Wood's (or Colville's) Function

I. Mathematical Expression:

$$f(X)=\left[100\left(x_2-x^2_1\right)\right]^2+\left(1-x_1\right)^2+90\left(x_4-x^2_3\right)^2+\left(1-x_3\right)^2+$$

$$10.1\left[\left(x_2-1\right)^2+\left(x_4-1\right)^2\right]+19.8\left(x_2-1\right)\left(x_4-1\right)$$

where:

\(\bullet\) \(-10\leq x_i\leq 10\) , \(i=1,2,3,4\)

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

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

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. S. Rao, Engineering Optimization: Theory and Practice, 4th ed. Hoboken, New Jersey: John Wiley & Sons, 2009.
[2] X. Zhao and X.-S. Gao, "Affinity Genetic Algorithm," Journal of Heuristics, vol. 13, no. 2, pp.133-150, Apr. 2007.
[3] E. P. Adorio, "MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization," Quezon City, Metro Manila, Philippines, Jan. 2005. [Online]. Available: http://geocities.ws/eadorio/mvf.pdf
[4] S. Rahnamayan, H. R. Tizhoosh, and M. M. A. Salama, "A Novel Population Initialization Method for Accelerating Evolutionary Algorithms," Computers & Mathematics with Applications, vol. 53, no. 10, pp. 1605-1614, May 2007.
[5] A. D. Belegundu and T. R. Chandrupatla, Optimization Concepts and Applications in Engineering, 2nd ed. New York: Cambridge University Press, 2011.
[6] 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.
[7] A. Gavana, "Test Functions Index," Feb. 2013, [Accessed April 01, 2013]. [Online]. Available: http://infinity77.net/global_optimization/test_functions.html
[8] 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