On Applying Cutting Planes in DLL-Based Algorithms for Pseudo-Boolean Optimization

Abstract

AbstractThe utilization of cutting planes is a key technique in Integer Linear Programming (ILP). However, cutting planes have seldom been applied in Pseudo-Boolean Optimization (PBO) algorithms derived from the Davis-Logemann-Loveland (DLL) procedure for Propositional Satisfiability (SAT). This paper proposes the utilization of cutting planes in a DLL-style PBO algorithm, which incorporates the most effective techniques for PBO. We propose the utilization of cutting planes both during preprocessing and during the search process. Moreover, we also establish conditions that enable clause learning and non-chronological backtracking in the presence of conflicts involving constraints generated by cutting plane techniques. The experimental results, obtained on a large number of classes of instances, indicate that the integration of cutting planes with backtrack search is an extremely effective technique for PBO.KeywordsInteger Linear ProgramCutting PlaneLinear Programming RelaxationSimplex TableauBacktrack SearchThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.