## 3 Results and Discussion
Considering Figure 8, the ANFIS-ABC-M04 and SVM-PSO-M04 models exhibit the most analogous distributions that align with the normal distribution of observation values. Notably, the range of the predicted values obtained from ANFIS-ABC-M04 are within the same range as the observed values, making it the most successful model among the others. In Figure 8, the excess data in the third quartile of the normal distribution line for the observation values; that is, in the upper range, is aligned in both location and amount with the ANFIS-ABC-M04 model. Additionally, the median and mean values of this model are consistent with the observed values, compared to other methods. Figure 7: Ridge graph for some models the most compatible with observation, where ANFIS-ABC-M04 analysis of ANFIS with ABC optimization for M02, SVM-PSO-M06 analysis of SVM with PSO optimization for M06, etc. The Taylor diagram is a widely preferred method among scientists working with machine learning for comprehensively comparing the model performance based on multiple criteria. Figure 9 illustrates the findings obtained from the Taylor diagram generated for this study. Upon examining Figure 9, one of the first noticeable results is the significant overlap among the models, which makes it difficult to infer variations among the models in terms of performance alone. On the other hand, it can be depicted from the Taylor diagram that the SVM-PSO-M02 and ANFIS-ABC-M02 models demonstrate relatively lower performance compared to other algorithms. For more nuanced analyses, a violin plot is provided in the following section. The violin plot is another method for model performance comparison. By displaying the kernel density, average, quartiles, prediction values, and percentages for each predicted model, seen on related observation values, this visualization technique provides a thorough evaluation. Examination of Figure 10 reveals that the ANFIS-ABC-M04 model demonstrates the highest compatibility with the observation and aligned well with the statistical performance values. Moreover, there are discrepancies especially in extreme values and the third quartile between the predicted and observed values for the SVM-PSO-M02 and ANFIS-ABC-M02 models. As a result, these two models lag behind the others in terms of performance. Figure 8: Box-normal graph of some models with the best performance values, where ANFIS-ABC-M04 analysis of ANFIS with ABC optimization for M02, SVM-PSO-M06 analysis of SVM with PSO optimization for M06, etc. Figure 11 presents the time series graphs for the two models, ANFIS-ABC-M04 and SVM-PSO-M06, identified as the most successful based on the various comparison methods and statistical evaluations discussed previously. Additionally, Figure 11 also includes  
Figure 10: Violin graph some models with the best performance values, where ANFIS-ABC-M04 analysis of ANFIS with ABC optimization for M02, SVM-PSO-M06 analysis of SVM with PSO optimization for M06, etc. Figure 9: Taylor graph of some models with the best performance values, where ANFIS-ABC-M04 analysis of ANFIS with ABC optimization for M02, SVM-PSO-M06 analysis of SVM with PSO optimization for M06, etc. scatter plots of these two models. A visual inspection of the scatter diagram indicates a high degree of similarity between the predicted values generated by the ANFIS-ABC-M04 and SVM-PSO-M06 models. Although both models exhibited strong predictive capabilities for the peak values, the ANFIS-ABC-M04 model consistently outperformed the SVM-PSO-M06 model in terms of accuracy. Figure 11 also displays the time series and scatter plots for the ANFIS-GA-M05 and ANFIS-PSO-M04 models. When looking at the time series, although both models are quite good at capturing peak values, they are behind ANFIS-ABC-M04 and SVM-PSO-M06 in statistical evaluation, except for initial values of observation. This situation does not change in the scatter diagrams.