timokoethe/testopti2d

TestOpti2D is a Swift framework for macOS that provides a comprehensive collection of target functions designed specifically for testing optimization algorithms aimed at finding global minima. These functions, often used as benchmarks in optimization research, are characterized b

Functions

Please note that each optimization function in this framework has a specific input domain. The global minimum can only be found within this designated domain. Make sure to consult the documentation for the precise input ranges before testing the algorithms.

Plate-Shaped Functions

|Name |Input Domain |Function |Global Minimum | |-------------------|-----------------------------------------------|--------------------------------------------------------------------------|-------------------------------------------------| | Booth Function | $x \in [-10, 10] \times [-10, 10]$ | $f(x) = (x_1 + 2x_2 - 7)^2 + (2x_1 + x_2 - 5)^2$ | $f(x^ ) = 0$, at $x^ = (1, 3)$ | | Matyas Function | $x \in [-10, 10] \times [-10, 10]$ | $f(x) = 0.26(x_1^2 + x_2^2) - 0.48x_1x_2$ | $f(x^ ) = 0$, at $x^ = (0, 0)$ | | McCormick Function| $x \in [-1.5, 4] \times [-3, 4]$ | $f(x) = sin(x_1 + x_2) + (x_1 - x_2)^2 - 1.5x_1 + 2.5x_2 + 1$ | $f(x^ ) = -1.9133$, at $x^ = (-0.54719, -1.54719)$ |

Bowl-Shaped Functions

|Name |Input Domain |Function |Global Minimum | |----------------------|---------------------------------------------------|------------------------------------------------------------------------------|-------------------------------------------------| | Bohachevsky Function | $x \in [-100, 100] \times [-100, 100]$ | $f(x) = x_1^2+2x_2^2 - 0.3cos(3\pi x_1) - 0.4cos(4\pi x_2) + 0.7$ | $f(x^ ) = 0$, at $x^ = (0, 0)$ | | Sphere Function | $x \in [-5.12, 5.12] \times [-5.12, 5.12]$ | $f(x) = x_1^2 + x_2^2$ | $f(x^ ) = 0$, at $x^ = (0, 0)$ | | Sum of different Powers Function | $x \in [-1, 1] \times [-1, 1]$ | $f(x) = \mid x_1\mid^2 + \mid x_2\mid^3 $ | $f(x^ ) = 0$, at $x^ = (0, 0)$ |

Installation

Please copy the following package URL to import the framework in your Xcode project:

https://github.com/timokoethe/TestOpti2D.git

Add the following import statement at the top of the Swift file where you want to use TestOpti2D:

import TestOpti2D

You’re all set! You can now use the functionality provided by TestOpti2D in your project.

Check out our documentation here.

Contributing & Support

If you encounter any bugs or have feature requests, please feel free to open an issue on our GitHub repository. If you have any questions, feedback, or need assistance with TestOpti2D, please don't hesitate to contact us. We're here to help!

License

TestOpti2D is released under the MIT License.

Feel free to adjust and expand upon this template to better suit your project's needs!

Package Metadata

Repository: timokoethe/testopti2d

Default branch: main

README: README.md