This study deals with the development of Artificial Neural Network (ANN) and Multiple Regression (MR) models for estimating the critical factor of safety $\left(F_s\right)$ value of a typical artificial slope subjected to earthquake forces. To achieve this, while the geometry of the slope and the properties of the man-made soil are kept constant, the natural subsoil properties, namely, cohesion, internal angle of friction, the bulk unit weight of the layer beneath the ground surface and the seismic coefficient, varied during slope stability analyses. Then, the $F_s$ values of this slope were calculated using the simplified Bishop method, and the minimum (critical) $F_s$ value for each case was determined and used in the development of the ANN and MR models. The results obtained from the models were compared with those obtained from the calculations. Moreover, several performance indices, such as determination coefficient, variance account for, mean absolute error and root mean square error, were calculated to check the prediction capacity of the models developed. The obtained indices make it clear that the ANN model has shown a higher prediction performance than the MR model.

A graph theory‐based methodology is proposed for the sewer system optimization problem in this study. Sewer system optimization includes two subproblems: layout optimization and hydraulic design optimization, which can be solved independently or solved simultaneously. No matter which method is chosen for the solution of the optimization problem, a feasible layout that satisfies the restrictions of the sewer system must be obtained in any step of the solution. There are two different layout options encountered: the layouts containing all sewer links and the layouts not containing all sewer links. The method proposed in this study generates a feasible sewer layout that contains all sewer links and satisfies all restrictions of a sanitary sewer system by using graph theory without any additional strategies unlike other studies. The method is applied to two different case studies. The results of the case studies have shown that graph theory is well applicable to sewer system optimization and the methodology proposed based on it is capable of generating a feasible layout. This study is expected to stimulate the use of graph theory on similar studies.