Journal of Automated Reasoning

, Volume 46, Issue 1, pp 81–102

A Framework for Certified Boolean Branch-and-Bound Optimization


    • Technical Univ. of Catalonia
  • Robert Nieuwenhuis
    • Technical Univ. of Catalonia
  • Albert Oliveras
    • Technical Univ. of Catalonia
  • Enric Rodríguez-Carbonell
    • Technical Univ. of Catalonia

DOI: 10.1007/s10817-010-9176-z

Cite this article as:
Larrosa, J., Nieuwenhuis, R., Oliveras, A. et al. J Autom Reasoning (2011) 46: 81. doi:10.1007/s10817-010-9176-z


We consider optimization problems of the form (S, cost), where S is a clause set over Boolean variables x1 ... xn, 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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© Springer Science+Business Media B.V. 2010