## 3 Results and Discussion
### Summary Results of Optimization Algorithms  
The set of optimal transesterification conditions that maximize the biodiesel yield was predicted by applying three algorithms (BB-BC, GWO, and FA). Equation (5) serves as an objective function to conduct optimization for maximum biodiesel yield. The algorithm search with the upper and lower bounds of transesterification variables was used for experimentation (see Table 2). The efficacy of all three algorithms was evaluated on the basis of computation time and solution accuracy. Note that the common algorithm parameters, such as population size and iterations to terminate the program, are kept fixed to 100 and 1000, respectively. The results attained from each algorithm were tested 10 times, and the best solution corresponds to the fitness value and computation time is recorded (see Table 6). Tuning algorithm-specific parameters (GWO: convergence constant, FA: randomness, absorption coefficient, randomness reduction; BB-BC: exploration factor) is of the utmost importance, as it could determine the optimization efficiency [78; 90; 91]. Tuning algorithm-specific parameters was carried out to maximize the fitness values (biodiesel yield (%)) and the optimal parameters were selected after the algorithm ran for successive trials. The optimal transesterification conditions were thus determined after fixing algorithm-specific parameters and common parameters (population size: 100 and iterations: 1000) that could result in maximum biodiesel yield. The fitness value (i.e., maximum yield)  
Figure 5: Predicted versus actual biodiesel yield. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of Squares** & **DF** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline MO \(\times\) Rt & 0.8100 & 1 & 0.8100 & 5.69 & 0.0318 \\ CC \(\times\) RT & 1.44 & 1 & 1.44 & 10.11 & 0.0067 \\ CC \(\times\) Rt & 7.56 & 1 & 7.56 & 53.10 & 0.0001 \\ RT \(\times\) Rt & 0.4225 & 1 & 0.4225 & 2.97 & 0.1070 \\ MO 2 & 76.54 & 1 & 76.54 & 537.41 & 0.0001 \\ CC 2 & 12.44 & 1 & 12.44 & 87.37 & 0.0001 \\ RT 2 & 0.3211 & 1 & 0.3211 & 2.25 & 0.1554 \\ Rt 2 & 6.78 & 1 & 6.78 & 47.62 & 0.0001 \\ Residual & 1.99 & 14 & 0.1424 & & \\ Lack of Fit & 1.35 & 10 & 0.1346 & 0.8308 & 0.6322 \\ Pure Error & 0.6480 & 4 & 0.1620 & & \\ Cor Total & 152.77 & 28 & & & \\ \hline \end{tabular}
\end{table} 
Table 5: _Cont._corresponding to all three algorithms (GWO, FA, and BB-BC) was found to be equal to 94.15%, 94.15%, and 93.07%, respectively. Note that GWO and FA resulted in identical optimal conditions, as opposed to that obtained for BB-BC. GWO uses a constant convergence parameter (wherein the search radius of grey wolves makes a better trade-off between exploration and exploitation), which ensures better results. Confirmation experiments were conducted corresponding to the optimal transesterification conditions (M:O: 9.32, CC: 1.5 wt.%, RT: 65 \({}^{\circ}\)C, and RT: 60 s), resulting in experimental values of biodiesel yield equal to 95.3% \(\pm\) 0.5%. Table 1 details the biodiesel yield conversion that corresponds to various feedstocks [35; 37; 40; 42; 43; 47; 51; 53], which is comparatively less than that of NS-based biodiesel yield equal to 95.3% \(\pm\) 0.5%; however, NS-based biodiesel yield was comparatively less than other feedstocks [41; 44; 45; 47; 48; 50; 52; 54; 56]. The difference in biodiesel yield for various feedstocks is dependent primarily on the FFA of the feed stocks used, which in turn affects the cost [92]. The presence of higher FFA (>2%) in oil resulted in decreased biodiesel yield and it varied with the type of feedstocks used for biodiesel production [93; 94]. The niger seed oil possesses 7% FFA, and hence acid-catalyzed esterification was adopted before the actual transesterification process. Note that the increase in the number of steps in producing biodiesel resulted in a decrease in biodiesel yield. Similar outcomes have been reported by other researchers [95; 96].