Journal of Automated Reasoning

, Volume 46, Issue 1, pp 81-102

First online:

A Framework for Certified Boolean Branch-and-Bound Optimization

  • Javier LarrosaAffiliated withTechnical Univ. of Catalonia Email author 
  • , Robert NieuwenhuisAffiliated withTechnical Univ. of Catalonia
  • , Albert OliverasAffiliated withTechnical Univ. of Catalonia
  • , Enric Rodríguez-CarbonellAffiliated withTechnical Univ. of Catalonia

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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.


SAT Optimization Proofs