Simpleton Problem

I. Mathematical Expression:

$$f(X)=\frac{\displaystyle x_1 \cdot x_2 \cdot x_3 \cdot x_4 \cdot x_5}{\displaystyle x_6 \cdot x_7 \cdot x_8 \cdot x_9 \cdot x_{10}}$$

where:

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

\(\bullet\) \(f_{max}(X^*)=10^5\)

\(\bullet\) \(x^*_i =(10,10,10,10,10,1,1,1,1,1)\)

\(\bullet\) This benchmark function is presented in [1] as a trivial \(10-\)dimensional maximization problem. The maxima can be easily obtained by maximizing the numerator and minimizing the denominator [2].

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] 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