Reformulation based MaxSAT robustness

Abstract

The presence of uncertainty in the real world makes robustness a desirable property of solutions to constraint satisfaction problems (CSP). A solution is said to be robust if it can be easily repaired when unexpected events happen. This issue has already been addressed in the frameworks of Boolean satisfiability (SAT) and Constraint Programming (CP). Most existing works on robustness implement search algorithms to look for robust solutions instead of taking the declarative approach of reformulation, since reformulation tends to generate prohibitively large formulas, especially in the CP setting. In this paper we consider the unaddressed problem of robustness in weighted MaxSAT, by showing how robust solutions to weighted MaxSAT instances can be effectively obtained via reformulation into pseudo-Boolean formulae. Our encoding provides a reasonable balance between increase in size and performance, as shown by our experiments in the robust resource allocation framework. We also address the problem of flexible robustness, where some of the breakages may be left unrepaired if a totally robust solution does not exist. In a sense, since the use of SAT and MaxSAT encodings for solving CSP has been gaining wide acceptance in recent years, we provide an easy-to-implement new method for achieving robustness in combinatorial optimization problems.