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I. Mathematical Expression:

$$f(X)=\left(e^{\displaystyle x_1}-x_2\right)^4+100\left(x_2-x_3\right)^6+\left[\tan\left(x_3-x_4\right)\right]^4+x^8_1$$

where:

\(\bullet\) \(-1\leq x_i\leq 1\) , \(j=1,2,3,4\)

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

\(\bullet\) \(x^*_i=(0,1,1,1)\)

 

II. References:

[1] M. M. Ali, C. Khompatraporn, and Z. B. Zabinsky, "A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems," Journal of Global Optimization, vol. 31, no. 4, pp. 635-672, Apr. 2005.
[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

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