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On the performance of MaxSAT and MinSAT solvers on 2SAT-MaxOnes

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Abstract

We analyze and compare two solvers for Boolean optimization problems: WMaxSatz, a solver for Partial MaxSAT, and MinSatz, a solver for Partial MinSAT. Both MaxSAT and MinSAT are similar, but previous results indicate that when solving optimization problems using both solvers, the performance is quite different on some cases. For getting insights about the differences in the performance of the two solvers, we analyze their behaviour when solving 2SAT-MaxOnes problem instances, given that 2SAT-MaxOnes is probably the most simple, but NP-hard, optimization problem we can solve with them. The analysis is based first on the study of the bounds computed by both algorithms on some particular 2SAT-MaxOnes instances, characterized by the presence of certain particular structures. We find that the fraction of positive literals in the clauses is an important factor regarding the quality of the bounds computed by the algorithms. Then, we also study the importance of this factor on the typical case complexity of Random-p 2SAT-MaxOnes, a variant of the problem where instances are randomly generated with a probability p of having positive literals in the clauses. For the case p=0, the performance results indicate a clear advantage of MinSatz with respect to WMaxSatz, but as we consider positive values of p WMaxSatz starts to show a better performance, although at the same time the typical complexity of Random-p 2SAT-MaxOnes decreases as p increases. We also study the typical value of the bound computed by the two algorithms on these sets of instances, showing that the behaviour is consistent with our analysis of the bounds computed on the particular instances we studied first.

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Authors and Affiliations

  1. Department of Computer Science, Universitat de Lleida, Jaume II, 69, Lleida, Spain

    Josep Argelich, Ramón Béjar, Cèsar Fernández, Carles Mateu & Jordi Planes

Authors
  1. Josep Argelich
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  2. Ramón Béjar
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  3. Cèsar Fernández
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  4. Carles Mateu
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  5. Jordi Planes
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Corresponding author

Correspondence to Jordi Planes.

Additional information

The research was partially supported by the Spanish MICINN Project TASSAT2 (TIN2013-48031-C4-4-P) and MINECO Project TIN2014-53234-C2-2-R.

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Argelich, J., Béjar, R., Fernández, C. et al. On the performance of MaxSAT and MinSAT solvers on 2SAT-MaxOnes. Ann Math Artif Intell 77, 43–66 (2016). https://doi.org/10.1007/s10472-016-9502-1

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  • DOI: https://doi.org/10.1007/s10472-016-9502-1

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Mathematics Subject Classfication (2010)

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