基于决策偏好信息的n维Pareto前沿可视化
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摘要
针对现有可视化技术不能有效显示高维多目标优化问题的难题,提出了一种基于决策偏好信息的n维图表可视化技术。首先,针对两种不同的决策情况分别提出对应的目标信息共享机制;然后,根据目标共享信息将分层后的Pareto前沿,通过子图表进行绘制,有效显示了各维目标数据信息、性能优劣变化趋势和决策者的偏好信息。基于此思想设计了可视化模型并通过实验加以分析,达到了方便决策者对Pareto最优解集进行分析和决策的目的。
In order to overcome the shortcomings that currently visualization technology cannot display high dimension multi-objective optimization problems effectively,a new graphical visualization technology of n-dimensional Pareto front based on the weighted preference information is proposed.Firstly,the corresponding objective information sharing mechanism for the two different decision-making situations is proposed.Secondly,according to the sharing information the Pareto front will be stratified and drawn by graphs.It effectively shows the data information of each dimension objective,the variation tendency towards performance and the preference information for decision-makers.This paper devises the visualization model and provides the extensive experimental analyses so as to analyze the Pareto optimal solutions for decision-makers.
In order to overcome the shortcomings that currently visualization technology cannot display high dimension multi-objective optimization problems effectively,a new graphical visualization technology of n-dimensional Pareto front based on the weighted preference information is proposed.Firstly,the corresponding objective information sharing mechanism for the two different decision-making situations is proposed.Secondly,according to the sharing information the Pareto front will be stratified and drawn by graphs.It effectively shows the data information of each dimension objective,the variation tendency towards performance and the preference information for decision-makers.This paper devises the visualization model and provides the extensive experimental analyses so as to analyze the Pareto optimal solutions for decision-makers.
引文
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[6]Ortiz M C,Sarabia L A,Sánchez M S,et al.Improving the visu-alization of the Pareto-optimal front for the multi-response opti-mization of chromatographic determinations[J].AnalyticaChimica Acta,2011,687(2):129-136.
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[9]Blasco X,Herrero J M,Sanchis J,et al.A new graphical visual-ization of n-dimensional Pareto front for decision-making inmulti-objective optimization[J].Information Sciences,2008,178(20):3908-3924.
[10]Zio E,Bazzo R.Multiobjective optimization of the inspection in-tervals of a nuclear safety system:a clustering-based frame-work for reducing the Pareto front[J].Annals of Nuclear En-ergy,2010,37(6):798-812.
[11]Zio E,Bazzo R.A clustering procedure for reducing the numberof representative solutions in the Pareto front of multiobjectiveoptimization problems[J].European Journal of OperationalResearch,2011,210(3):624-634.
[12]Deb K,Thiele L,Laumanns M,et al.Scalable multi-objectiveoptimization test problems[C]∥Proc.of the Congress on Evo-lutionary Computation,2002:825-830.
[2]Efremov R,Insua D R,Lotov A.A framework for participatorydecision support using Pareto frontier visualization,goal identifi-cation and arbitration[J].European Journal of Operational Re-search,2009,199(2):459-467.
[3]Agrawal G,Bloebaum C L,Lewis K.Intuitive design selectionusing visualized n-dimensional pareto frontier[C]∥Proc.of theCollection of Technical Papers-AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Confer-ence,2005:145-158.
[4]Bernataviciene J,Dzemyda G,Kurasova O,et al.Optimal decisions incombining the SOM with nonlinear projection methods[J].EuropeanJournal of Operational Research,2006,173(3):729-745.
[5]Masafumi Y,Tomohiro Y,Takeshi F.A study on interactivesearch in MOGA with island model based on user’s requirementsusing visualization in NSP[C]∥Proc.of the 2nd World Con-gress on Nature and Biologically Inspired Computing,2010:490-495.
[6]Ortiz M C,Sarabia L A,Sánchez M S,et al.Improving the visu-alization of the Pareto-optimal front for the multi-response opti-mization of chromatographic determinations[J].AnalyticaChimica Acta,2011,687(2):129-136.
[7]Claessen J H T,Van Wijk J J.Flexible linked axes for multivari-ate data visualization[J].IEEE Trans.on Visualization andComputer Graphics,2011,17(12):2310-2316.
[8]Stump G,Lego S,Yukish M,et al.Visual steering commands fortrade space exploration:user-guided sampling with example[J].Journal of Computing and Information Science in Engineer-ing,2009,9(4):1-10.
[9]Blasco X,Herrero J M,Sanchis J,et al.A new graphical visual-ization of n-dimensional Pareto front for decision-making inmulti-objective optimization[J].Information Sciences,2008,178(20):3908-3924.
[10]Zio E,Bazzo R.Multiobjective optimization of the inspection in-tervals of a nuclear safety system:a clustering-based frame-work for reducing the Pareto front[J].Annals of Nuclear En-ergy,2010,37(6):798-812.
[11]Zio E,Bazzo R.A clustering procedure for reducing the numberof representative solutions in the Pareto front of multiobjectiveoptimization problems[J].European Journal of OperationalResearch,2011,210(3):624-634.
[12]Deb K,Thiele L,Laumanns M,et al.Scalable multi-objectiveoptimization test problems[C]∥Proc.of the Congress on Evo-lutionary Computation,2002:825-830.