-tray function

| [[File:Cross-in-tray contour.svg|200px|Cross-in-tray function]]

| <math>f(x,y) = -0.0001 \left[ \left| \sin x \sin y \exp \left(\left|100 - \frac{\sqrt{x^{2} + y^{2}}}{\pi} \right|\right)\right| + 1 \right]^{0.1}</math>

| <math>\text{Min} =

\begin{cases}

Line 180 ⟶ 183:

| <math>-39.16617n < f(\underbrace{-2.903534, \ldots, -2.903534}_{n \text{ times}} ) < -39.16616n</math>

| <math>-5\le x_{i} \le 5</math>, <math>1\le i \le n</math>..

|

|-

| [[Shekel function]]

| [[Image:Shekel_2D.jpg|200px|A Shekel function in 2 dimensions and with 10 maxima]]

| <math>

f(\vec{x}) = \sum_{i = 1}^{m} \; \left( c_{i} + \sum\limits_{j = 1}^{n} (x_{j} - a_{ji})^2 \right)^{-1}

</math>