## 4 Simulation Results and Discussion
### Implementation of JS-MFO for Solving OPF Problems  
Two test systems were used to investigate the aptitude of the proposed JS-MFO algorithm to reach the near-global OPF solution for different cases of mono-objective optimization problems: the IEEE 30-bus, a real part of the USA network, and the RIM 27-bus. The modeling of the tested networks was carried out in the MATLAB 2009b environment using a personal computer running Windows XP Professional, Pentium P-IV CPU 3 GHz processor, and RAM of 1 GB. _A. IEEE 30-bus test system_  
The IEEE 30-bus model has 6 generators, 41 branches (37 lines and 4 transformers with off-nominal tap ratios), and 24 load buses as shown in Figure 2. Shunt Volt Ampere Reactive (VAR) compensators are installed in buses 10, 12, 15, 17, 20, 21, 23, 24, and 29, where the reactive power injection is controlled between 0 and 5 MVAR as the lower and upper limits, respectively [11]. The total system demand was (2.834 + j1.262) p.u. for the apparent power at the 100 MVA base. Bus 1 was taken as the slack bus. The upper and lower limits of active power generation, the reactive power limits, and the generator cost coefficients are taken from [34]. In the base case, the system presents the following data: Fc (quadratic fuel cost) = 901.935 USD/h, F\({}_{\text{Em}}\) = 0.23908 ton/h, F\({}_{\text{Ploses}}\) = 5.8332 MW, F\({}_{\text{VD}}\) = 1.1663 p.u., and L\({}_{\text{max}}\) = 0.1731. The parameters of the JS, MFO. and JS-MFO algorithms are as follows: the population number (population size) N\({}_{\text{PPO}}\) is 50, the maximum number of iterations _Maxlt_ = 100, and the number of control variables is \(D\) = 25. For the present test system, six cases (six objective functions) were studied to evaluate the performance of the proposed JS-MFO compared to that of JS and MFO in order to reach the optimal solution. In order to validate the proposed JS-MFO in dealing with and solving complex OPF problems, 30 independent trial runs were performed for each case study by implementing JS, MFO, and JS-MFO. Three complex cases, particularly 1, 3, and 4, were considered to provide the minimum, average, maximum, and standard deviation (SD) for each objective function as shown in Table 3. A comparative report of each index between the JS, MFO, and JS-MFO algorithms, shown in the previous table, can clearly prove the superiority of JS-MFO over JS and MFO in providing the best solution quality and stability over the trial runs. The optimal control variable settings and the corresponding objective function value are depicted for each case in Tables 4 and 5. Executing 30 independent runs for each case led to extracting the solution for the run that provided the best solution. Figure 2: IEEE 30-bus single-line diagram. Case 1: Minimization of the quadratic total fuel cost function  
The objective function in Equation (12) was evaluated for the optimal settings of the control variables by running the JS, MFO, and JS-MFO algorithms, and the simulation results are indicated in Table 4 for case 1. The optimal total fuel costs obtained were 799.085 USD/h, 801.02 USD/h, and 800.79 USD/h using JS-MFO, JS, and MFO, respectively. The best solution of the total fuel cost for JS-MFO was compared with that of the JS and MFO algorithms and other optimization techniques in the literature shown in Table 6, such as the Novel Improved Social Spider Optimization algorithm (NISSO) [35], Firefly Algorithm (FFA) [15], Moth Swarm Algorithm (MSA) [15], Efficient Sine Cosine Algorithm  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Control Variables/**} & \multicolumn{3}{c}{**Case 1**} & \multicolumn{3}{c}{**Case 2**} & \multicolumn{3}{c}  
(ESCA) [36], Symbiotic Organism Search algorithm (SOS) [35], Harris Hawks Optimization (HHO) [16], Dragonfly Algorithm (DA) [13], Adaptive Gaussian Teaching-Learning-based Optimization (AGLBO) [14], PSO-PS [21], DA-PSO [23], HF-PSO [24], Artificial Bee Colony based on hybrid fruit fly (HF-ABC) [25] and HFA-JAYA [27].