Extended belief rule-based system using bi-level joint optimization for environmental investment forecasting

Abstract

Scientific investment forecasting can effectively avoid the blind investments of environmental management. Among existing studies in developing investment forecasting models, the extended belief rule-based system (EBRBS) showed its potential to accurately predict environment investments but also exposed two challenges to be further addressed: (1) how to select antecedent attributes from various environmental indicators for the EBRBS; (2) how to optimize basic parameters of the EBRBS based on the selected antecedent attributes. Since these two challenges are connected, a bi-level joint optimization model is proposed to improve the EBRBS for better environmental investment forecasting, in which the selection of antecedent attributes is described as an upper-level optimization model using Akaike information criterion (AIC) and the optimization of basic parameters is as a lower-level optimization model using mean absolute error (MAE). Moreover, a corresponding bi-level joint optimization algorithm is proposed to solve the bi-level joint optimization model, where ensemble feature selection and swarm intelligence optimization are regarded as the engine of upper-level and lower-level optimizations, respectively. The real environmental data collected from 2005 to 2020 of 30 Chinese provinces are studied to verify the effectiveness of the proposed approach. Experimental results show that the EBRBS with bi-level joint optimization not only can effectively predict environmental investments, but also is able to have desired accuracy better than previous investment forecasting models.