Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms

Lucas S. Batista, Felipe Campelo, Frederico G. Guimaraes, Jaime A. Ramirez, RHC Takahashi

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Abstract

Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal front with a widely spread distribution of solutions. A popular concept is the ε-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the ε-dominance concept, there are still difficulties in computing an appropriate value of ε that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the convergence and the diversity of the estimate set. We propose the concept of cone ε-dominance, which is a variant of the ε-dominance, to overcome these limitations. Cone ε-dominance maintains the good convergence properties of ε-dominance, provides a better control over the resolution of the estimated Pareto front, and also performs a better spread of solutions along the front. Experimental validation of the proposed cone ε-dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the ε-dominance.
Original languageEnglish
Title of host publicationLecture Notes in Computer Science
Subtitle of host publicationEMO 2011: Evolutionary Multi-Criterion Optimization
PublisherSpringer
Pages76-90
Volume6576
ISBN (Electronic)978-3-642-19893-9
ISBN (Print)978-3-642-19892-2
DOIs
Publication statusPublished - 2011
Event6th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2011 - Ouro Preto, Brazil
Duration: 5 Apr 20118 Apr 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
Volume6576
ISSN (Electronic)0302-9743

Conference

Conference6th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2011
CountryBrazil
CityOuro Preto
Period5/04/118/04/11

Fingerprint

Evolutionary algorithms
Cones

Cite this

Batista, L. S., Campelo, F., Guimaraes, F. G., Ramirez, J. A., & Takahashi, RHC. (2011). Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms. In Lecture Notes in Computer Science: EMO 2011: Evolutionary Multi-Criterion Optimization (Vol. 6576, pp. 76-90). (Lecture Notes in Computer Science; Vol. 6576). Springer. https://doi.org/10.1007/978-3-642-19893-9_6
Batista, Lucas S. ; Campelo, Felipe ; Guimaraes, Frederico G. ; Ramirez, Jaime A. ; Takahashi, RHC. / Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms. Lecture Notes in Computer Science: EMO 2011: Evolutionary Multi-Criterion Optimization. Vol. 6576 Springer, 2011. pp. 76-90 (Lecture Notes in Computer Science).
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Batista, LS, Campelo, F, Guimaraes, FG, Ramirez, JA & Takahashi, RHC 2011, Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms. in Lecture Notes in Computer Science: EMO 2011: Evolutionary Multi-Criterion Optimization. vol. 6576, Lecture Notes in Computer Science, vol. 6576, Springer, pp. 76-90, 6th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2011, Ouro Preto, Brazil, 5/04/11. https://doi.org/10.1007/978-3-642-19893-9_6

Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms. / Batista, Lucas S.; Campelo, Felipe; Guimaraes, Frederico G.; Ramirez, Jaime A.; Takahashi, RHC.

Lecture Notes in Computer Science: EMO 2011: Evolutionary Multi-Criterion Optimization. Vol. 6576 Springer, 2011. p. 76-90 (Lecture Notes in Computer Science; Vol. 6576).

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

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T1 - Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms

AU - Batista, Lucas S.

AU - Campelo, Felipe

AU - Guimaraes, Frederico G.

AU - Ramirez, Jaime A.

AU - Takahashi, RHC

PY - 2011

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N2 - Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal front with a widely spread distribution of solutions. A popular concept is the ε-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the ε-dominance concept, there are still difficulties in computing an appropriate value of ε that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the convergence and the diversity of the estimate set. We propose the concept of cone ε-dominance, which is a variant of the ε-dominance, to overcome these limitations. Cone ε-dominance maintains the good convergence properties of ε-dominance, provides a better control over the resolution of the estimated Pareto front, and also performs a better spread of solutions along the front. Experimental validation of the proposed cone ε-dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the ε-dominance.

AB - Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal front with a widely spread distribution of solutions. A popular concept is the ε-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the ε-dominance concept, there are still difficulties in computing an appropriate value of ε that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the convergence and the diversity of the estimate set. We propose the concept of cone ε-dominance, which is a variant of the ε-dominance, to overcome these limitations. Cone ε-dominance maintains the good convergence properties of ε-dominance, provides a better control over the resolution of the estimated Pareto front, and also performs a better spread of solutions along the front. Experimental validation of the proposed cone ε-dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the ε-dominance.

UR - https://link.springer.com/chapter/10.1007%2F978-3-642-19893-9_6

U2 - 10.1007/978-3-642-19893-9_6

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M3 - Chapter (peer-reviewed)

SN - 978-3-642-19892-2

VL - 6576

T3 - Lecture Notes in Computer Science

SP - 76

EP - 90

BT - Lecture Notes in Computer Science

PB - Springer

ER -

Batista LS, Campelo F, Guimaraes FG, Ramirez JA, Takahashi RHC. Pareto Cone ε-Dominance: Improving Convergence and Diversity in Multiobjective Evolutionary Algorithms. In Lecture Notes in Computer Science: EMO 2011: Evolutionary Multi-Criterion Optimization. Vol. 6576. Springer. 2011. p. 76-90. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-642-19893-9_6