## 5 Numerical Results
### Performance Comparison Criteria for Different Methods
Thus, they have suggested that the total number of newly produced solutions \(N_{spr}\) or the number of quality solution evaluations over one run \(N_{sqe}\) should be employed as the main comparison factor. Methods with the same or smaller number of quality solution evaluations but finding better optimal solutions become more powerful methods. Due to the suggestion, we construct different \(N_{sqe}\) for different compared methods as follows:  
\[N_{sqe}=N_{pop}.N_{Iter} \tag{35}\]  
\[N_{sqe}=2.N_{pop}.N_{Iter} \tag{36}\]  
\[N_{sqe}=\Big{(}N_{pack}.N_{coyote}+N_{pack}\Big{)}.N_{Iter} \tag{37}\]  
The three abovementioned formulas are applied for different methods with a different number of generations and different number of new solutions per generation. Formula (35) can calculate the number of solution quality evaluations for methods producing the number of new solutions equaling population size such as PSO, DE, SSA, GWO, BBO, etc. Formula (36) provides the number of solution quality evaluations for methods having two generations per iteration, and there is a population size of new solutions per generation such as ABC, TLBO, QOTLBO, CSA, etc. The model of Formula (37), which is applied for COA and the proposed method, is different than that of (35) and (36), because COA and ICOA have different search procedures than other methods. (\(N_{coyote}.N_{pack}\)) is the number of quality solution evaluations for the first generation, while \(N_{pack}\) is the number of solution quality evaluations for the second generation. On the other hand, (\(N_{coyote}.N_{pack}\)) is equal to population size, and Formula (37) can be rewritten as follows:  
\[N_{sqe}=\Big{(}N_{pop}+N_{pack}\Big{)}.N_{Iter} \tag{38}\]  
With the form, if we set (\(N_{coyote}.N_{pack}\)) equally to the population size of other methods, COA and the proposed ICOA method produce a higher number of new solutions and spend more time than other methods with Formula (35) but the two methods produce a smaller number of new solution and use a shorter time for evaluating solution than other methods with Formula (36). Although unlikely, the authors in [65] have suggested using computation time for fair comparison of performance. They did not consider \(N_{sqc}\), but they did consider the processor of computers as a strict factor. They have defined a time index of the compared method _has_, \(T_{i}\) by using the following model:  
\[T_{i}\ (Per\,unit)=\frac{GH_{i}}{GH}\times\frac{Sintine_{i}}{Sintine} \tag{39}\]  
In Equation (39), \(GH_{i}\) and \(GH\) (in GHz) are the processor of computers, which have been used to run the compared method _has_ and the proposed method. _Simtime_\(i\) and _Simtime_ (in second) are the simulated time of the compared method _has_ and the proposed method. According to the viewpoint of the authors, the compared method _has_ is slower than the proposed method if \(T_{i}\) is higher than 1 and vice versa. The stable search ability: The stable search ability is not the most important factor for evaluating the performance of method, but it can be used for further investigation in the case that two compared methods have the same optimal solution and the same search speed. Normally, the stability of the solution search is reflected via the average fitness of all runs. On the other hand, a better comparison can be made if the best fitness of all runs is plotted in the same figure. For comparison with other methods available in previous studies, we compare the average, but for implemented methods in the study, we plot all runs in the same figure, and a clear view can point out which method is superior to others. The applied comparison criteria cannot provide a fair comparison with the accuracy of 100%, but a general comparison with acceptable accuracy can be useful for concluding the performance of the proposed method as compared to other ones.