Belief Rule Base Inference Algorithm Based on Mixed Pareto Archived Evolutionary Strategy

Most of the existing methods for belief rule based (BRB) focus on single objective optimization for parameter or structure. However, according to the existing research, improving reasoning accuracy and reducing the complexity of BRB system usually conflict each other. Thus, designing a suitable algorithm to find right trade-off for the two goals is necessary. For this purpose, an algorithm named M-PAES-BRB (belief rule base inference method based on multi-objective optimization) is proposed to determine an approximation of the optimal Pareto front by concurrently minimizing the root mean squared error and the complexity. The algorithm adopts an improved mixed pareto archived evolutionary strategy (M-PAES) to build a multi-objective optimization model, M-PAES use recombination operator and mutation operator to generate candidate solutions. In the experiment, we select two standard time series, Mackey-Glass and Box-Jenkins as the experimental datasets, to test the feasibility and effectiveness of M-PAES-BRB. Compared to fuzzy rule base multi-objective evolutionary algorithms (FRBSs), the experiment results show that M-PAES-BRB's reasoning accuracy is higher and the complexity is lower.