Boosting branch-and-bound MaxSAT solvers with clause learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

Gaussian Elimination Meets Maximum Satisfiability

Given a set of constraints F and a weight function W over the assignments, the problem of MaxSAT is to compute a maximum weighted solution of F. MaxSAT is a fundamental problem with applications in numerous areas. The success of MaxSAT solvers has prompted researchers in AI and formal methods communities to develop algorithms that can use MaxSAT solver as oracle. One such problem that stands to benefit from advances in MaxSAT solving is discrete integration. Recently, Ermon et al. achieved a significant breakthrough by reducing the problem of integration to polynomially many queries to an optimization oracle where $F$ is conjuncted with randomly chosen XOR constraints. Unlike approximate model counting, where hashing-based approaches have been able to achieve scalability as well as rigorous formal guarantees, the practical evaluation of Ermon et al's approach, called WISH, often sacrifice theoretical guarantees, largely due to lack of existing MaxSAT solvers with native XOR support. The primary contribution of this paper is a new MaxSAT solver, GaussMaxHS, with built-in XOR support. The architecture of GaussMaxHS is inspired by CryptoMiniSAT, which has been the workhorse of hashing-based approximate model counting techniques. The resulting solver, GaussMaxHS, outperforms MaxHS over 9628 benchmarks arising from spin glass models and network reliability domains. In particular, with a timeout of 5000 seconds, MaxHS could solve only 5473 benchmarks while GaussMaxHS could solve 6120 benchmarks.

Abstract Cores in Implicit Hitting Set MaxSat Solving (Extended Abstract)

Maximum satisfiability (MaxSat) solving is an active area of research motivated by numerous successful applications to solving NP-hard combinatorial optimization problems. One of the most successful approaches for solving MaxSat instances from real world domains are the so called implicit hitting set (IHS) solvers. IHS solvers decouple MaxSat solving into separate core-extraction (i.e. reasoning) and optimization steps which are tackled by a Boolean satisfiability (SAT) and an integer linear programming (IP) solver, respectively. While the approach shows state-of-the-art performance on many industrial instances, it is known that there exists instances on which IHS solvers need to extract an exponential number of cores before terminating. Motivated by the simplest of these problematic instances, we propose abstract cores, a compact representation for a potentially exponential number of regular cores. We demonstrate how to incorporate abstract core reasoning into the IHS algorithm and report on an empirical evaluation demonstrating, that including abstract cores into a state-of-the-art IHS solver improves its performance enough to surpass the best performing solvers of the 2019 MaxSat Evaluation.

Dynamic Initial Weight Assignment for MaxSAT

The Maximum Satisfiability (Maximum Satisfiability (MaxSAT)) approach is the choice, and perhaps the only one, to deal with most real-world problems as most of them are unsatisfiable. Thus, the search for a complete and consistent solution to a real-world problem is impractical due to computational and time constraints. As a result, MaxSAT problems and solving techniques are of exceptional interest in the domain of Satisfiability (Satisfiability (SAT)). Our research experimentally investigated the performance gains of extending the most recently developed SAT dynamic Initial Weight assignment technique (InitWeight) to handle the MaxSAT problems. Specifically, we first investigated the performance gains of dynamically assigning the initial weights in the Divide and Distribute Fixed Weights solver (DDFW+Initial Weight for Maximum Satisfiability (DDFW+InitMaxSAT)) over Divide and Distribute Fixed Weights solver (DDFW) when applied to solve a wide range of well-known unweighted MaxSAT problems obtained from DIMACS. Secondly, we compared DDFW+InitMaxSAT’s performance against three known state-of-the-art SAT solving techniques: YalSAT, ProbSAT, and Sparrow. We showed that the assignment of dynamic initial weights increased the performance of DDFW+InitMaxSAT against DDFW by an order of magnitude on the majority of problems and performed similarly otherwise. Furthermore, we showed that the performance of DDFW+InitMaxSAT was superior to the other state-of-the-art algorithms. Eventually, we showed that the InitWeight technique could be extended to handling partial MaxSAT with minor modifications.

Chapter 24. Maximum Satisfiabiliy

Maximum satisfiability (MaxSAT) is an optimization version of SAT that is solved by finding an optimal truth assignment instead of just a satisfying one. In MaxSAT the objective function to be optimized is specified by a set of weighted soft clauses: the objective value of a truth assignment is the sum of the weights of the soft clauses it satisfies. In addition, the MaxSAT problem can have hard clauses that the truth assignment must satisfy. Many optimization problems can be naturally encoded into MaxSAT and this, along with significant performance improvements in MaxSAT solvers, has led to MaxSAT being used in a number of different application areas. This chapter provides a detailed overview of the approaches to MaxSAT solving that have in recent years been most successful in solving real-world optimization problems. Further recent developments in MaxSAT research are also overviewed, including encodings, applications, preprocessing, incomplete solving, algorithm portfolios, partitioning-based solving, and parallel solving.

Unsatisfiable Core Analysis and Aggregates for Optimum Stable Model Search

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and later on adapted to ASP. In this paper, we present the porting to ASP of another state-of-the-art algorithm introduced for MaxSAT, namely K, which generalizes ONE and PMRES. Moreover, we present a new algorithm called OLL-IN-ONE that compactly encodes all aggregates of OLL by taking advantage of shared aggregate sets propagators. The performance of the algorithms have been empirically compared on instances taken from the latest ASP Competition.