Accurate prediction of transport-related accidents is considered an important step in assessing the magnitude of the transport-related problems and accelerating decision-making to mitigate them. Therefore, such studies are of great importance for decision makers. In this study, it is aimed to accurately determine (estimate) the annual total number of railway accidents in Türkiye, considering the track length, train-km and Gross National Product (GNP) variables obtained from Türkiye Statistical Institute. In this context, firstly, four different computational models, three of which are optimization-based (one linear, the others nonlinear) and one based on Artificial Neural Network (ANN), are created. Subsequently, the goal was to minimize the Mean Square Error (MSE) between the observed and modeled data for each computational model developed. In the optimization-based models, the selection of the most suitable internal weighting coefficients was accomplished by utilizing the Differential Evolution Algorithm. Finally, within the scope of the study, all statistical results (mean square error, coefficient of determination) obtained for four different calculation models are compared with each other. Consequently, the analysis of the total number of railway accidents in Türkiye reveals that the quadratic model yields more realistic results compared to the other models.