Table 2.

Different artificially generated functions using Uniform noise and Gaussian noise with their definition and domain of definition

Function name	Function definition	Domain of definition	Noise Type
Function1 Function2	$\text{f(x)}=\left(\frac{4}{|x_1|+2}\right)+cos(2x_1)+sin(3x_1)+\Theta$	${\text{x}}_1\in [-10,10]$	Type A:$\Theta \in U(-0.2,0.2)$ Type B:$\Theta \in N(0,0.1^2)$
Function3 Function4	$\begin{array}{cc}\hfill {\text{f(x}}_1,{\text{x}}_2,{\text{x}}_3,{\text{x}}_4,{\text{x}}_5)& =0.79+1.27{\text{x}}_1{\text{x}}_2+1.56{\text{x}}_1{\text{x}}_4\hfill \\ \hfill & +3.42{\text{x}}_2{\text{x}}_5+2.06{\text{x}}_3{\text{x}}_4{\text{x}}_5+\Theta \hfill \end{array}$	${\text{x}}_{\text{i}}\in [0,1]$ $\text{i}\in \text{{ 1,2,3,4,5}}$	Type A:$\Theta \in U(-0.2,0.2)$ Type B:$\Theta \in N(0,0.1^2)$
Function5 Function6	${\text{f(x}}_1,{\text{x}}_2)=42.659(0.1{\text{+ x}}_1(0.05{\text{+ x}}_1^4{\text{- 10x}}_1^2{\text{x}}_2^2{\text{+ 5x}}_2^4))+\Theta$	${\text{x}}_1,{\text{x}}_2\in [-0.5,0.5]$	Type A:$\Theta \in U(-0.2,0.2)$ Type B:$\Theta \in N(0,0.1^2)$
Function7 Function8	$\begin{array}{c}\hfill {\text{f(x}}_1,{\text{x}}_2,{\text{x}}_3,{\text{x}}_4,{\text{x}}_5{)=10\text{sin}\pi {\text{x}}_1{\text{x}}_2{\text{+ 20(x}}_3-0.5)}^2{\text{+ 10x}}_4{\text{+ 5x}}_5+\Theta \end{array}$	${\text{x}}_{\text{i}}\in [0,1]$ $\text{i}=1,2,3,4,5$	Type A:$\Theta \in U(-0.2,0.2)$ Type B:$\Theta \in N(0,0.1^2)$
Function9 Function10	${\text{f(x}}_1)=\left(\frac{4}{|x_1|+2}\right)+cos(2x_1)+sin(3x_1)+\Theta$	${\text{x}}_1\in [-10,10]$	Type A:$\Theta \in U(-0.2,0.2)$ Type B:$\Theta \in N(0,0.2^2)$
Function11 Function12	$\begin{array}{c}\hfill {\text{f(x}}_1,{\text{x}}_2)=1.3356\left(exp,\left(3\left({\text{x}}_2-0.5\right)\right),sin,\left(4\pi \left(x_2-0.9\right)\right)\right)\\ \hfill \left(+,1.5,\left(1-x_1\right)\right)+1.5\left(1-x_1\right)+exp\left(2x_1-1\right)\\ \hfill sin\left(3\pi \left(x_1-0.6\right)\left(x_1-0.6\right)\right)+\Theta \end{array}$	${\text{x}}_{\text{i}}\in [0,1]$ $\text{i}\in \text{{ 1,2}}$	Type A:$\Theta \in U(-0.2,0.2)$ Type B:$\Theta \in N(0,0.2^2)$
Function13 Function14	$\begin{array}{c}\hfill {\text{f(x}}_1)=\left(\frac{1}{0.3\sqrt{2\pi }}\right)exp\left(-\left(\left(x_1-2\right)\left(x_1-2\right)\right)/\left(2\left(0.3^2\right)\right)\right)\\ \hfill +\left(\frac{1}{1.2\sqrt{2\pi }}\right)exp\left(-\left(\left(x_1-7\right)\left(x_1-7\right)\right)/\left(2\left(1.2^2\right)\right)\right)+\Theta \\ \hfill \end{array}$	${\text{x}}_1\in [0,10]$	Type A:$\Theta \in U(-0.5,0.5)$ Type B:$\Theta \in N(0,0.1^2)$
Function15 Function16	$f_1(x)=\frac{sin(x)}{x}$ such that $y_i=f_1(x_i)+\left(0.5-\frac{|x_i|}{8\pi }\right){\Theta }_i$	$\begin{array}{cc}& x_i\in U(-4\pi ,4\pi ),\hfill \\ \hfill & i=1,2,\dots ,200\hfill \end{array}$	Type A: $\Theta \in U(-1,1)$ Type B: $\Theta \in N(0,0.5^2)$
Function17 Function18	$\text{f(x)}={\text{x + 2exp( - 16x}}^2)$ such that ${\text{y}}_{\text{i}}={\text{f(x}}_{\text{i}}){\text{+ (x}}_{\text{i}}+0.5){\Theta }_i$	${\text{x}}_{\text{i}}=0.01(\text{i - 1) - 1,}$ $i=1,2,\dots ,200$	Type A: $\Theta \in U(-1,1)$ Type B: $\Theta \in N(0,0.5^2)$