A collection of Benchmark functions for optimization algorithm testing. Plugin your algorithm with 54 benchmark functions.

## 📂 Download MATLAB Code (Zip)

1:40 Unimodal and Multimodal functions ^{1}. 40:50 Custom Composite Functions. 51:54 Engineering Problems ^{2}.

## 📓 Functions Details (Word.docx)

## What are the benchmark functions for optimization algorithms❓

Benchmark optimization functions are mathematical functions that have been established and widely accepted as standards for testing and evaluating optimization algorithms. They are used to assess the performance of an algorithm in terms of accuracy, speed, robustness, and other criteria. Some of the popular benchmark optimization functions include the sphere function, Rosenbrock’s function, Rastrigin’s function, Ackley’s function, Griewank’s function, and Schwefel’s function, among others. These functions vary in complexity, dimensionality, and the presence of multiple local optima, which makes them suitable for testing different types of optimization algorithms. The use of benchmark functions helps to provide a fair and standardized assessment of optimization algorithms and aids in the comparison of different algorithms on a common ground.

# List of function:

Function | Description |
---|---|

F1 | Sphere function |

F2 | Powell Sum function |

F3 | Ridge function |

F4 | Brown function |

F5 | Exponential function |

F6 | Xin-She Yang N.3 function |

F7 | Zakharov function |

F8 | Schwefel 220 function |

F9 | Schwefel 2.21 function |

F10 | Schwefel 2.22 function |

F11 | Rosenbrock function |

F12 | Schwefel function |

F13 | Rastrigin function |

F14 | Xin-She Yang N.2 function |

F15 | Xin-She Yang N.4 function |

F16 | Happy Cat function |

F17 | Periodic function |

F18 | Quartic function |

F19 | Shubert 3 function |

F20 | Salomon function |

F21 | Three-Hump Camel function |

F22 | Drop Wave function |

F23 | Leon function |

F24 | Booth function |

F25 | Matyas function |

F26 | Brent function |

F27 | Schaffer N.1 function |

F28 | Ackley N.2 function |

F29 | Bohachevsky N.1 function |

F30 | Schaffer N.4 function |

F31 | Keane function |

F32 | Levi N.13 function |

F33 | Bukin N.6 function |

F34 | Holder Table function |

F35 | Cross-in-Tray function |

F36 | Wolfe function |

F37 | Egg Crate function |

F38 | McCormick function |

F39 | Decker’s Arts function |

F40 | Bartels Conn function |

F41 | Composition Function 1 (3 functions) |

F42 | Composition Function 2 (3 functions) |

F43 | Composition Function 3 (4 functions) |

F44 | Composition Function 4 (4 functions) |

F45 | Composition Function 5 (6 functions) |

F46 | Composition Function 6 (6 functions) |

F47 | Composition Function 7 (8 functions) |

F48 | Composition Function 8 (8 functions) |

F49 | Composition Function 9 (10 functions) |

F50 | Composition Function 10 (10 functions) |

F51 | Welded Beam Design |

F52 | Tension/Compression Spring Design |

F53 | Pressure vessel design problem |

F54 | Cantilever beam design problem |

## 📓 LaTeX Equations (Word.docx)

## 📂 Functions plots (Zip)

## 🔗 YUKI Algorithm 2.0

## 📑 Cite as

YUKI Algorithm and POD-RBF for Elastostatic and dynamic crack identification. *Journal of Computational Science*. 2021. https://doi.org/10.1016/j.jocs.2021.101451 **(Download Preprint PDF)**

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