Advances in Maximum Satisfiability

Abstract

Many important AI problems involve an optimization component. Maximum satisfiability (MaxSAT) is an optimization version of Boolean satisfiability (SAT) that can be applied to a variety of computationally hard optimization problems that arise in AI. Constituting a declarative approach to optimization, modern state-of-the-art MaxSAT solvers allow for efficiently tackling NP-hard optimization problems arising from different applications via simple propositional encodings. This can be much less time-consuming than building a customized algorithmic solution specific to a particular optimization problem. Indeed, a well-engineered, generic MaxSAT solver can often be more efficient than a custom solution. Furthermore, MaxSAT offers an alternative to the more classical declarative optimization paradigm of integer programming (IP), especially in the many AI applications where the underlying problems are naturally represented with logical constraints. In this tutorial, we will introduce MaxSAT, give an overview of the different techniques that have been developed for solving MaxSAT, focusing on recent advances and covering both complete and incomplete MaxSAT solving, and explain via case studies how MaxSAT has been used to solve problems from different areas of AI. We will also outline major current research directions in MaxSAT. After this tutorial, you should be better equipped to apply modern MaxSAT technology in real-world settings.