SAT4JPseudo: replacing resolution by cutting planes

SAT4J [1] is an open-source library of conflict-driven clause learning SAT solvers in the spirit of GRASP, zChaff and MiniSAT in Java. Its extension to pseudoboolean optimization is done by replacing the resolution performed between clauses by cutting planes, in the spirit of PBChaff [5] or Galena [4]. Compared to the version submitted to the PB05 evaluation, the solver is representing each kind of constraints specifically, instead of translating everything into pseudo boolean constraints. Thus, cutting planes can be performed on any combination of them. Furthermore, some simplifications inherited from PBChaff have been added to reduce the cost of applying cutting planes for conflict analysis. Each kind of constraints is represented specifically: clauses and cardinality constraints using watched literals, pseudo boolean constraints using counters. Finally, one version of the solver uses the objective function to guide the heuristics in optimization problems. From clauses to constraints The main issue when dealing with Pseudo Boolean constraints and cutting planes in a conflict driven solver such as GRASP or Chaff is the conflict analysis and learning scheme. Indeed, those solvers need to learn a new constraint each time a conflict is met. Furthermore, the new constraint must propagate some variable truth values. While those solvers are certainly the best framework for solving pure SAT problems, it is not clear that a similar approach is really appropriate for other kind of constraints. After the first pseudo boolean evaluation, it was not clear if extending conflict driven clause learning solvers for pseudo boolean constraint was a good approach. The aim of submitting the SAT4JPseudo solver in the second pseudo boolean evaluation is to provide a reasonably efficient and tuned full-cutting-planebased solver extending existing CDCL solvers. Unlike solvers such as PBS [2] and Pueblo [6], also based on a CDCL framework, the idea is to keep the full power of cutting planes, without any tradeoff for efficiency (clause or hybrid learning, fixed-size integer arithmetic). There might be smarter ways to implement such approach, so poor performances of SAT4JPseudo should not mean that CDCL extended with cutting plane are not good for PBO. Basically, the algorithm implemented in SAT4JPseudo to ensure to obtain conflictual constraint after cutting plane, as well as the algorithm to detect assertive constraints are the ones described in the article by D. Chai and A. Kuehlmann [4]. The only difference is that SAT4JPseudo uses the following property presented by H. Dixon [5] : Let c1 and c2 be two pseudo-boolean constraints such that c1 propagates the literal y and c2 propates ¬y, and the coefficient of y is 1. Then the result of applying a cutting plane between c1 and c2 is a falsified constraint. This property avoids some computations, especially when clauses or cardinalities are involved in cutting planes. Dealing with specificities Clauses and cardinality constraints can be seen as a special case of linear pseudo boolean constraints. Pseudo-boolean constraint l1 + l2 + . . . + ln ≥ 1 translates to the clause l1 ∨ l2 ∨ . . . ln; l1 + l2 + . . . + ln ≥ k translates to the cardinality constraint atleast(k, {l1, l2, . . . , ln}). Pseudo-boolean constraints offer more expressivity than boolean constraints, and cutting plane inference is stronger than