## 3 Proposed Improved Hybrid SSA with an EDO (ISSAEDO) Algorithm
### Results of the Proposed ISSAEDO Compared with Other Recent Algorithms  
This subsection compares the performance of the proposed ISSAEDO against various current algorithms, including an improved gaining-sharing knowledge (IGSK) [8], a modified teaching-learning-based optimization (MTLBO) [45], a Memory-based Improved Go-rilla Troops Optimizer (MIGTO) [46], reinforcement learning-based differential evolution (DERL) [22], self-adaptive ensemble-based DE (SEDE) [47], Opposition-based JAYA with population reduction (EJAYA) optimization algorithm [48], and hybrid adaptive teaching-learning-based optimization with DE (ATLDE) [49], which were carried out under the same experimental settings. Table 12 presents the five unknown parameter values \(l_{ph}\), \(I_{sd}\), \(R_{s}\), \(R_{sh}\), \(\gamma\), and RMSE for SDM. Based on the values of RMSE shown in Table 12, ISSAEDO, IGSK, MIGTO, DERL, and EJAYA obtained the lowest RMSE value (9.8602187789E-04). Table 13 presents the minimum, maximum, mean, and STD of the RMSE values of the proposed ISSAEDO and their counterpart algorithms. The approaches (ISSAEDO, IGSK, MIGTO, \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Algorithm** & \(I_{ph}\) **(A)** & \(I_{sd}\) **(in A)** & \(R_{s}(\Omega)\) & \(R_{sh}(\Omega)\) & \(\gamma_{1}\) & \(I_{sd}\) **(in A)** & \(\gamma_{2}\) & **RMSE** \\ \hline SSA & 0.7607292070 & 0.0962466377 & 0.0335449530 & 66.7972347000 & 1.8260237200 & 0.6065940090 & 1.5498233600 & 1.8536310762E-03 \\ EDO & 0.3920021250 & 0.1988300750 & 0.272707010 & 96.9255478000 & 1.2826811200 & 0.1131069910 & 1.871131950 & 6.5929103094E-03 \\ SSAEDO & 0.760760010 & 0.4846699400 & 0.0360174473 & 63.7180802000 & 1.53585089000 & 0.0024107608 & 1.2508950300 & 1.2588395188E-03 \\ DE & 0.7607818090 & 0.2236078160 & 0.0367528712 & 55.5095593000 & 1.4501308800 & 0.7684338980 & 1.9999971250 & 9.824887651E-04 \\ SSAED & 0.7607811140 & 0.2295090230 & 0.036740557 & 55.8485939000 & 1.451007700 & 0.79459450350 & 1.99999998000 & 9.8248485256E-04 \\ EDODE & 0.7607741680 & 0.1465681030 & 0.0363745501 & 53.7224790000 & 1.488549700 & 0.1777515470 & 1.47604430000 & 9.8602227227E-04 \\ ISSAEDO & 0.7607810790 & 0.2259739760 & 0.0367404315 & 55.4854436000 & 1.4510166600 & 0.74934989100 & 2.0000000000 & **9.8248485179E-04** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Optimum parameters obtained by the diverse components of the ISSAEDO for SDM. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Algorithm** & \(I_{ph}\) **(A)** & \(I_{sd}\) **(in A)** & \(R_{s}(\Omega)\) & \(R_{sh}(\Omega)\) & \(\gamma_{1}\) & \(I_{sd}\) **(in A)** & \(\gamma_{2}\) & **RMSE** \\ \hline SSA & 0.7611237070 & 0.2553533450 & 0.0372915872 & 46.3936672000 & 1.4578304200 & 1.1351825925E-03 \\ EDO & 0.1494502860 & 0.64163660 & 0.2519534990 & 85.2178070000 & 1.4772455100 & 8.7962970619E-03 \\ SSAEDO & 0.9631364110 & 0.0491793204 & 0.2857274100 & 79.7732647000 & 1.3100563200 & 1.5303729578E-03 \\ DE & 0.7607755300 & 0.3230207970 & 0.0363707928 & 53.718523000 & 1.4811835900 & **9.860218779E-04** \\ SSAED & 0.7607755240 & 0.3230210790 & 0.036370790 & 53.7186219000 & 1.4811836700 & 9.8602187790E-04 \\ EDODE & 0.3842538840 & 0.0994869333 & 0.16755090700 & 65.4048061000 & 1.0850875010 & 9.9793333516E-04 \\ ISSAEDO & 0.7607755300 & 0.323020207850 & 0.0363707930 & 53.7185252000 & 1.4811835800 & **9.8602187789E-04** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Optimum parameters obtained by the diverse components of the ISSAEDO for SDM.