ClusFuDE: Forecasting low dimensional numerical data using an improved method based on automatic clustering, fuzzy relationships and differential evolution

Abstract

In this paper, a novel hybrid model for forecasting low dimensional numerical data is proposed which is named as ClusFuDE. The proposed method uses an improved automatic clustering approach for clustering the historical numerical data. Further fuzzy logical relationships are used to forecast the approximate values which are then defuzzified to calculate the exact forecasted values of the data. The fuzzy logical relationships are useful in modelling the fuzzy relations and help in forecasting the fuzzy time series data in a very simplified manner. The forecasted sub-optimal candidate solutions are optimized using Differential Evolution. The Differential Evolution method uses a dynamic differential crossover rate (Cri) for the ith solution, for identifying and discarding suboptimal candidate solutions in early stages of the iterative run. This makes the method more suitable for iterative modification of candidate solutions by using differential mutation and crossover, and suitable for global search. The proposed method is applied for forecasting, the year wise enrollments of the University of Alabama, Lahi (crop) production, monthly amount of outpatients visit in a hospital, inventory demand and population of India from years 1930–2000 and the results are consistent. We have compared our method with the recent forecasting methods available in literature and the proposed method outperforms all the existing methods in the literature. The accuracy of the proposed method is computed by calculating the Mean square error (MSE) and Mean Absolute percentage error (MAPE). The proposed method provides the lowest MSE and MAPE when compared to all other methods available in the literature.