# 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. 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