Some Demonstrations about the Cardinality of Important Sets of Non---dominated Sets

Authors:
Giovanni Lizárraga;Arturo Hernández;Salvador Botello
Affiliations:
Department of Computer Science, Center for Research in Mathematics (CIMAT), Guanajuato, México Gto. 36240;Department of Computer Science, Center for Research in Mathematics (CIMAT), Guanajuato, México Gto. 36240;Department of Computer Science, Center for Research in Mathematics (CIMAT), Guanajuato, México Gto. 36240
Venue:
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Year:
2008

Citing 3
Cited 0

Multi-Objective Optimization Using Evolutionary Algorithms

Multi-Objective Optimization Using Evolutionary Algorithms
Evolutionary Algorithms for Solving Multi-Objective Problems

Evolutionary Algorithms for Solving Multi-Objective Problems
Performance assessment of multiobjective optimizers: an analysis and review

IEEE Transactions on Evolutionary Computation

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Abstract

In multiobjective optimization, a very important element is thespace of objective functions, usually called Z. The set of¿of all non---dominated sets that we can generatewith elements of Zis especially interesting, because itrepresent all possible output from an evolutionary multiobjectivealgorithm. In this study, we make some theoretical demonstrationsabout the cardinality of Ωand others important setsof non---dominated sets. After, we use these demonstrations toprove some theorems in the area of performance measures forevolutionary multiobjective algorithms.