## 5 Numerical Results
### Performance Comparison Criteria for Different Methods  
In the evaluation of the performance of optimization tools, while solving ORPD problem solutions, the sole key factor that has been used to point out the performance of compared methods is the best optimal solution reflected via fitness function [23; 24]. Some of the previous studies [19; 61] have used more comparison factors such as execution time in seconds, but computers, which have been used for simulation, have not been mentioned. It is obvious that computers with a higher processor spend less time for the same condition of control parameters or Matlab code. There is also another view point about the comparison of performance depending on the setting of adjustment parameters [64]. The higher population size and number of iterations can produce the higher number of new solutions, but it takes a long time to find optimal solutions. However, the statement is not completely accurate because there are some methods with complicated and time-consuming computation steps, although these methods and other ones produce the same number of new solutions for per iteration and per run. The simplest example for demonstrating the point is the comparison between PSO and DE. The two methods produce a set of new solutions equaling population size per iteration, and the same number of new solutions per run, but PSO has a smaller number of computation steps and simpler  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test Case**} & \multirow{2}{*}{**Description**} & \multirow{2}{*}{**Control Variables**} & \multicolumn{2}{c}{**Control Parameter Selection**} \\ \cline{3-4}  & & & **For SSA, SFOA, and WCA** & **For COA** \\ \hline \multirow{4}{*}{The IEEE 30-bus system [63]} & 6 generator buses, & & \\  & 24 load buses, & \(V_{Gen,\text{has}}\) (\(i=1,\,\ldots,\,6\)) & & \\  & 41 branches, & \(Q_{cap,\text{has}}\) (\(i=1,\,\ldots,\,9\)) & \(N_{pop}=20\) & \(N_{coyote}=4\) \\  & 9 VAR & \(TT_{i}\) (\(i=1,\,\ldots,\,4\)) & \(N_{Iter}=100\) & \(N_{\text{{\color[rgb]{0,0,0}Iter}}}=100\) \\  & compensators, & 4 transformers. & & \\  & 7 generator buses, & & & \\  & 50 load buses, & \(V_{Gen,\text{has}}\) (\(i=1,\,\ldots,\,7\)) & & \(N_{\text{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0} \pgfsys@color@gray@stroke{0}\pgfsys@color@gray@  
computation steps than those of DE. PSO updates velocity and position for all particles at the same time, leading to short simulation time, but DE must perform mutation for one solution by one solution, and then the crossover operation must be conducted. Thus, DE tends to spend longer simulation time. Consequently, we suggest applying acceptably clear and fair comparison criteria for the evaluation of the performance of the proposed method and other ones. We focus on the following main issues:  
The best optimal solution: The best optimal solution comparison can point out the robustness of the method. The method with the better solution is considered to be stronger in the search process. The solution search speed: It is also a very important factor for providing an accurate assessment of methods performance. A method with better solutions but with much longer simulation time is not a method with more potential. A method that finds better solutions and uses shorter simulation time is considered to be a better method, if the time comparison is carried out in the same conditions such as the same program language, the same program way, and the same computer. However, the expected conditions are hardly ever reached. For dealing with the issue, studies in [64; 65] have proposed different comparison criteria for evaluating the optimal solution search speed of compared methods. Authors [64] have suggested a persuasive argument in regard to \(N_{pop}\) and \(N_{Iter}\) that the two factors directly influence the performance of implemented methods. The setting with higher values for the two factors can improve optimal solutions considerably, but convergence process to these solutions is time consuming and vice versa.