Home

Awesome

optimization-test-functions

A set of test functions to evaluate optimization algorithms

Test Functions

NameDefinition
Beale<a href="https://www.codecogs.com/eqnedit.php?latex=f(\mathbf{x})&space;=&space;(1.5&space;-&space;x_1&space;&plus;&space;x_1&space;x_2)^2&space;&plus;&space;(2.25&space;-&space;x_1&space;&plus;&space;x_1&space;x_2^2)^2&space;&plus;&space;(2.625&space;-&space;x_1&space;&plus;&space;x_1&space;x_2^3)^2" target="_blank"><img src="https://latex.codecogs.com/svg.latex?f(\mathbf{x})&space;=&space;(1.5&space;-&space;x_1&space;&plus;&space;x_1&space;x_2)^2&space;&plus;&space;(2.25&space;-&space;x_1&space;&plus;&space;x_1&space;x_2^2)^2&space;&plus;&space;(2.625&space;-&space;x_1&space;&plus;&space;x_1&space;x_2^3)^2" title="f(\mathbf{x}) = (1.5 - x_1 + x_1 x_2)^2 + (2.25 - x_1 + x_1 x_2^2)^2 + (2.625 - x_1 + x_1 x_2^3)^2" /></a>
Rosenbrock<a href="https://www.codecogs.com/eqnedit.php?latex=f(\mathbf{x})&space;=&space;\sum_{i&space;=&space;1}^{n&space;-&space;1}&space;\{&space;100&space;(x_{i&space;&plus;&space;1}&space;-&space;x_{i}^{2})^{2}&space;&plus;&space;(1&space;-&space;x_{i})^{2}&space;\}" target="_blank"><img src="https://latex.codecogs.com/svg.latex?f(\mathbf{x})&space;=&space;\sum_{i&space;=&space;1}^{n&space;-&space;1}&space;\{&space;100&space;(x_{i&space;&plus;&space;1}&space;-&space;x_{i}^{2})^{2}&space;&plus;&space;(1&space;-&space;x_{i})^{2}&space;\}" title="f(\mathbf{x}) = \sum_{i = 1}^{n - 1} \{ 100 (x_{i + 1} - x_{i}^{2})^{2} + (1 - x_{i})^{2} \}" /></a>
Sphere<a href="https://www.codecogs.com/eqnedit.php?latex=f(\mathbf{x})&space;=&space;\sum_{i&space;=&space;1}^{n}&space;x_{i}^{2}" target="_blank"><img src="https://latex.codecogs.com/svg.latex?f(\mathbf{x})&space;=&space;\sum_{i&space;=&space;1}^{n}&space;x_{i}^{2}" title="f(\mathbf{x}) = \sum_{i = 1}^{n} x_{i}^{2}" /></a>

Projects using optimization-test-functions