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### Highlights from Test functions for global optimization algorithms

• zettl.m
• ackley.m
• beale.m
• bird.m
• booth.m
• bukin4.m
• bukin6.m
• carromtable.m
• crossfunc.m
• crossintray.m
• crosslegtable.m
• crownedcross.m
• cube.m
• easom.m
• eggholder.m
• giunta.m
• goldsteinprice.m
• griewank.m
• helicalvalley.m
• himmelblau.m
• wood.m
• leon.m
• levi13.m
• matyas.m
• mccormick.m
• modschaffer1.m
• modschaffer2.m
• modschaffer3.m
• modschaffer4.m
• penholder.m
• powell.m
• rastrigin.m
• rosenbrock.m
• schweffel.m
• sinenvsin.m
• sixhumpcamel.m
• styblinskitang.m
• testtubeholder.m
• threehumpcamel.m
• trigonometric.m
• holdertable.m
• ezimage(fun)
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# Test functions for global optimization algorithms

### Rody Oldenhuis (view profile)

28 Feb 2009 (Updated )

Test functions for global optimization algorithms

File Information
Description

This is a set of test functions which can be used to test the effectiveness of global optimization algorithms. Some are rather easy to optimize (rosenbruck, leon, ...), others next to impossible (crosslegtable, bukin6, ...).
All the test-functions are taken from either [1], [2] or [3] (see below). All functions may be called in two ways:
[dims, lb, ub, sol, fval_sol] = fun
(e.g., no input arguments) This returns the number of dimensions of the function, the default lower and upper bounds, the solution vectors for all global minima and the corresponding function values. To calculate the function value for input X, use:

val = fun( [x1, x2, ..., xn] )

with the dimension [n] depending on the specific function [fun] (for most functions, n=2). Note the single vector argument--this is done in order to easily insert the function into a global optimizer that inserts a [N x n] matrix of trial vectors in these functions.

I also included a function to display most of the functions. This is called EZIMAGE, and can be called with a function handle argument:

ezimage(@himmelblau) (to plot the himmelblau function)
ezimage(@sinenvsin) (see screenshot)
...

or just as-is:

ezimage

which lists all functions and waits for user input. This is meant to get a first impression of what the challenges are the test function has to offer.

FUTURE WORK:
- constrained single-objective functions
- (constrained ) multi-objective functions

sources:
[1] Mishra, Sudhanshu. "Some new test functions for global optimization and performance of repulsive particle swarm method". MPRA, 23rd august 2006. http://mpra.ub.uni-muenchen.de/2718/

[2] Z.K. Silagadze. "Finding two-dimensional peaks". 11th mar 2004. arXiv preprint: arXiv:physics/0402085v3

[3] W. Sun, Ya-X. Yuan. "Optimization theory and Methods. Nonlinear Programming". Springer verlag, 2006. ISBN-13:978-0-387-24975-9.

If you find this work useful, please consider a donation:
https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=6G3S5UYM7HJ3N

MATLAB release MATLAB 7.9 (R2009b)
Other requirements None that I know of
22 Mar 2012 Gilberto A. Ortiz

### Gilberto A. Ortiz (view profile)

11 Feb 2010 1.1

- updated all functions to automate finding its dimensions/bounds
- cleaned up EZIMAGE() , and made it suitable for future extentions

14 Feb 2014 1.2

- Corrected bug in leon function (square -> cube)
- Contact info updated

17 Aug 2015 1.4

Fixed all bugs found by Jeffrey Larson (thanks!)

18 Aug 2015 1.3