# Extended Evolutionary Algorithms with Stagnation-Based Extinction Protocol
## 4 Experimental Design and Result
### Results and Discussion  
The summarized experimental results of Simple GA (SGA) and SDEP-GA using random and targeted extinction is shown in Table 1.  
With reference to the third column of Table 1, we can see that SDEP with targeted extinction has a lower fitness value when compared to SGA for Rastrigin, Schwefel, and Griewank. As these three test functions are all minimization problems, the lower fitness value indicates that the algorithm scores better in terms of accuracy. In terms of _Pen_, we can see that SDEP-GA has a lower or equal value when compared against SGA. This indicates that the algorithm is able to find a better result within a shorter number of generations. In other words, SDEP with targeted extinction evolves towards the right direction at a faster rate compared to SGA. The lower value of SDEP-GA in _Mgn_ shows that it is able to find a close approximation of the ideal solution faster than SGA. Figure 6 shows the fitness values of the three algorithms over the generations for Rastrigin, which supports our argument. In Figure 6, note that we reversed the fitness for convenience in understanding the graph. It can be seen that SDEP with targeted extinction  
reaches near-optimum earlier than SGA and achieves near-optimum points multiple times. These results suggest that SDEP with targeted extinction is better in terms of accuracy as well as the computation time to reach the solution when compared against SGA. The overall running time of SDEP-GA is a slightly longer than that of SGA because of the extinction overhead. Table 2 shows the running time in milliseconds for Rastrigin, Schwefel, and Griewank functions, respectively. However, for complicated problems like Griewank, there is not much difference in running time among the algorithms, because the additional overhead for random and targeted extinction is relatively small. Tables 3-5 show the fitness results of SDEP-GA Random Extinction with various parameters on Rastrigin, Schwefel, and Griewank functions, respectively. Note that the optimal value is in bold. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Function** & **Algorithm** &
\begin{tabular}{c} **Running Time (in** \\ **Milliseconds)** \\ \end{tabular} \\ \hline \multirow{3}{*}{Rastrigin} & SGA & 433.13 \(\pm\) 5.23 \\ \cline{2-3}  & Random Extinction & 628.23 \(\pm\) 16.79 \\ \cline{2-3}  & Targeted Extinction & 913.33 \(\pm\) 82.83 \\ \hline \multirow{3}{*}{Schwefel} & SGA & 455.36 \(\pm\) 5.25 \\ \cline{2-3}  & Random Extinction & 719.36 \(\pm\) 66.26 \\ \cline{2-3}  & Targeted Extinction & 832.13 \(\pm\) 69.66 \\ \hline \multirow{3}{*}{Griewank} & SGA & 830.70 \(\pm\) 104.79 \\ \cline{2-3}  & Random Extinction & 870.00 \(\pm\) 104.87 \\ \cline{2-3}  & Targeted Extinction & 996.8 \(\pm\) 53.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overall running time (in milliseconds) of SGA, and SDEP-GA with random and targeted extinction; 95% confidence interval is presented after \(\pm\) sign. Figure 6: Fitness values over the generations for Rastrigin. Fitness values are inverted for convenience (i.e., higher values are more accurate).