License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SAT.2022.29
URN: urn:nbn:de:0030-drops-167030
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16703/
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Cabral, Miguel ; Janota, Mikoláš ; Manquinho, Vasco

SAT-Based Leximax Optimisation Algorithms

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LIPIcs-SAT-2022-29.pdf (1.0 MB)

Abstract

In several real-world problems, it is often the case that the goal is to optimise several objective functions. However, usually there is not a single optimal objective vector. Instead, there are many optimal objective vectors known as Pareto-optima. Finding all Pareto-optima is computationally expensive and the number of Pareto-optima can be too large for a user to analyse. A compromise can be made by defining an optimisation criterion that integrates all objective functions.
In this paper we propose several SAT-based algorithms to solve multi-objective optimisation problems using the leximax criterion. The leximax criterion is used to obtain a Pareto-optimal solution with a small trade-off between the objective functions, which is suitable in problems where there is an absence of priorities between the objective functions. Experimental results on the Multi-Objective Package Upgradeability Optimisation problem show that the SAT-based algorithms are able to outperform the Integer Linear Programming (ILP) approach when using non-commercial ILP solvers. Additionally, experimental results on selected instances from the MaxSAT evaluation adapted to the multi-objective domain show that our approach outperforms the ILP approach using commercial solvers.

BibTeX - Entry

@InProceedings{cabral_et_al:LIPIcs.SAT.2022.29,
  author =	{Cabral, Miguel and Janota, Mikol\'{a}\v{s} and Manquinho, Vasco},
  title =	{{SAT-Based Leximax Optimisation Algorithms}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{29:1--29:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16703},
  URN =		{urn:nbn:de:0030-drops-167030},
  doi =		{10.4230/LIPIcs.SAT.2022.29},
  annote =	{Keywords: Multi-Objective Optimisation, Leximax, Sorting Networks}
}

Keywords: Multi-Objective Optimisation, Leximax, Sorting Networks
Collection: 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)
Issue Date: 2022
Date of publication: 28.07.2022
Supplementary Material: Software (Source Code): https://github.com/miguelcabral/leximaxIST

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