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View all- Li MYao X(2019)Quality Evaluation of Solution Sets in Multiobjective OptimisationACM Computing Surveys10.1145/330014852:2(1-38)Online publication date: 18-Mar-2019
On the possibility to create a compatible--complete unary comparison method for evolutionary multiobjective algorithms
Authors: 
Giovanni Lizárraga-Lizárraga, Arturo Hernández-Aguirre, Salvador Botello-RiondaAuthors Info & Claims
Giovanni Lizárraga-Lizárraga, Arturo Hernández-Aguirre, Salvador Botello-RiondaAuthors Info & ClaimsPages 759 - 760
Abstract
There are several studies on the desirable properties that a performance measure for evolutionary multiobjective algorithms must have. One of these properties is called "compatibility and completeness". There is a theorem that proves that in the general case, it is not possible to create a unary comparison method with the property mentioned before. Many important conclusions have been derived from this theorem, so its correctness is fundamental for future research. In this work we demonstrate that under practical conditions, the theorem mentioned before does not hold.
References
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C. A. Coello, D. Van Veldhuizen, and G. B. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic/Plenum Publishers, New York, USA, 2002.
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K. Deb. Multi-objective Optimization Using Evolutionary Algorithms. John Wiley and Sons, Chichester, UK, 2001.
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E. Kamke. Theory of Sets. Dover Publications, Inc., New York, USA, 1950.
[4]
G. Lizarraga, A. Hernandez, and S. Botello. On the Possibility to Create a Compatible-Complete Unary Comparison Method for Evolutionary Multiobjective Algorithms. Technical report i-08-09 (cc) 15.04.2008, Centro de Investigacion en Matematicas, 2008.
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E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. Grunert da Fonseca. Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation, 7(2):529--533, May 2003.
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- On the possibility to create a compatible--complete unary comparison method for evolutionary multiobjective algorithms
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July 2008
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Published: 12 July 2008
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View all- Li MYao X(2019)Quality Evaluation of Solution Sets in Multiobjective OptimisationACM Computing Surveys10.1145/330014852:2(1-38)Online publication date: 18-Mar-2019
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