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A Framework for Certified Boolean Branch-and-Bound Optimization

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Abstract

We consider optimization problems of the form (S, cost), where S is a clause set over Boolean variables x 1 ... x n , with an arbitrary cost function \(\mathit{cost}\colon \mathbb{B}^n \rightarrow \mathbb{R}\), and the aim is to find a model A of S such that cost(A) is minimized. Here we study the generation of proofs of optimality in the context of branch-and-bound procedures for such problems. For this purpose we introduce \(\mathtt{DPLL_{BB}}\), an abstract DPLL-based branch-and-bound algorithm that can model optimization concepts such as cost-based propagation and cost-based backjumping. Most, if not all, SAT-related optimization problems are in the scope of \(\mathtt{DPLL_{BB}}\). Since many of the existing approaches for solving these problems can be seen as instances, \(\mathtt{DPLL_{BB}}\) allows one to formally reason about them in a simple way and exploit the enhancements of \(\mathtt{DPLL_{BB}}\) given here, in particular its uniform method for generating independently verifiable optimality proofs.

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Authors and Affiliations

  1. Technical Univ. of Catalonia, Barcelona, Spain

    Javier Larrosa, Robert Nieuwenhuis, Albert Oliveras & Enric Rodríguez-Carbonell

Authors
  1. Javier Larrosa
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  2. Robert Nieuwenhuis
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  3. Albert Oliveras
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  4. Enric Rodríguez-Carbonell
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Corresponding author

Correspondence to Javier Larrosa.

Additional information

Partially supported by Spanish Min. of Science and Innovation through the projects TIN2009-13591-C02-01 and TIN2007-68093-C02-01 (LogicTools-2).

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Larrosa, J., Nieuwenhuis, R., Oliveras, A. et al. A Framework for Certified Boolean Branch-and-Bound Optimization. J Autom Reasoning 46, 81–102 (2011). https://doi.org/10.1007/s10817-010-9176-z

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