Hypervolume Subset Selection with Small Subsets

The hypervolume subset selection problem (HSSP) aims at approximating a set of multidimensional points in with an optimal subset of a given size. The size of the subset is a parameter of the problem, and an approximation is considered best when it maximizes the hypervolume indicator. This problem ha...

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Bibliographic Details
Published in:Evolutionary computation 2019-12, Vol.27 (4), p.611-637
Main Authors: Groz, Benoît, Maniu, Silviu
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Biological Evolution
Computer Science
Computer Simulation
Computing Methodologies
Evolutionary algorithms
Formulas (mathematics)
hypervolume contributions
Hypervolume subset selection
Mathematical Computing
minimal triples in weighted hypergraphs
Multiple objective analysis
Social and Information Networks
Software
Web
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Summary:The hypervolume subset selection problem (HSSP) aims at approximating a set of multidimensional points in with an optimal subset of a given size. The size of the subset is a parameter of the problem, and an approximation is considered best when it maximizes the hypervolume indicator. This problem has proved popular in recent years as a procedure for multiobjective evolutionary algorithms. Efficient algorithms are known for planar points ( ), but there are hardly any results on HSSP in larger dimensions ( ). So far, most algorithms in higher dimensions essentially enumerate all possible subsets to determine the optimal one, and most of the effort has been directed toward improving the efficiency of hypervolume computation. We propose efficient algorithms for the selection problem in dimension 3 when either or is small, and extend our techniques to arbitrary dimensions for .
ISSN:1063-6560
1530-9304
DOI:10.1162/evco_a_00235