## 4 Simulation Results
### Results on the Benchmark Test-Suite
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multirow{2}{*}{**PopSize**} & \multirow{2}{*}{**Gens**} & \multicolumn{3}{c}{**Best-of-Run Fitness**} & \multicolumn{3}{c}{**FirstHitFvals**} \\ \cline{3-10}  & & & **Best** & **Mean** & **Std Dev** & **Success** & **Best** & **Mean** & **Std Dev** \\ \hline Ackley & 100 & 3000 & \(4.2232\times 10^{-6}\) & \(7.6506\times 10^{-6}\) & \(1.9595\times 10^{-6}\) & 0 & — & — & — \\  & 150 & 5000 & \(3.9148\times 10^{-8}\) & \(8.2624\times 10^{-8}\) & \(2.5913\times 10^{-8}\) & 30 & 620,422 & 651,813.4333 & 11,801,5819 \\ Rosenbrock & 100 & 3000 & 0.0310 & 26.8113 & 27.5200 & 0 & — & — \\  & 150 & 5000 & 0.0521 & 37.0939 & 32.6063 & 0 & — & — \\ Chu-Rey & 100 & 3000 & \(6.1251\times 10^{-23}\) & \(2.2695\times 10^{-21}\) & \(2.7432\times 10^{-21}\) & 30 & 122,216 & 130,083.4667 & 3283,9261 \\  & 150 & 5000 & \(1.1798\times 10^{-30}\) & \(1.1626\times 10^{-29}\) & \(1.2429\times 10^{-29}\) & 30 & 230,733 & 245,191.6 & 6139,8179 \\ Step & 100 & 3000 & 0.0 & 0.0 & 0.0 & 30 & 82115 & 88940.6 & 4467,5422 \\  & 150 & 5000 & 0.0 & 0.0 & 0.0 & 30 & 154,374 & 166,652.7667 & 6105,3915 \\ Alpine-1 & 100 & 3000 & 0.0240 & 9.7502 & 5.6913 & 0 & — & — & — \\  & 150 & 5000 & 0.0381 & 6.2610 & 5.6690 & 0 & — & — & — \\ SumSquares & 100 & 3000 & \(1.5297\times 10^{-10}\) & \(4.5700\times 10^{-10}\) & \(2.2292\times 10^{-10}\) & 30 & 213,427 & 222,775.1667 & 3910,2976 \\  & 150 & 5000 & \(4.9038\times 10^{-15}\) & \(3.7103\times 10^{-14}\) & \(1.7512\times 10^{-14}\) & 30 & 406,918 & 421,195.1 & 7055,2581 \\ Sphere & 100 & 3000 & \(1.2410\times 10^{-9}\) & \(4.6650\times 10^{-9}\) & \(2.4779\times 10^{-9}\) & 30 & 231,137 & 245,599.1667 & 4874,0277 \\  & 150 & 5000 & \(8.6993\times 10^{-14}\) & \(3.6152\times 10^{-13}\) & \(2.3875\times 10^{-13}\) & 30 & 441,574 & 464,684.3667 & 10,701,7923 \\ Boha-3 & 15 & 5000 & 0.0 & 0.0301 & 0.1624 & 29 & 947 & 1368,5817 & 257,8614 \\ Boha-2 & 20 & 5000 & 0.0 & 0.0 & 0.0 & 30 & 1461 & 1877,333 & 275,2529 \\  & 15 & 5000 & 0.0 & 0.0347 & 0.1866 & 29 & 809 & 1102.7931 & 158,0520 \\ Boha-2 & 20 & 5000 & 0.0 & 0.0 & 0.0 & 30 & 1160 & 1590,8667 & 243,5768 \\ Bartels & 15 & 5000 & 1.0 & 1.0 & 0.0 & 30 & 995 & 1238,767 & 91,8632 \\  & 20 & 5000 & 1.0 & 1.0 & 0.0 & 30 & 1375 & 1684,0667 & 152,4998 \\ Gold-Pr & 15 & 5000 & 3.0000 & 3.0000 & \(1.4203\times 10^{-5}\) & 5 & 36,981 & 57,683.4 & 12,921,8507 \\  & 20 & 5000 & 3.0000 & \(3.0000\) & \(1.7344\times 10^{-5}\) & 3 & 37,550 & 52,030.0 & 15,017,5414 \\  & 15 & 5000 & 0.0 & \(1.6173\times 10^{-11}\) & \(8.7092\times 10^{-11}\) & 30 & 572 & 906,9667 & 261.1821 \\ Matyas & 20 & 5000 & 0.0 & \(1.9566\times 10^{-58}\) & \(1.0537\times 10^{-54}\) & 30 & 761 & 1286.0 & 264.6156 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of Java on the 12-function test-suite (each row corresponds to 30 independent runs). Most numbers are shown with rounding at the fourth place after the decimal. Table 4 presents the \(t\)-scores and one-tailed \(p\)-values from Smith-Satterthwaite tests ([PERSON]'s tests) ([PERSON], 1960) (corresponding to unequal population variances) run on the data in Tables 2 and 3 for examining whether or not the difference between the means of Jaya and SJaya (for the best-of-run fitnesses metric and, separately, for the FirstHitEvals metric) is significant. Using the subscripts 1 and 2 for Jaya and SJaya respectively, we obtain the test statistic as a \(t\)-score given by  
\[t=\frac{\bar{x}_{1}-\bar{x}_{2}-0}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^ {2}}{n_{2}}}},\]  
and the degrees of freedom of the \(t\)-distribution (this \(t\)-distribution is used to approximate the sampling distribution of the difference between the two means) as  
\[\frac{\left(\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}\right)^{2}}{\frac {\left(\frac{s_{1}^{2}/n_{1}}{}\right)^{2}}{n_{1}-1}+\frac{\left(\frac{s_{2}^ {2}/n_{2}}{}\right)^{2}}{n_{2}-1}},\]  
where the symbols \(\bar{x},s\) and \(n\) represent mean, standard deviation and sample size, respectively.