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I. Mathematical Expression:

$$f(X)=\sum_{j=1}^{m}\left[\left(x_1+x_2e^{\displaystyle -x_4 tj}+x_3e^{\displaystyle -x_5 t_j}\right)-y_j\right]^2 \ \ , \ \ \ m=33$$

where:

\(\bullet\) \(t_j=10\left(j-1\right) \ \ , \ \ \ j=1,2,...,m\)

\(\bullet\) \(y_j=\begin{pmatrix}
0.844, & 0.908, & 0.932, & 0.936, & 0.925, & 0.908, & 0.881, & 0.850, & 0.818, & 0.784, & 0.751, \\
0.718, & 0.685, & 0.658, & 0.628, & 0.603, & 0.580, & 0.558, & 0.538, & 0.522, & 0.506, & 0.490, \\
0.478, & 0.467, & 0.457, & 0.448, & 0.438, & 0.431, & 0.424, & 0.420, & 0.414, & 0.411, & 0.406
\end{pmatrix}\)

\(\bullet\) \(0\leq x_1,x_2,x_4,x_5\leq 3\) , \(-3\leq x_3\leq 0\)

\(\bullet\) \(f_{min}(X^*)\approx 5.46 \times 10^{-5}\)

\(\bullet\) \(x^*_i\cong (0.3753,1.9358,-1.4647,0.01287,0.02212)\)

 

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] David R. Monismith JR., "The Uses of the Slime Mold Lifecycle as a Model for Numerical Optimization," Ph.D. Dissertation, Oklahoma State University, Oklahoma City, OK, 2010, [Accessed May. 11, 2015]. [Online]. Available: https://shareok.org/bitstream/handle/11244/6493/Computer%20Science%20Department_11.pdf
[2] D. Kundu and A. Mitra, "Estimating the Parameters of the Linear Compartment Model," Journal of Statistical Planning and Inference, vol. 70, no. 2, pp. 317-334, May 1998.
[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