## 6 Discussion
A comparison of the values in Tables 9 and 10 reveals that the overall prediction performance of the MR model based on linear regression is weaker than the performance of EoNN-based models (specifically, the \(\text{SAV}_{\text{ENS}}\) and the \(\text{GAVE}_{\text{ENS}}\) models) developed by this study for the purposes of sewerage projects construction costs prediction. As described in the preceding section, the research results are satisfactory. The models developed using EoNN have demonstrated their ability to predict construction costs for sewerage projects, for either stormwater runoffs or wastewater runoffs, with acceptable accuracy, meeting the requirements of the expected range of errors in over 90% of the test cases. The \(\text{SAV}_{\text{ENS}}\) and \(\text{GAVE}_{\text{ENS}}\) models exhibit improved predictive capabilities when compared to individual ANNs, selected to be the ensemble members, used as standalone models. This improvement can be attributed to the effective compensation of errors inherent in single ANNs when they are combined within the ensemble. Moreover, combining several ANNs provides more objective cost predictions, as a certain bias of single ANNs acting in isolation is inevitable due to the size of the training set used in the course of research. The two applied approaches, specifically simple averaging for the \(\text{SAVE}_{\text{ENS}}\) model and generalized averaging for the \(\text{GAVE}_{\text{ENS}}\) model, differ in terms of the computational effort required to determine the weights of the member ANNs. The first approach is straightforward--in fact, it involves taking the arithmetical average of predictions as the EoNN output. In contrast, the second approach demands more effort. However, this can be \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(RMSE_{C}\) & \(RMSE_{T}\) & \(MAP_{C}\) & \(MAP_{T}\) & \(max\) & \(max\) \\  & & & & & \([APE^{p}\)_c] & \([APE^{p}\)_r]_ \\ \hline MR & 647.04 & 743.31 & 29.5\% & 19.3\% & 81.9\% & 111.5\% \\ \hline \end{tabular}
\end{table} 
Table 10: Values of general predictive performance measures for the MR model. Figure 7: Scatter plot of real-life values \(y\) and predicted values \(\hat{y}\) of costs for benchmark MR model. (a) C subset, (b) \(T\) subset. efficiently accomplished using a calculation sheet or through programming and automation of computations. The generalized averaging approach, with its weight optimization, allows for a more nuanced differentiation of the influence of individual member ANNs on the final cost prediction. In summary, both approaches are user-friendly and easily applicable. The key advantage of an ensemble-based approach, as affirmed by the research presented, lies in the efficient utilization of training and testing efforts across ANNs rather than focusing solely on a single network. This observation carries particular significance in the contemporary context, where rapid progress in computer technology and the availability of efficient software enables the exploration of numerous networks within a relatively short timeframe. It is also essential to acknowledge the limitations of the developed models. Firstly, the models are explicitly tailored to the specific local conditions. This is a consequence of the evident fact that the data used for training and testing were collected in the Czech Republic. However, it is worth noting that the application of the proposed approach in other locations is feasible, making the conceptual framework broadly applicable. The second significant limitation stems from the data update scheduled for mid-2023. In this regard, the proposed model and approach do not provide dynamic and automatic adjustment to cost variations over time. This issue will be the subject of further research. Figure 8: Distribution of \(PE^{\prime}\) errors for benchmark MR model. (**a**) C subset, (**b**) \(T\) subset.