Gulf Research Problem

I. Mathematical Expression:

$$f(X)=\sum^m_{j=1}\left(e^{\displaystyle-\frac{\displaystyle\left|y_j-x_2\right|^{x_3}}{\displaystyle x_1}}-t_j\right) \ \ , \ \ m=99$$

where:

\(\bullet\) \(t_j=\frac{j}{100}\)

\(\bullet\) \(y_j=25+\sqrt{\left[-50\log\left(t_j\right)\right]^2}\)

\(\bullet\) \(0.1\leq x_1\leq 100\) , \(0\leq x_2\leq 25.6\) , \(0\leq x_3\leq 5\)

\(\bullet\) In [2], the same side constraints are used for all the independent variables:

$$0\leq x_i\leq 60 \ \ , \ \ i=1,2,3$$

\(\bullet\) \(f_{min}(X^*)=0\)

\(\bullet\) \(x^*_i=(50,25,1.5)\)

II. Citation Policy:

If you publish material based on databases obtained from this repository, then, in your acknowledgments, please note the assistance you received by using this repository. This will help others to obtain the same data sets and replicate your experiments. We suggest the following pseudo-APA reference format for referring to this repository:

Ali R. Al-Roomi (2015). Unconstrained Single-Objective Benchmark Functions Repository [https://www.al-roomi.org/benchmarks/unconstrained]. Halifax, Nova Scotia, Canada: Dalhousie University, Electrical and Computer Engineering.

Here is a BiBTeX citation as well:

@MISC{Al-Roomi2015,
author = {Ali R. Al-Roomi},
title = {{Unconstrained Single-Objective Benchmark Functions Repository}},
year = {2015},
address = {Halifax, Nova Scotia, Canada},
institution = {Dalhousie University, Electrical and Computer Engineering},
url = {https://www.al-roomi.org/benchmarks/unconstrained}
}

III. References:

[1] M. Jamil and X. S. Yang, "A Literature Survey of Benchmark Functions for Global Optimization Problems," International Journal of Mathematical Modelling and Numerical Optimisation, vol. 4, no. 2, pp. 150–194, Aug. 2013.
[2] A. Gavana, "Test Functions Index," Feb. 2013, [Accessed April 01, 2013]. [Online]. Available: http://infinity77.net/global_optimization/test_functions.html
[3] Ali R. Alroomi, "The Farm of Unconstrained Benchmark Functions," University of Bahrain, Electrical and Electronics Department, Bahrain, Oct. 2013. [Online]. Available: http://www.al-roomi.org/cv/publications