# An Innovative Enhanced JAYA Algorithm for the Optimization of Continuous and Discrete Problems
## 4 Results and Discussion
### Numerical Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline
**Test Function** & **Iteration** & **Dimension** & **Range** \\ \hline \(F_{1}(x)=\sum\limits_{i=1}^{n}x_{i}^{2}\) & 1000 & 30 & \([-100,100]\) \\ \(F_{2}(x)=\sum\limits_{i=1}^{n}|x_{i}|+\prod\limits_{i=1}^{n}x_{i}\) & 1000 & 30 & \([-10,10]\) \\ \(F_{3}(x)=(1.5-x_{1}+x_{1}\times x_{2})^{2}+\big{(}2.25-x_{1}+x_{1}\times x_{2 }\big{)}^{2}+\big{(}2.625-x_{1}+x_{1}\times x_{2}\big{)}^{2}+\big{(}2.625-x_{1} +x_{1}\times x_{2}\big{)}^{2}\) & 1000 & 30 & \([-4.5,4.5]\) \\ \(F_{4}(x)=\max\limits_{i}\{|x_{i}|\ \,\ \ 1\leq i\leq n\}\) & 1000 & 30 & \([-100,100]\) \\ \(F_{5}(x)=\sum\limits_{i=1}^{n-1}\Big{[}100\big{(}x_{i+1}+x_{i}^{2}\big{)}^{2}+ (x_{i}-1)^{2}\Big{]}\) & 1000 & 30 & \([-30,30]\) \\ \(F_{6}(x)=0.5+\frac{sin^{2}\big{(}x_{1}^{2}-x_{2}^{2}\big{)}-0.5}{[1+0.001(x_{ 1}^{2}+x_{2}^{2})]^{2}}\) & 1000 & 30 & \([-100,100]\) \\ \(F_{7}(x)=\sum\limits_{i=1}^{n}ix_{i}^{4}+random[0,\ 1)\) & 1000 & 30 & \([-1.28,\) \\ \(F_{8}(x)=sin^{2}(\pi w_{1})+\sum\limits_{i=1}^{d-1}(x_{1}-1)^{2}\Big{[}1+10 \text{sin}^{2}(\pi w_{i}+1)\Big{]}+(w_{d}-1)^{2}\) & & 1.28 \\ \([1+10\text{sin}^{2}(2\pi w_{d})]\) & & & \\ \(w_{i}=1+\frac{x_{i}-1}{4}\) & & & \\ \(F_{9}(x)=sin^{2}(3\pi x_{1})+(x_{1}-1)^{2}\Big{[}1+sin^{2}(3\pi x_{2})\Big{]}+( x_{2}-1)^{2}\Big{[}1+sin^{2}(2\pi x_{2})\Big{]}\) & 1000 & 30 & \([-10,10]\) \\ \(F_{10}(x)=-20\text{exp}\Bigg{(}-0.2\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}x_{ i}^{2}}\Bigg{)}-exp\ \bigg{(}\frac{1}{n}\sum\limits_{i=1}^{n}\cos(2\pi x_{i})+20+e\bigg{)}\) & 1000 & 30 & \([-32,32]\) \\ \(F_{11}(x)=\frac{1}{4000}\sum\limits_{i=1}^{n}x_{i}^{2}-\prod\limits_{i=1}^{n} \cos\bigg{(}\frac{x_{i}^{2}}{\sqrt{i}}\bigg{)}+1\) & 1000 & 30 & \([-600,600]\) \\ \(F_{12}(x)=\frac{\pi}{n}\bigg{\{}10\text{sin}(\pi y_{i})+\sum\limits_{i=1}^{n-1 }(y_{i}-1)^{2}\Big{[}1+10\text{sin}^{2}(\pi y_{i+1})+(y_{n}-1)^{2}\Big{]}\bigg{\}}\) & & \\ \(+\sum\limits_{i=1}^{n}u\Big{(}x^{i},\ 10,100,4\Big{)}\) & & & \\ \(y_{i}=1+\frac{x_{i}+1}{4}\) & 1000 & 30 & \([-50,50]\) \\ \(u(x^{i},\ a,k,m)=\begin{cases}k(x_{i}-a)^{m}&x_{i}>a\\ 0&-a<x_{i}<a\\ k(-x_{i}-a)^{m}&x_{i}<-a\end{cases}\) & & \\ \(F_{13}(x)=0.1\{sin^{2}(3\pi x_{1})\}\) & 1000 & 30 & \([-50,50]\) \\ \(+\sum\limits_{i=1}^{n}(x_{i}-1)^{2}[1+sin^{2}(3\pi x_{i}+1)]+(x_{n}-1)^{2}\) & & & \\ \(+(x_{n}-1)^{2}[1+sin^{2}(3\pi x_{n})]\) & & & \\ \(F_{14}(x)=\sum\limits_{i=2}^{n}i(2\pi_{i}^{2}-x_{i-1}^{2})^{2}+(x_{1}-1)^{2}\) & 1000 & 30 & \([-10,10]\) \\ \(F_{15}(x)=\sum\limits_{i=1}^{n}|x_{i}\text{sin}(x_{i})+0.1x_{i}|\) & 1000 & 30 & \([-1,1]\) \\ \(F_{16}(x)=\sum\limits_{i=1}^{n}(10\theta)\frac{i-1}{n-1}x_{i}^{2}\) & 1000 & 30 & \([-100,100]\) \\ \(F_{17}(x)=\ (x_{1}-1)^{2}+\sum\limits_{i=1}^{n}i(2\pi_{i}^{2}-x_{i-1})^{2}\) & 1000 & 30 & \([-1,1]\) \\ \(F_{18}(x)=\sum\limits_{i=1}^{n}ix_{i}^{2}\) & 1000 & 30 & \([-100,100]\) \\ \(F_{19}(x)=\sum\limits_{i=1}^{n}(x_{i}-1)^{2}-\sum\limits_{i=2}^{n}x_{i}x_{i-1}\) & 1000 & 30 & \([-n^{2},\ n^{2}]\) \\ \(F_{20}(x)=1-\cos\Bigg{(}2\pi\Bigg{(}\sqrt{\sum\limits_{i=1}^{2}x_{i}^{2}} \Bigg{)}\Bigg{)}+0.1\sqrt{\sum\limits_{i=1}^{n}x_{i}^{2}}\) & 1000 & 30 & \([-100,100]\) \\ \hline \end{tabular}
\end{table} 
Table 1: The benchmark functions. Figure 1: Cont. Figure 1: The search space of the functions is presented. Table 2 displays the fitness findings for functions 1-6, including the mean, best value, and standard deviation (STD). Based on these findings, each algorithm that can provide the least fitness function is ranked higher. As can be observed, EJAYA is ranked as the best algorithm for optimizing F1, since it has the lowest mean, standard deviation, and worst and best values. Similarly, the mean value in F2, obtained by EJAYA and the SCA, accounting for 1.04480E\(-\)35 and 3.21435E\(-\)07, respectively. EJAYA was able to identify a higher-quality solution in optimizing F2, although the SCA is ranked as the second algorithm. Regarding optimizing F3, basic JAYA and EJAYA have the same efficiency in finding the optimal solution.