Mishra Function No.09 (or Dodecal Polynomial Function)

I. Mathematical Expression:

$$f(X)=\left[f_1 f^2_2 f_3 + f_1 f_2 f^2_3 + f^2_2 +\left(x_1+x_2-x_3\right)^2\right]^2$$

where:

\(\bullet\) \(f_1=2x^3_1+5x_1x_2+4x_3-2x^2_1x_3-18\)

\(\bullet\) \(f_2=x_1+x^3_2+x_1x^2_2+x_1x^2_3-22\)

\(\bullet\) \(f_3=8x^2_1+2x_2x_3+2x^2_2+3x^3_2-52\)

\(\bullet\) \(-10\leq x_i\leq 10\) , \(i=1,2,3\)

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

\(\bullet\) \(x^*_i=(1,2,3)\)

\(\bullet\) Its name is "Dodecal Polynomial Function" as in [1], while it is called "Mishra Function No.09" in [2, 3] because it is designed by Mishra in [1]. Thus, we want to clarify this hidden point by adding both names as: "Mishra Function No.09 (or Dodecal Polynomial Function)".

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] S. Mishra, "Repulsive Particle Swarm Method on Some Difficult Test Problems of Global Optimization," Shillong, India, Oct. 2006. [Online]. Available: http://mpra.ub.uni-muenchen.de/1742/1/MPRA_paper_1742.pdf
[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