## 6 Conclusions  
Researchers have made efforts to develop different models aimed at forecasting unpleasant environmental problems caused by blasting, such as blast-induced ground vibration, air overpressure, and flyrock occurrence. However, most of their efforts have been directed towards mine production blasting, while the unwanted environmental problems from rock excavation by blasting at construction sites have rarely been studied. In addition, despite the large number of soft computing models for the prediction of airblast overpressure in the literature, most of these models are not in the form of explicit and closed-form equations and are limited to one or two sites at most. This study proposed closed-form and explicit ANN-based soft computing equations for forecasting AOp generation in multiple-construction rock excavation blasting with high accuracy. The proposed model used ANN as its base model and improved its performance by using two metaheuristic algorithms, SMA and MVO. The predictive performances of SMA-ANN and MVO-ANN were evaluated using six error metrics. To evaluate the robustness of the developed ANN-based hybrid models, their performance was compared with those of the stand-alone ANN, MLR, and USBM models. Closed-form and explicit equations were generated using the bias and weights of the training network to ensure the general applicability of the developed ANN-based model. The following conclusions can be drawn from the findings of this study:  
1. The SMA-ANN model had the best performance among all the developed models, with MAE, MSE, RMSE, MAPE, RMSE, and R\({}^{2}\) values of 2.363, 10.803, 3.286, 3.576, 0.051, and 0.809 for the training datasets and 2.102, 8.084, 2.843, 3.245, 0.045, and 0.867 for the test datasets, respectively. This is followed closely by the MVO-ANN and ANN models.
2. The performance of the two linear models (MLR and USBM) was poor, as they both underestimated or overestimated the AOp values at most of the data points. Hence, they are not recommended for use in forecasting AOp at construction sites.
3. Based on the relevance importance scores, both controllable and uncontrollable factors (RMR) are important for predicting AOp at construction sites.
4. The developed ANN-based closed-form and explicit equations proved to be reliable and recommended for use in forecasting AOp at construction sites, provided the range of data is the same or similar to that used in this study.
5. Although the developed ANN-based models' accuracy is ideal for this study, it would be significant if meteorological factors such as wind speed and direction, as well as temperature, were considered. Future studies may benefit from incorporating drilling, blasting, explosives, geological, and meteorological factors for more robust models.  
Conceptualization, N.O.O. and S.C.; methodology, N.O.O., S.C., and A.I.L.; software, N.O.O. and A.I.L.; validation, N.O.O., C.S., and S.C.; formal analysis, N.O.O. and A.I.L.; investigation, Y.-K.K.; resources, Y.-K.K. and S.C.; data curation, N.O.O. and C.S.; writing--original draft preparation, N.O.O.; writing--review and editing, N.O.O.; visualization, N.O.O., A.I.L., and C.S.; supervision, S.C.; project administration, S.C. and Y.-K.K.; funding acquisition, S.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported by a grant (22 CTAP-C164314-02) from development of integrated technology for smart demolition system based on 3D digital information construction in response to safe demolition of old and damaged buildings funded by the Ministry of Land, Infrastructure, and Transport of the Korean government.  
Not applicable.  
The authors declare no conflict of interest.