Abstract
In multiobjective optimization, a very important element is the space of objective functions, usually called Z. The set of Ω of all non–dominated sets that we can generate with elements of Z is especially interesting, because it represent all possible output from an evolutionary multiobjective algorithm. In this study, we make some theoretical demonstrations about the cardinality of Ω and others important sets of non–dominated sets. After, we use these demonstrations to prove some theorems in the area of performance measures for evolutionary multiobjective algorithms.
Keywords
- Comparison Method
- Pareto Front
- Cardinal Number
- Multiobjective Problem
- Evolutionary Multiobjective Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2008 Springer-Verlag Berlin Heidelberg
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Lizárraga, G., Hernández, A., Botello, S. (2008). Some Demonstrations about the Cardinality of Important Sets of Non–dominated Sets. In: Gelbukh, A., Morales, E.F. (eds) MICAI 2008: Advances in Artificial Intelligence. MICAI 2008. Lecture Notes in Computer Science(), vol 5317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88636-5_42
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DOI: https://doi.org/10.1007/978-3-540-88636-5_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88635-8
Online ISBN: 978-3-540-88636-5
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