## 6 Concluding Remarks  
The CC of soil is a crucial geotechnical engineering parameter that is required in the design phase of high-rise housing projects. To avoid the cumbersomeness of the oedometer test, this study proposes a machine learning-based solution for obtaining CC parameter. The machine learning model is established by using ANN with a novel hybrid training method of the ABC and LM algorithms. The ABC metaheuristic acts as a global optimizer which searches for an ANN model that provides the best fit to the collected data. In addition, to accelerate the ABC searching process, the LM backpropagation is performed on a randomly chosen individual of the ABC population. A dataset consisting of 12 predictor variables including sample depth, sand content, loam content clay content, moisture content, wet density, dry density, void ratio, liquid limit, plastic limit, plastic index, and liquid index and 441 soil samples was collected during the construction phase of a large-scale housing project in Vietnam. This dataset is, then, employed to train and verify the prediction performance of the newly constructed ABC-LM-ANN model. Experimental results confirm that ABC-LM-ANN can deliver the prediction result of CC which is superior to those of other benchmark approaches. Therefore, the newly established model can be a promising alternative to assist the decision-making process in the design phase of high-rise housing projects. Future research works could consider new robust optimization algorithms to improve the prediction performance of CC. As can be confirmed by the reported experimental results, one significant advantage of the hybrid ABC-LM-ANN model is that it combines the two powerful methods of training neural network regression to achieve a good predictive performance of CC parameter estimation. Therefore, the model is capable of delivering reliable estimations of this property of soil to quickly assist the engineering decision-making process. However, one difficulty of using the model is that there are a set of model hyper-parameters (e.g., the population size of the ABC, the maximum number of epochs used in the LM training operator, and the number of neurons in the hidden layer) needed to be tuned empirically. Furthermore, the current model does not integrate with the feature selection method, and therefore employing metaheuristic-based feature evaluation could be a potential extension of this study. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**(a)**} \\ \hline  & **ABC-LM-ANN** & **LM-ANN** & **ABC-ANN** & **RegTree** \\ \hline ABC-LM-ANN & x & 0.11792 & 0.0018945 & 1.14E–07 \\ LM-ANN & 0.11792 & x & 0.095532 & 7.83E–05 \\ ABC-ANN & 0.0018945 & 0.095532 & x & 0.020189 \\ RegTree & 1.14E–07 & 7.83E–05 & 0.020189 & x \\ \hline  & \multicolumn{4}{c}{**(b)**} \\ \hline  & **ABC-LM-ANN** & **LM-ANN** & **ABC-ANN** & **RegTree** \\ \hline ABC-LM-ANN & x & + & ++ & ++ \\ LM-ANN & - & x & + & ++ \\ ABC-ANN & – & - & x & ++ \\ RegTree & ++ & ++ & ++ & x \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The \(t\)-test results which compare the models’ performances in terms of R\({}^{2}\): (**a**) \(p\)-values and (**b**) model pairwise comparison. Note: “++”, “+”, “-”, and “-” denote a significant win, a win, a significant loss, and a loss, respectively. **Author Contributions:** Conceptualization, P.S. and N.-D.H.; methodology, P.S., N.-D.H., D.T.B., V.-H.N., and P.T.T.N. ; validation, D.T.B., V.-H.N., P.T.T.N., and M.-L.N. ; formal analysis, D.T.B., V.-H.N., P.T.T.N., and M.-L.N. ; investigation, V.-H.N. and M.-L.N. ; writing--original draft preparation, N.-D.H. and D.T.B. writing--review and editing, N.-D.H. and D.T.B. **Funding:** This research was supported by the Geographic Information System group, Ton Duc Thang University, Ho Chi Minh City (Vietnam) and the University of South-Eastern Norway (Norway).