Dolan's Function No.02

I. Mathematical Expression:

$$f(X)=\left(x_1+1.7x_2\right)\sin\left(x_1\right)-1.5x_3-0.1x_4\cos\left(x_5+x_4-x_1\right)+0.2x_5^2-x_2-1$$

where:

\(\bullet\) \(-100\leq x_i\leq 100\) , \(i=1,2,\cdots,5\)

\(\bullet\) Best known solution: \(f_{min}(X^*)=-529.8714387324576\)

\(\bullet\) \(x^*_i =(98.964258312237106,100,100,99.224323672554704,-0.249987527588471)\)

\(\bullet\) This benchmark function is presented in [1], but without much details. The given optima in [2] is wrong, and the absolute function in [3] is also wrong. The best known optimal solution of this benchmark function is obtained by us, which is shown above.

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] Ariel Dolan, "A General GA Toolkit Implemented in JAVA, for Experimenting with Genetic Algorithms and Handling Optimization Problems," Jun. 1998, [Accessed August 06, 2015]. [Online]. Available: http://www.aridolan.com/ofiles/ga/gaa/gaa.aspx
[2] 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.
[3] A. Gavana, "Test Functions Index," Feb. 2013, [Accessed April 01, 2013]. [Online]. Available: http://infinity77.net/global_optimization/test_functions.html
[4] 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