Research And Application Of Belief Rule Base Inference Method Based On Multi-objective Optimization Algorithm

Based on the Dempster-Shafer evidence theory,decision theory,fuzzy theory and traditional IF-THEN rule,Yang Jianbo et al proposed a belief Rule-base Inference Methodology using the Evidential Reasoning(RIMER)approach.This method has the obvious advantage in solving various types of uncertain and incomplete information,especially the uncertain multiple attribute decision making problem.RIMER method mainly includes the Belief Rule Base(BRB)and Evidential Reasoning(ER)algorithm.In the BRB system,the parameters directly affect the reasoning accuracy,and the structure affects the system complexity.In recent years,the experts conducted in-depth study for the parametric learning problems and structural optimization problems of the BRB system.However,there are still some limitations in the existing BRB parameter learning methods.Therefore,this paper studies and improves the Shuffled Frog Leaping Algorithm(SFLA),and proposes a new BRB training model based on it.At the same time,Most of the existing research for 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.In view of this,this paper focuses on BRB's multi-objective optimization problem.The main work is summarized as follows:(1)In order to overcome the shortcomings of premature convergence of traditional shuffled frog leaping algorithm,this paper using "individual cognitive"ability and Gaussian perturbation to proposes an SFLA algorithm based on Gaussian perturbation,which makes the improved shuffled frog leaping algorithm more powerful.And Study the basic knowledge of RIMER,including the structure of BRB and the reasoning mechanism,and discusse the existing method of BRB parameter optimization,which is the theoretical foundation for further study of BRB optimization.(2)For the existing BRB parameter learning model,there are some problems,such as low convergence efficiency or low reasoning accuracy.In this paper,the parameter learning method of BRB based on shuffled frog leaping algorithm is proposed,which also extend the optimized parameters.In the experimental part,the multi-extremal function and the oil pipeline leak detection example are used to verify the capability of the method to solve practical problems.(3)In order to improve the reasoning accuracy of the BRB system and reduce the complexity of the system,the paper based on the study of parametric learning propose an algorithm named M-PAES-BRB(Belief Rule Base Inference Method based on Multi-Objective Optimization)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 Pareto Archived Evolutionary Strategy to build a multi-objective optimization model.In the experiment,the method is applied to solve the Mackey-glass time series and to predict the carbon dioxide concentration in the gas furnace.The experimental results show that the method has higher accuracy and lower system complexity.