article

A note on the ε-indicator subset selection

Authors:

Daniel Vaz,

Luís Paquete,

Aníbal PonteAuthors Info & Claims

Theoretical Computer Science, Volume 499

Pages 113 - 116

https://doi.org/10.1016/j.tcs.2013.05.013

Published: 01 August 2013 Publication History

Abstract

The @e-indicator subset selection selects a subset of a nondominated point set that is as close as possible to a reference point set with respect to the @e-indicator. This selection procedure is used by population-based heuristic approaches for multiobjective optimization problems. Given that this procedure is called very often during the run of the heuristic approach, efficient ways of computing the optimal subset are strongly required. In this note, we give a correctness proof of the @e-indicator subset selection algorithm proposed by Ponte et al. (2012) [1] for the bidimensional case as well as several algorithmic improvements in terms of time complexity. Extensions to larger dimension are also discussed.

References

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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
https://dl.acm.org/doi/10.1145/3300148
Vaz DPaquete LFonseca CKlamroth KStiglmayr M(2015)Representation of the non-dominated set in biobjective discrete optimizationComputers and Operations Research10.1016/j.cor.2015.05.00363:C(172-186)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1016/j.cor.2015.05.003
Bringmann KFriedrich TKlitzke PArnold D(2014)Two-dimensional subset selection for hypervolume and epsilon-indicatorProceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation10.1145/2576768.2598276(589-596)Online publication date: 12-Jul-2014
https://dl.acm.org/doi/10.1145/2576768.2598276

A note on the ε-indicator subset selection
1. Theory of computation

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 499, Issue

August, 2013

115 pages

ISSN:0304-3975

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Elsevier Science Publishers Ltd.

United Kingdom

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Published: 01 August 2013

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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
https://dl.acm.org/doi/10.1145/3300148
Vaz DPaquete LFonseca CKlamroth KStiglmayr M(2015)Representation of the non-dominated set in biobjective discrete optimizationComputers and Operations Research10.1016/j.cor.2015.05.00363:C(172-186)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1016/j.cor.2015.05.003
Bringmann KFriedrich TKlitzke PArnold D(2014)Two-dimensional subset selection for hypervolume and epsilon-indicatorProceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation10.1145/2576768.2598276(589-596)Online publication date: 12-Jul-2014
https://dl.acm.org/doi/10.1145/2576768.2598276

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Cited By

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Greedy hypervolume subset selection in low dimensions

Experiments on Greedy and Local Search Heuristics for ddimensional Hypervolume Subset Selection

Greedy Hypervolume Subset Selection in the Three-Objective Case

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