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SAT-Based Leximax Optimisation Algorithms

Authors Miguel Cabral, Mikoláš Janota , Vasco Manquinho

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Author Details

Miguel Cabral
  • INESC-ID, IST, University of Lisbon, Portugal
Mikoláš Janota
  • Czech Technical University in Prague, Czech Republic
Vasco Manquinho
  • INESC-ID, IST, University of Lisbon, Portugal

Funding

This work was partially supported by Portuguese national funds through FCT, under projects UIDB/50021/2020, PTDC/CCI-COM/31198/2017, PTDC/CCI-COM/32378/2017 and DSAIPA/AI/0044/2018. The results were supported by the Ministry of Education, Youth and Sports within the dedicated program ERC CZ under the project POSTMAN no. LL1902. This article is part of the RICAIP project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 857306.

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Miguel Cabral, Mikoláš Janota, and Vasco Manquinho. SAT-Based Leximax Optimisation Algorithms. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 29:1-29:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SAT.2022.29

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Optimization algorithms
Keywords
  • Multi-Objective Optimisation
  • Leximax
  • Sorting Networks

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References

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