## 4 Simulation Results and Discussion
### Implementation of JS-MFO for Solving OPF Problems
It is very clear from Table 6 that the JS-MFO approach is able to reduce the fuel cost to the lowest value of 799.085 USD/h. The percent cost savings with respect to the base cases of JS, MFO and JS-MFO are 11.188%, 11.2137%, and 11.4028 %, respectively, which lead to annual cost savings for JS-MFO of 16,951 USD/year compared to JS and 14,936 USD/year compared to MFO. The evolution of the total fuel cost during the simulation is indicated in Figure 3. It can be seen that the optimal total fuel cost converges towards the best optimal solution using JS-MFO. \begin{table} \begin{tabular}{c c c c} \hline
**Technique** & **Total Fuel Cost (USD/h)** & **Technique** & **Total Fuel Cost (USD/h)** \\ \hline JS-MFO & 799.085 & DA [13] & 802.316 \\ JS & 801.02 & AGTLBO [14] & 800.481 \\ MFO & 800.79 & PSO-PS [21] & 799.8723 \\ NilsSO [35] & 799.762 & DA-PSO [23] & 802.124 \\ FFA [15] & 802.130 & HF-PSO [24] & 799.123 \\ MSA [15] & 802.223 & HF-ABC [26] & 800.212 \\ ESCA [36] & 800.219 & HFA-JAYA [27] & 800.480 \\ SOS [35] & 801.5733 & \\ HHO [16] & 801.829 & \\ \hline \end{tabular}  \  
Case 2: Minimization of Total Gas Emissions  
The total gas emission function in (13) was minimized using the proposed JS-MFO, MFO, and JS algorithms. The gas emission coefficients are given in [34]. The optimal solutions achieved using JS-MFO, MFO, and JS are 0.2047, 0.2048, and 0.2049 ton/h, respectively, based on the optimal setting of the control variables shown in Table 4 for case 2. Table 7 gives a statistical comparison report considering other optimization methods applied to the same test system and the same number of control variables as the Harris Hawks optimization algorithm (HHO) [16], Turbulent Flow Of Water-Based Optimization algorithm (TFWO) [17], hybrid DA-PSO [23], Adaptive Gaussian AGTLBO [14], and Social Spider Optimization algorithm (SSO) [37]. By examining the previous table, the minimum total gas emissions obtained by the proposed JS-MFO algorithm was shown to be better than that of the JS and MFO algorithms and the comparison optimization techniques reported in the literature. The percent gas emission reductions were 14.30%, 14.34%, and 14.38% for JS, MFO, and JS-MFO, respectively, referring to the base case. It can be seen that the proposed hybrid technique JS-MFO achieves total gas emission reductions of 1.752 tons/year and 0.876 tons/year compared to JS and MFO, respectively. The convergence of the total gas emission function with respect to the number of iterations is depicted in Figure 4, showing that the proposed JS-MFO algorithm gives faster convergence to the optimal solution with a better solution quality than the JS and MFO algorithms. Case 3: Minimization of total fuel cost considering valve point effect  
The objective function given by (14) is provided for the non-smooth curve of the total fuel cost function and that for the two generators in buses 1 and 2, where their cost coefficients are taken from [10]. The fuel cost curves of the remaining generators keep the same characteristics as in case 1. The minimum total fuel costs obtained using the proposed JS-MFO, JS, and MFO algorithms are 918.073 USD/h, 922.48 USD/h, and 924.02 USD/h, respectively, considering the valve point effect. The optimal solution reflects the optimal control variables presented in Table 4 for case 3. The percent cost savings considering the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Technique** & **Total Gas Emissions (ton/h)** & **Technique** & **Total Gas Emissions (ton/h)** \\ \hline JS-MFO & 0.2047 & AGTLBO [14] & 0.2048 \\ JS & 0.2049 & SSO [35] & 0.2315 \\ MFO & 0.2048 & NISSO [35] & 0.2048 \\ HHO [16] & 0.2850 & SSA [37] & 0.205 \\ TFWO [17] & 0.2050 & PSO-SSA [37] & 0.205 \\ DA-PSO [23] & 0.2048 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison report provided for case 2 of the IEEE 30-bus system. Figure 3: Convergence curves of JS, MFO and JS-MFO algorithms for case 1.  
value point effect for JS, MFO, and JS-MFO are 15.01%, 14.87%, and 15.42%, respectively, compared to the base case.