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Boolean lexicographic optimization: algorithms & applications

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Abstract

Multi-Objective Combinatorial Optimization (MOCO) problems find a wide range of practical application problems, some of which involving Boolean variables and constraints. This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic. The proposed algorithms build on existing algorithms for either Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO), or Integer Linear Programming (ILP). Experimental results, obtained on problem instances from haplotyping with pedigrees and software package dependencies, show that the proposed algorithms can provide significant performance gains over state of the art MaxSAT, PBO and ILP algorithms. Finally, the paper also shows that lexicographic optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations, motivating the development of dedicated algorithms that can exploit lexicographic optimization conditions in general MaxSAT problem instances.

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Authors and Affiliations

  1. CSI/CASL, University College Dublin, Dublin, Ireland

    Joao Marques-Silva

  2. INESC-ID/IST, Technical University of Lisbon, Lisbon, Portugal

    Joao Marques-Silva & Inês Lynce

  3. DIEI, Universitat de Lleida, Lleida, Spain

    Josep Argelich

  4. Engineering Faculty, Portuguese Catholic University, Lisbon, Portugal

    Ana Graça

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  1. Joao Marques-Silva
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  2. Josep Argelich
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Correspondence to Inês Lynce.

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Marques-Silva, J., Argelich, J., Graça, A. et al. Boolean lexicographic optimization: algorithms & applications. Ann Math Artif Intell 62, 317–343 (2011). https://doi.org/10.1007/s10472-011-9233-2

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