## 4 Simulation Results and Discussion
### Implementation of JS-MFO for Solving OPF Problems
It is clearly shown that JS-MFO gives the highest cost saving. The annual cost savings of JS-MFO correspond to 38,632 USD/year and 52,122 USD/year with respect to those of JS and MFO, respectively. The JS-MFO algorithm shows a better solution than that of the JS and MFO algorithms, and the other methods displayed in Table 8 such as the Improved Salp Swarm Algorithm (ISSA) [38], Salp Swarm Algorithm (SSA) [38], Teaching-Learning-based Optimization Algorithm (TLBO) [39], Gbest-guided ABC (Gbest-ABC) [40], and ABC-based Grenade Explosion Method (GABC) [41]. The progress of the non-quadratic total fuel cost with respect to the iteration evolutions is given in Figure 5 for the JS, MFO, and JS-MFO algorithms. These curves confirm the superiority of JS-MFO over JS and MFO in attaining the best global solution. Case 4: Minimization of Total Active Losses  
Active transmission losses in Equation (15) are adopted as an objective function in this case and are minimized by carrying out the proposed JS-MFO, JS, and MFO techniques. The optimal total active losses resulting from the simulation are given in Table 5 for case 4, along with their corresponding control and state variables. It is reported that JS-MFO is able to reduce the active transmission losses to the lowest value of 2.8810 MW, while JS and MFO lead to 3.232 MW and 3.049 MW, respectively. The percent loss savings of the presented techniques JS, MFO, and JS-MFO are, respectively, 44.59%, 47.72%, and 50.60% with reference to the base case. For comparison purposes, Table 9 depicts the optimal active transmission losses for JS-MFO, JS, MFO, and other techniques inspired from previous works in the literature such as AGTLBO [14], FFA [15], MSA [15], DE-HS [22], DA [23], DA-PSO [23], HFA-JAYA [27], SS0 [35], NISSO [35], ESCA [36], and Adaptive Multiple-Team Perturbation-Guiding JAYA [42]. From this table, it can be observed that the results obtained using JS-MFO are better than those of the other methods presented in the current literature. Figure 6 shows the evolution of total active losses with respect to the progression of iterations during the simulation, depicting the convergence characteristics of the JS and JS-MFO algorithms for this case. Case 7: Minimization of the total fuel cost along with the deviation of the total load bus voltage  
This case study is devoted to the simultaneous minimization of the quadratic total fuel cost and the total load bus voltage deviation as the objective function depicted in Equation (21). The problem is solved by running the JS, MFO, and JS-MFO algorithms separately. The simulation results for case 7 are listed in Table 5 by showing the numerical optimal settings of the control and state variables. Table 10 is provided to compare the optimal total fuel cost and the total load bus voltage deviation of the JS-MFO method to  
Figure 6: Convergence rates of JS, MFO, and JS-MFO for Case 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Technique**} & **Total Transmission** & \multirow{2}{*}{**Technique**} & **Total Transmission** \\  & **Losses (MW)** & & **Losses (MW)** \\ \hline JS-MFO & 2.881 & DA [23] & 3.198 \\ JS & 3.232 & DA-PSO [23] & 3.189 \\ MFO & 3.049 & HFA-JAYA [27] & 4.529 \\ AGTLBO [14] & 3.090 & SS0 [35] & 3.911 \\ FFA [15] & 3.643 & NISSO [35] & 2.945 \\ MSA [15] & 3.649 & ESCA [36] & 3.021 \\ DE-HS [22] & 3.054 & AMTFC-JAYA [42] & 3.080 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of the results for Case 4 of the IEEE 30-bus system. those of the JS and MFO algorithms and the other techniques given by recently published works in the literature. It is clearly shown that JS-MFO dominates all other comparison techniques in terms of the optimal fuel cost with a slightly higher optimal voltage deviation compared to AGTLBO [14], HFA-JAYA [27], ESCA [36], PSO-SSA [37], MVO [43] and ECHT-DE [44]. The ESCA is reported to present the best optimal voltage deviation among all other techniques, but it provides the highest optimal voltage deviation.