基于单目标拟合度的高维多目标可视化
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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这一难题,提出了一种以单目标拟合为绘图基准的子图表可视化技术。该方法以与目标数相同的子图表形式显示Pareto标准解集,并在子图表中通过拟合位置绘制Pareto近似集。其图形有效地显示了Pareto近似集的收敛性和分布性,同时对单个解各维目标上性能的相对优劣性及不同解在同一目标上性能的对比情况都达到了有效的可视化显示。基于此思想设计了可视化模型并通过试验加以分析,达到了方便决策者对多目标优化问题进行分析和决策的目的。
Current visualization techniques failed to effectively display the high dimension multiobjective optimization problems.To overcome this disadvantage,a new sub-diagram visualization technology based on single objective fitting is proposed.The new visualization technology displays the Pareto solution set in sub-diagram form whose number is the same as objectives.Additionally,the Pareto approximate set is drawn by the fitting location in the sub-diagram.The proposed method displays effectively the convergence and distribution of the Pareto approximate set;meanwhile,the relative merits of the performance on a single solution in each dimension objective and the comparison of the performance of different solutions in the same objective are displayed effectively.Numerical experiments show that the new visualization technique plays a key role in helping decision-makers carry on analysis and decision for multi-objective optimization problems.
Current visualization techniques failed to effectively display the high dimension multiobjective optimization problems.To overcome this disadvantage,a new sub-diagram visualization technology based on single objective fitting is proposed.The new visualization technology displays the Pareto solution set in sub-diagram form whose number is the same as objectives.Additionally,the Pareto approximate set is drawn by the fitting location in the sub-diagram.The proposed method displays effectively the convergence and distribution of the Pareto approximate set;meanwhile,the relative merits of the performance on a single solution in each dimension objective and the comparison of the performance of different solutions in the same objective are displayed effectively.Numerical experiments show that the new visualization technique plays a key role in helping decision-makers carry on analysis and decision for multi-objective optimization problems.
引文
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[4]Zou Xiu-fen,Chen Yu,Liu Min-zhong.A new evolutionary algorithm for solving many-objective optimization problems[J].IEEE Transactions on Systems,Man,and Cybernetics—Part B:Cybernetics,2008,38(5):1402-1412.
[5]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.
[6]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&Materials Conference,Austin,T X,USA,2005:1813-1826.
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[8]Po-Wen C,Christina L B.Hyper-radial visualization(HRV)method with range-based preferences for multi-objective decision making[J].Struct Multidisc Optim,2010 40(1):97-115.
[9]BernataviienéJ,Dzemyda Gintautas,Kurasova O.Optimal decisions in combining the SOM with nonlinear projection methods[J].European Journal of Operational Research,2006,173(3):729-745.
[10]Masafumi Y,Tomohiro Y,Takeshi F.Study on effect of MOGA with interactive island model using visualization[C]∥2010IEEE Congress on Evolutionary Computation(CEC),Barcelona,Spain,2010:1-6.
[11]Ivosev G,Burton L,Bonner R.Dimensionality reduction and visualization in principal component analysis[J].Analytical Chemistry,2008,80(13):4933-4944.
[12]Deb K,Thiele L,Laumanns M.Scalable multi-objective optimization test problems[C]∥Proceedings of the 2002Congress on Evolutionary Computation,Honolulu,H I,2002:825-830.
[13]Problems included in jMetal[DB/OL].[2012-04-27].http://jmetal.sourceforge.net/problems.html.
[14]Pham M T,Zhang D,Koh,C S.Multi-guider and cross-searching approach in multi-objective particle swarm optimization for electromagnetic problems[J].IEEE Transactions on Magnetics,2012,48(2):539-542.
[15]Zitzler E,Thiele L.Multi-objective evolutionary algorithms:A comparative case study and the strength Pareto approach[J].IEEE Transactions on Evolutionary Computations,1999,6(2):182-197.