Evolutionary Optimization for the Belief-Rule-Based System: Method and Applications

Evolutionary optimization (EO) has been proven to be highly effective computation means in solving asymmetry problems in engineering practices. In this study, a novel evolutionary optimization approach for the belief rule base (BRB) system is proposed, namely EO-BRB, by constructing an optimization model and employing the Differential Evolutionary (DE) algorithm as its optimization engine due to its ability to locate an optimal solution for problems with nonlinear complexity. In the EO-BRB approach, the most representative referenced values of the attributes which are pre-determined in traditional learning approaches are to be optimized. In the optimization model, the mean squared error (MSE) between the actual and observed data is taken as the objective, while the initial weights of all the rules, the beliefs of the scales in the conclusion part, and the referenced values of the attributes are taken as the restraints. Compared with the traditional learning approaches for the BRB system, the EO-BRB approach (1) does not require transforming the numerical referenced values of the attributes into linguistic terms; (2) does not require identifying any initial solution; (3) does not require any mathematical deduction and/or case-specific information which verifies it as a general approach; and (4) can help downsize the BRB system while producing superior performances. Thus, the proposed EO-BRB approach can make the best use of the nonlinear modeling ability of BRB and the optimization superiority of the EO algorithms. Three asymmetry numerical and practical cases are studied to validate the efficiency of the proposed EO-BRB approach.