Improvement of Grey System Model using Particle Swarm Optimization

Abstract

An improvement of the traditional grey system model, GM(1,1), to enhance forecast accuracy, has been realized using the particle swarm optimization (PSO) algorithm. Unlike the GM(1,1) which uses a fixed adjacent neighbor weight for all data sets, the proposed PSO-improved model, PSO-GM(1,1), determines an optimal adjacent neighbor weight, based on the presented data set. This optimal adjacent neighbor weight so determined is the principal factor that enhances forecast accuracy. The performance of the proposed model was evaluated using generated monotonic increasing and decreasing data sets as well as measured energy consumption data for a laptop computer, desktop computer, printer, and photocopier. The performance of PSO-GM(1,1) was compared with that of GM(1,1), and two other models in literature that sought to improve the performance of GM(1,1). The PSO-GM(1,1) outperformed the traditional model and the two other models. For the monotonic increasing data, the mean absolute percentage error (MAPE) for the proposed model was 0.007% as against a MAPE value of 20.383% for the GM(1,1). For the monotonic decreasing data, the PSO-GM(1,1) again outperformed GM(1,1), yielding a MAPE of 0.057% compared to a value of 13.407% for the traditional model. For the measured laptop computer energy data, the obtained MAPE for the PSO-GM(1,1) was 0.675% while the values for the two models were 4.052% and 2.991%. For the measured desktop computer energy data, the obtained MAPE for the PSO-GM(1,1) was 0.0018% while the values for the two models were 0.0018% and 1.163%. For the data associated with the printer, the MAPEs were 8.414% for the PSO-GM(1,1), 20.957% for the first model and 9.080% for the second model. For the measured photocopier energy data, the obtained MAPE for the PSO-GM(1,1) was 0.901% while the values for the two models were 3.799% and 0.943%. Thus, the proposed PSO-GM(1,1) greatly improves forecast accuracy and is recommended for adoption, for forecasting.