## 5 Iwoa-Iga--Enhanced WOA Algorithm Featuring Improved Genetic Mechanism
### Iwoa-Iga: Modified Iwo Algorithm Featuring IGA Characteristics
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Task Graph** & **Over PSO** & **Over SA** & **Over GA** \\ \hline
32 Cores & 45.66\% & 50.56\% & 48.15\% \\
64 Cores & 40.29\% & 33.70\% & 41.33\% \\
128 Cores & 30.60\% & 33.31\% & 26.67\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percent communication cost savings with IWOA-IGA compared to other algorithms for extensive task graphs. 2.4 Performance Comparison of IWOA and IFOA-IGA: Optimizing Latency for 2D NoC Benchmark Applications

Network communication latency is a crucial factor to consider when evaluating mapping solutions. This subsection discusses the average latency derived with various approaches. Utilizing the NoC simulator [39], the proposed work was evaluated on a \(4\times 4\) mesh topology with an X-Y routing algorithm and wormhole-based routers. The evaluation showed that the IWO algorithm yielded latency improvements of 1.91% over PSO, 5.14% over SA, 5.7% over GA, and 1% over iHPSA. The extended IWOA-IGA version showed improvements of 2.87% over PSO, 6.08% over SA, 6.61% over GA, and 2% over iHPSA. The comparison is illustrated in the Figure 11.

Figure 11: Average latency for standard benchmarks. Figure 10: Energy estimation for standard benchmarks (normalized). Figure 9: Power estimation for standard benchmarks. #### 6.2.5 Convergence Evaluation Based on Convergence Factor

Convergence of any algorithm is one of the most important factors of an application mapping technique intended to acquire optimal mapping in a lesser number of iterations. Different algorithms running different applications may utilize different numbers of iterations and communication costs for the calculation of optimal mapping. Mathematically exact methods are able to solve small-scale problems (less than 20 cores) in around 7-8 h. While heuristic techniques are much faster, they may not offer optimal communication cost. They normally achieve near-optimal cost after the algorithm has run for a specific number of iterations. An algorithm that requires fewer iterations to achieve the lowest communication cost is considered to converge well, and is rated as highly suitable for the application mapping problem domain. Thus, one of the performance metrics considered in this paper is the convergence factor, which evaluates the algorithm's ability to converge effectively. Performance based on algorithm convergence ability is measured by calculating the average number of times the algorithm successfully converges, taking into account the number of hits achieved by the algorithm out of the total number of runs. To evaluate performance based on the convergence factor, the algorithms were tested 30 times while measuring the convergence factor for a range of real-time and synthetic task graphs of varying sizes. The proposed method was compared with PSO, SA, GA, and iHPSA based on the number of times the algorithms achieved the lowest communication cost over a certain number of runs. The equation for calculating the convergence factor is provided by

\[Perf_{cf}=Nav_{c}/NR_{total}, \tag{36}\]

where \(Perf_{cf}\) is the performance based on the convergence factor, \(Nav_{c}\) is the average number of times the algorithm converged, and \(NR_{total}\) is the total number of times the algorithm was run. The comparison results for the real-world and synthetic applications are shown in Table 6, which shows that the algorithm converged several times when being run 30 times. The table shows \(Nav_{c}\), the average number of times the algorithm converged for the specific application, which is calculated here based on half of the algorithm's executions R1-R15 (average halved) instead of 30, which is \(NR_{total}\), the total number of times the algorithm was run for a specific application. The average value of convergence \(Nav_{C}\) calculated for PSO, SA, GA, IWOA, and IWOA-IGA against real and synthetic benchmarks was found to be 10.71, 10.28, 11.14, 11.42, and 12.42, respectively.