Mineshaft Function No.01

I. Mathematical Expression:

$$f(x)=\cos(x)+\left|(7-x)^{2/15}\right|+2\left|(5-x)^{4/35}\right|$$

where:

\(\bullet\) \(0\leq x \leq 10\)

\(\bullet\) \(f_{min}(x^*)=1.380487165157852\)

\(\bullet\) \(x^*=5\) (determined by us using MapleSoft 2015)

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. 2D-Plot:

IV. MATLAB M-File:

% Mineshaft Function # 1
% Range of initial points: 0 <= x <= 10
% Global minima: x=5;
% f(x)=1.380487165157852

clear
clc
warning off

x=0:0.0005:10;

for i=1:length(x)
    f(i)=cos(x(i))+abs(((7-x(i))^(2/15)))+2*abs(((5-x(i))^(4/35)));
end

plot(x,f,'r','LineWidth',2);grid;set(gca,'FontSize',12);
xlabel('x','FontName','Times','FontSize',20,'FontAngle','italic');
ylabel('f(x)','FontName','Times','FontSize',20,'FontAngle','italic');

Click here to download m-file

V. References:

[1] D. R. M. Jr., "The Uses of the Slime Mold Lifecycle as a Model for Numerical Optimization," Ph.D. Dissertation, Oklahoma State University, Oklahoma City, OK, Jul. 2010, [Accessed Apr. 30, 2013]. [Online]. Available: http://www.cs.okstate.edu/~monismi/dissertation/MonismithDissertation.pdf
[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