Boolean lexicographic optimization: algorithms & applications

  • Joao Marques-Silva
  • Josep Argelich
  • Ana Graça
  • Inês Lynce
Article

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.

Keywords

Boolean optimization Lexicographic optimization Maximum satisfiability Pseudo-Boolean optimization Haplotyping with pedigrees Software package dependencies 

Mathematics Subject Classifications (2010)

90C27 90C29 68T20 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Joao Marques-Silva
    • 1
    • 2
  • Josep Argelich
    • 3
  • Ana Graça
    • 4
  • Inês Lynce
    • 2
  1. 1.CSI/CASLUniversity College DublinDublinIreland
  2. 2.INESC-ID/ISTTechnical University of LisbonLisbonPortugal
  3. 3.DIEIUniversitat de LleidaLleidaSpain
  4. 4.Engineering FacultyPortuguese Catholic UniversityLisbonPortugal

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