基于混合PAES的置信规则库推理算法
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摘要
目前对置信规则库(BRB)的研究主要是关于BRB系统的参数或结构的单目标优化。然而,BRB系统中提高推理准确性和减少系统复杂度往往是两个相互冲突的目标。因此,设计合适算法来寻找到两个目标上的最优解具有重要意义。鉴于此,该文提出基于混合Pareto存档进化策略(M-PAES)的置信规则库推理方法(M-PAES-BRB),通过最小化系统的均方根误差和系统复杂性来寻找到近似的Pareto最优前沿。该算法采用了改进型M-PAES算法来构建多目标优化模型,通过重组和变异操作生成候选解。该文选取两个标准时间序列,Mackey-Glass和Box-Jenkins作为实验数据,对M-PAES-BRB的可行性及有效性进行分析。实验结果表明,相比于模糊规则库的多目标优化方法(FRBSs),该文方法的推理准确性更高,同时系统复杂度更低。
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.
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.
引文
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[2]LIN Y Q,LI M,CHEN X C,et al.A belief rule base approach for smart traffic lights[C]//International Symposium on Computational Intelligence and Design.Hangzhou:IEEE,2017:460-463.
[3]YANG J B,LIU J,XU D L,et al.Optimal learning method for training belief rule based systems[J].IEEE Transactions on Systems,Man,and Cybernetics-Part A:Systems and Humans,2007,37(4):569-585.
[4]ZHOU Z J,HU C H,YANG J B,et al.Online updating belief rule based system for pipeline leak detection under expert intervention[J].Expert Systems with Applications,2009,36(4):7700-7709.
[5]ZHAO F J,ZHOU Z J,HU C H,et al.A new evidential reasoning-based method for online safety assessment of complex systems[J].IEEE Transactions on Systems Man&Cybernetics Systems,2018,48(6):954-966.
[6]YIN X,ZHANG B,ZHOU Z,et al.A new health estimation model for CNC machine tool based on infinite irrelevance and belief rule base[J].Microelectronics Reliability,2018,84:187-196.
[7]ZHOU Z J,HU C H,YANG J B,et al.Online updating belief-rule-base using the RIMER approach[J].IEEETransactions on Systems Man&Cybernetics Part A Systems&Humans,2011,41(6):1225-1243.
[8]吴伟昆,杨隆浩,傅仰耿,等.基于加速梯度求法的置信规则库参数训练方法[J].计算机科学与探索,2014,8(8):989-1001.WU Wei-kun,YANG Long-hao,FU Yang-geng,et al.Parameter training approach for belief rule base using the accelerating of gradient algorithm[J].Journal of Frontiers of Computer Science and Technology,2014,8(8):989-1001.
[9]苏群,杨隆浩,傅仰耿,等.基于变速粒子群优化的置信规则库参数训练方法[J].计算机应用,2014,34(8):2161-2165.SU Qun,YANG Long-hao,FU Yang-geng,et al.Parameter training approach based on variable particle swarm optimization for belief rule base[J].Journal of Computer Applications,2014,34(8):2161-2165.
[10]周志杰,杨剑波,胡昌华,等.置信规则库专家系统与复杂系统建模[M].北京:科学出版社,2011:1-119.ZHOU Zhi-jie,YANG Jian-bo,HU Chang-hua,et al.Belief rule base expert system and complex system[M].Beijing:Science Press,2011:1-119.
[11]CHANG L,ZHOU Y,JIANG J,et al.Structure learning for belief rule base expert system:a comparative study[J].Knowledge-Based Systems,2013,39:159-172.
[12]DEY A,CHOUDHURY A B.A comparative study between scalarization approach and pareto approach for multiobjective optimization problem using genetic algorithm(MOGA)formulated based on superconducting fault current limiter[C]//IEEE International Conference on Power Electronics,Intelligent Control and Energy Systems.Delhi:IEEE,2017:1-4.
[13]童晶.多目标优化的Pareto解的表达与求取[D].武汉:武汉科技大学,2009.TONG Jing.Expressing and obtaining pareto solutions in multi-objective optimization problem[D].Wuhan:Wuhan University of Science and Technology,2009.
[14]张自如.PAES多目标优化算法及其应用研究[D].兰州:兰州理工学院,2012.ZHANG Zi-ru.PAES-The algorithm of multi-objective optimization and its applied research[D].Lanzhou:Lanzhou University of Technology,2012.
[15]HUANG Ren-fang,LUO Xian-wu,JI Bin,et al.Multiobjective optimization of a mixed-flow pump impeller using modified NSGA-II algorithm[J].Science China(Technological Sciences),2015,58(12):2122-2130.
[16]MARCO C,PIETRO D,BEATRICE L,et al.A paretobased multi-objective evolutionary approach to the identification of mamdani fuzzy systems[J].Soft Computing,2007,11(11):1013-1031.