Maximizing Submodular or Monotone Functions under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms

Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions efficiently. While there have been many studies on the subject, most o...

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Veröffentlicht in:arXiv.org
Hauptverfasser: Anh Viet Do, Neumann, Frank
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 08.09.2020
Schlagworte:
Approximation
Evolutionary algorithms
Genetic algorithms
Greedy algorithms
Mathematical analysis
Maximization
Monotone functions
Multiple objective analysis
Optimization
Partitions
Polynomials
ISSN:2331-8422
Online-Zugang:Volltext
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Zusammenfassung:Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions efficiently. While there have been many studies on the subject, most of existing run-time analyses for GSEMO assume a single cardinality constraint. In this work, we extend the theoretical results to partition matroid constraints which generalize cardinality constraints, and show that GSEMO can generally guarantee good approximation performance within polynomial expected run time. Furthermore, we conducted experimental comparison against a baseline GREEDY algorithm in maximizing undirected graph cuts on random graphs, under various partition matroid constraints. The results show GSEMO tends to outperform GREEDY in quadratic run time.
Bibliographie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2006.12773