On the Estimation of Logistic Models with Banking Data Using Particle Swarm Optimization

Abstract

This paper presents numerical works on estimating some logistic models using particle swarm optimization (PSO). The considered models are the Verhulst model, Pearl and Reed generalization model, von Bertalanffy model, Richards model, Gompertz model, hyper-Gompertz model, Blumberg model, Turner et al. model, and Tsoularis model. We employ data on commercial and rural banking assets in Indonesia due to their tendency to correspond with logistic growth. Most banking asset forecasting uses statistical methods concentrating solely on short-term data forecasting. In banking asset forecasting, deterministic models are seldom employed, despite their capacity to predict data behavior for an extended time. Consequently, this paper employs logistic model forecasting. To improve the speed of the algorithm execution, we use the Cauchy criterion as one of the stopping criteria. For choosing the best model out of the nine models, we analyze several considerations such as the mean absolute percentage error, the root mean squared error, and the value of the carrying capacity in determining which models can be unselected. Consequently, we obtain the best-fitted model for each commercial and rural bank. We evaluate the performance of PSO against another metaheuristic algorithm known as spiral optimization for benchmarking purposes. We assess the robustness of the algorithm employing the Taguchi method. Ultimately, we present a novel logistic model which is a generalization of the existence model. We evaluate its parameters and compare the result with the best-obtained model.