Journal of Automated Reasoning

, Volume 46, Issue 1, pp 81–102

A Framework for Certified Boolean Branch-and-Bound Optimization

  • Javier Larrosa
  • Robert Nieuwenhuis
  • Albert Oliveras
  • Enric Rodríguez-Carbonell
Article

Abstract

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.

Keywords

SAT Optimization Proofs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Javier Larrosa
    • 1
  • Robert Nieuwenhuis
    • 1
  • Albert Oliveras
    • 1
  • Enric Rodríguez-Carbonell
    • 1
  1. 1.Technical Univ. of CataloniaBarcelonaSpain

Personalised recommendations