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The development of practical approaches to efficiently reasoning over pseudo-Boolean constraints has recently increasing attention as a natural generalization of Boolean satisfiability (SAT) solving. Analogously, solvers for pseudo-Boolean optimization draw inspiration from techniques developed for maximum satisfiability (MaxSAT) solving. Recently, the first practical solver lifting the implicit hitting set (IHS) approach - one of the most efficient approaches in modern MaxSAT solving - to the realm of PBO was developed, employing a PB solver as a core extractor together with an integer programming solver as a hitting set solver. In this work, we make practical improvements to the IHS approach to PBO. We propose the integration of solution-improving search to the PBO-IHS approach, resulting in a hybrid approach to PBO which makes use of both types of search towards an optimal solution. Furthermore, we explore the potential of different variants of core extraction within PBO-IHS - including recent advances in PB core extraction, allowing for extracting more general PB constraints compared to the at-least-one constraints typically relied on in IHS - in speeding up PBO-IHS search. We show that the empirical efficiency of PBO-IHS - recently shown to outperform other specialized PBO solvers - is further improved by the integration of these techniques., LIPIcs, Vol. 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022), pages 13:1-13:18

Boolean satisfiability (SAT) solvers allow for incremental computations, which is key to efficient employment of SAT solvers iteratively for developing complex decision and optimization procedures, including maximum satisfiability (MaxSAT) solvers. However, enabling incremental computations on the level of constraint optimization remains a noticeable challenge. While incremental computations have been identified to have great potential in speeding up MaxSAT-based approaches for solving various real-world optimization problems, enabling incremental computations in MaxSAT remains to most extent unexplored. In this work, we contribute towards making incremental MaxSAT solving a reality. Firstly, building on the IPASIR interface for incremental SAT solving, we propose the IPAMIR interface for implementing incremental MaxSAT solvers and for developing applications making use of incremental MaxSAT. Secondly, we expand our recent adaptation of the implicit hitting set based MaxHS MaxSAT solver to a fully-fledged incremental MaxSAT solver in terms of implementing the IPAMIR specification in full, and detail in particular how, in addition to weight changes, assumptions are enabled without losing incrementality. Thirdly, we provide further empirical evidence on the benefits of incremental MaxSAT solving under assumptions., LIPIcs, Vol. 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022), pages 14:1-14:19

Maximum satisfiability (MaxSAT) is a viable approach to solving NP-hard optimization problems. In the realm of core-guided MaxSAT solving - one of the most effective MaxSAT solving paradigms today - algorithmic variants employing so-called soft cardinality constraints have proven very effective. In this work, we propose to combine weight-aware core extraction (WCE) - a recently proposed approach that enables relaxing multiple cores instead of a single one during iterations of core-guided search - with a novel form of structure sharing in the cardinality-based core relaxation steps performed in core-guided MaxSAT solvers. In particular, the proposed form of structure sharing is enabled by WCE, which has so-far not been widely integrated to MaxSAT solvers, and allows for introducing fewer variables and clauses during the MaxSAT solving process. Our results show that the proposed techniques allow for avoiding potential overheads in the context of soft cardinality constraint based core-guided MaxSAT solving both in theory and in practice. In particular, the combination of WCE and structure sharing improves the runtime performance of a state-of-the-art core-guided MaxSAT solver implementing the central OLL algorithm., LIPIcs, Vol. 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021), pages 28:1-28:19

Recent developments in applying and extending Boolean satisfiability (SAT) based techniques have resulted in new types of approaches to pseudo-Boolean optimization (PBO), complementary to the more classical integer programming techniques. In this paper, we develop the first approach to pseudo-Boolean optimization based on instantiating the so-called implicit hitting set (IHS) approach, motivated by the success of IHS implementations for maximum satisfiability (MaxSAT). In particular, we harness recent advances in native reasoning techniques for pseudo-Boolean constraints, which enable efficiently identifying inconsistent assignments over subsets of objective function variables (i.e. unsatisfiable cores in the context of PBO), as a basis for developing a native IHS approach to PBO, and study the impact of various search techniques applicable in the context of IHS for PBO. Through an extensive empirical evaluation, we show that the IHS approach to PBO can outperform other currently available PBO solvers, and also provides a complementary approach to PBO when compared to classical integer programming techniques., LIPIcs, Vol. 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021), pages 51:1-51:20

Recent advances in solvers for the Boolean satisfiability (SAT) based optimization paradigm of maximum satisfiability (MaxSAT) have turned MaxSAT into a viable approach to finding provably optimal solutions for various types of hard optimization problems. In various types of real-world problem settings, a sequence of related optimization problems need to solved. This calls for studying ways of enabling incremental computations in MaxSAT, with the hope of speeding up the overall computation times. However, current state-of-the-art MaxSAT solvers offer no or limited forms of incrementality. In this work, we study ways of enabling incremental computations in the context of the implicit hitting set (IHS) approach to MaxSAT solving, as both one of the key MaxSAT solving approaches today and a relatively well-suited candidate for extending to incremental computations. In particular, motivated by several recent applications of MaxSAT in the context of interpretability in machine learning calling for this type of incrementality, we focus on enabling incrementality in IHS under changes to the objective function coefficients (i.e., to the weights of soft clauses). To this end, we explain to what extent different search techniques applied in IHS-based MaxSAT solving can and cannot be adapted to this incremental setting. As practical result, we develop an incremental version of an IHS MaxSAT solver, and show it provides significant runtime improvements in recent application settings which can benefit from incrementality but in which MaxSAT solvers have so-far been applied only non-incrementally, i.e., by calling a MaxSAT solver from scratch after each change to the problem instance at hand., LIPIcs, Vol. 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021), pages 44:1-44:19