Parallel multipopulation optimization for belief rule base learning

Abstract

As a rule-based expert system, the belief rule base (BRB) exhibits tremendous advantages in modeling nonlinearity for complex systems. Present BRB learning studies can be classified into three categories: BRB structure learning, BRB parameter learning, and BRB joint optimization but only in an iterative and separate fashion. In this study, a novel Parallel Multipopulation optimization approach for BRB, i.e., PMP-BRB, is proposed that simultaneously optimizes the structure and parameters of a BRB. In the optimization model of PMP-BRB, the structure of BRB, i.e., the number of rules, is used as another decisive variable. In the optimization algorithm of PMP-BRB, multiple populations are initialized and subsequently optimized, with different populations representing BRBs of varied sizes. Furthermore, a “completion and deletion” strategy is proposed, wherein individual BRBs in different populations are completed with additional genes that only engage in the optimization operations but not in fitness calculations. Moreover, a trade-off analysis is conducted for decision-makers to identify the final optimal configuration of a BRB based on their preference. The proposed PMP-BRB approach is validated by four cases, namely a numerical case, two practical cases, and a case study with five classification benchmarks. Four evolutionary algorithms are tested and compared. With the structure and parameters optimized simultaneously, all the four cases yield competitive results in comparison with those of previous studies.