基于特征解选取的高维多目标可视化研究
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摘要
为了解决高维多目标优化问题中有效可视化Pareto最优解集这一难题,提出了一种基于特征解选取的n维图表可视化技术.首先,针对多目标优化问题的特性,提取Pareto最优解集中特征性明显的特征解;然后,针对不同的决策需求提出2种目标信息共享机制,将特征解各目标信息共享后进行有效排序分层;最后,以子图表形式进行绘制.该方法有效去除Pareto最优解集中性能相近的冗余解,对特征解各目标数据信息、性能优劣变化趋势及决策者的决策信息进行可视化.基于此思想设计的高维多目标可视化模型,方便决策者对Pareto最优解集的分析和决策.
Current visualization techniques failed to effectively demonstrate the Pareto optimal solutions of high dimensional multi-objective optimization problems.In view of this problem,a new graphical visualization technology of n-dimensional Pareto front based on the selection of characteristic solutions was proposed.First,solutions with obvious characteristics in the optimal solutions were collected in allusion to the feature of multi-objective optimization problems.After that,two objective information sharing mechanisms were proposed aiming at different decision needs and the characteristic solutions were sorted effectively after sharing objective information.Finally,a subgraphic form was drawn.In this method,redundancy solutions of similar performance in Pareto optimal solutions were eliminated;objective information of characteristic solutions was sorted,the trend of performance and the decision information of decision-making were visualized effectively.The multi-dimensional objective visualization model was designed based on the idea.This method achieves the purpose that the decision-maker can conveniently analyze the Pareto optimal solutions and make decisions.
Current visualization techniques failed to effectively demonstrate the Pareto optimal solutions of high dimensional multi-objective optimization problems.In view of this problem,a new graphical visualization technology of n-dimensional Pareto front based on the selection of characteristic solutions was proposed.First,solutions with obvious characteristics in the optimal solutions were collected in allusion to the feature of multi-objective optimization problems.After that,two objective information sharing mechanisms were proposed aiming at different decision needs and the characteristic solutions were sorted effectively after sharing objective information.Finally,a subgraphic form was drawn.In this method,redundancy solutions of similar performance in Pareto optimal solutions were eliminated;objective information of characteristic solutions was sorted,the trend of performance and the decision information of decision-making were visualized effectively.The multi-dimensional objective visualization model was designed based on the idea.This method achieves the purpose that the decision-maker can conveniently analyze the Pareto optimal solutions and make decisions.
引文
[1]PARETO V.Cours dconomie politique[J].The ANNALS of the American Academy of Political and Social Science,1897,9(3):128-131.
[2]EFREMOV R,INSUA D R,LOTOV A.A framework for participatory decision support using Pareto frontier visualization goal identification and arbitration[J].European Journal of Operational Research,2009,199(2):459-467.
[3]AGRAWAL G,BLOEBAUM C L,LEWIS K.Intuitive design selection using visualized n-dimensional pareto frontier[C]//46th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference.Austin,TX,USA,2005:145-158.
[4]BERNATAVICIENE J,DZEMYDA G,KURASOVA O,et al.Optimal decisions in combining the SOM with nonlinear projection methods[J].European Journal of Operational Research,2006,173(3):729-745.
[5]MASAFUMI Y,TOMOHIRO Y,TAKESHI F.A study on interactive search in MOGA with island model based on user's requirements using visualization in NSP[C]//Proceedings-2010 2nd World Congress on Nature and Biologically Inspired Computing.Kitakyushu,Japan,2010:490-495.
[6]TAGHAVI T,PIMENTEL A D,SABEGHI M.VMODEX:a novel visualization tool for rapid analysis of heuristic-based multi-objective design space exploration of heterogeneous MPSoC architectures[J].Simulation Modelling Practice and Theory,2012,22(5):166-196.
[7]IVOSEV G,BURTON L,BONNER R.Dimensionality reduction and visualization in principal component analysis[J].Analytical Chemistry,2008,80(13):4933-4944.
[8]ORTIZ M C,SARABIA L A,SANCHEZ M S,et al.Improving the visualization of the Pareto-optimal front for the multi-response optimization of chromatographic determinations[J].Analytica Chimica Acta,2011,687(2):129-136.
[9]CLAESSEN J H T,VAN WIJK J J.Flexible linked axes for multivariate data visualization[J].IEEE Transactions on Visualization and Computer Graphics,2011,17(12):2310-2316.
[10]STUMP G,LEGO S,YUKISH M,et al.Visual steering commands for trade space exploration:user-guided sampling with example[J].Journal of Computing and Information Science in Engineering,2009,9(4):1-10.
[11]ZOU Xiufen,CHEN Yu,LIU Minzhong,et al.A new evolutionary algorithm for solving many-objective optimization problems[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2008,38(5):1043-1412.
[12]BLASCO X,HERRERO J M,SANCHIS J,et al.A new graphical visualization of n-dimensional Pareto front for decision-making in multi-objective optimization[J].Information Sciences,2008,178(20):3908-3924.
[13]ZIO E,BAZZO R.Multiobjective optimization of the inspection intervals of a nuclear safety system:a clusteringbased framework for reducing the Pareto Front[J].Annals of Nuclear Energy,2010,37(6):798-812.
[14]ZIO E,BAZZO R.A clustering procedure for reducing the number of representative solutions in the Pareto front of multiobjective optimization problems[J].European Journal of Operational Research,2011,210(3):624-634.
[15]DEB K,THIELE L,LAUMANNS M,et al.Scalable multiobjective optimization test problems[C]//Evolutionary Computation,2002.CEC'02.Honolulu,United States,2002:825-830.
[16]PHAM M T,ZHANG D,KOH C S.Multi-guider and crosssearching approach in multi-objective particle swarm optimization for electromagnetic problems[J].IEEE Transactions on Magnetics,2012,48(2):539-542.
[2]EFREMOV R,INSUA D R,LOTOV A.A framework for participatory decision support using Pareto frontier visualization goal identification and arbitration[J].European Journal of Operational Research,2009,199(2):459-467.
[3]AGRAWAL G,BLOEBAUM C L,LEWIS K.Intuitive design selection using visualized n-dimensional pareto frontier[C]//46th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference.Austin,TX,USA,2005:145-158.
[4]BERNATAVICIENE J,DZEMYDA G,KURASOVA O,et al.Optimal decisions in combining the SOM with nonlinear projection methods[J].European Journal of Operational Research,2006,173(3):729-745.
[5]MASAFUMI Y,TOMOHIRO Y,TAKESHI F.A study on interactive search in MOGA with island model based on user's requirements using visualization in NSP[C]//Proceedings-2010 2nd World Congress on Nature and Biologically Inspired Computing.Kitakyushu,Japan,2010:490-495.
[6]TAGHAVI T,PIMENTEL A D,SABEGHI M.VMODEX:a novel visualization tool for rapid analysis of heuristic-based multi-objective design space exploration of heterogeneous MPSoC architectures[J].Simulation Modelling Practice and Theory,2012,22(5):166-196.
[7]IVOSEV G,BURTON L,BONNER R.Dimensionality reduction and visualization in principal component analysis[J].Analytical Chemistry,2008,80(13):4933-4944.
[8]ORTIZ M C,SARABIA L A,SANCHEZ M S,et al.Improving the visualization of the Pareto-optimal front for the multi-response optimization of chromatographic determinations[J].Analytica Chimica Acta,2011,687(2):129-136.
[9]CLAESSEN J H T,VAN WIJK J J.Flexible linked axes for multivariate data visualization[J].IEEE Transactions on Visualization and Computer Graphics,2011,17(12):2310-2316.
[10]STUMP G,LEGO S,YUKISH M,et al.Visual steering commands for trade space exploration:user-guided sampling with example[J].Journal of Computing and Information Science in Engineering,2009,9(4):1-10.
[11]ZOU Xiufen,CHEN Yu,LIU Minzhong,et al.A new evolutionary algorithm for solving many-objective optimization problems[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2008,38(5):1043-1412.
[12]BLASCO X,HERRERO J M,SANCHIS J,et al.A new graphical visualization of n-dimensional Pareto front for decision-making in multi-objective optimization[J].Information Sciences,2008,178(20):3908-3924.
[13]ZIO E,BAZZO R.Multiobjective optimization of the inspection intervals of a nuclear safety system:a clusteringbased framework for reducing the Pareto Front[J].Annals of Nuclear Energy,2010,37(6):798-812.
[14]ZIO E,BAZZO R.A clustering procedure for reducing the number of representative solutions in the Pareto front of multiobjective optimization problems[J].European Journal of Operational Research,2011,210(3):624-634.
[15]DEB K,THIELE L,LAUMANNS M,et al.Scalable multiobjective optimization test problems[C]//Evolutionary Computation,2002.CEC'02.Honolulu,United States,2002:825-830.
[16]PHAM M T,ZHANG D,KOH C S.Multi-guider and crosssearching approach in multi-objective particle swarm optimization for electromagnetic problems[J].IEEE Transactions on Magnetics,2012,48(2):539-542.