Iterative and core-guided MaxSAT solving: A survey and assessment

Morgado, António; Heras, Federico; Liffiton, Mark H.; Planes, Jordi; Marques-Silva, João

doi:10.1007/s10601-013-9146-2

Cited by 126 publications

(101 citation statements)

References 87 publications

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“…In fact, ME-ASP, WASP+DLV, and WASP completed more runs on Optimization problems than LP2NORMAL+CLASP, which still achieved the highest scores, as given in Figure 3(a). This divergence is due to the use of different optimization strategies, namely model-versus core-guided approaches (Morgado, Heras, Liffiton, Planes, & Marques-Silva, 2013;Alviano et al, 2015a;Alviano, Dodaro, Marques-Silva, & Ricca, 2015b;, where the former are geared for producing good-quality solutions and the latter for confirming optimum solutions. 3 As ME-ASP, WASP+DLV, and WASP utilize core-guided optimization, they are able to complete more runs than LP2NORMAL+CLASP, whose model-guided approach yields better solutions in case of timeouts.…”

Section: Results In the Sp Categorymentioning

confidence: 99%

The Sixth Answer Set Programming Competition

Gebser¹,

Maratea²,

Ricca³

2017

jair

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Answer Set Programming (ASP) is a well-known paradigm of declarative programming with roots in logic programming and non-monotonic reasoning. Similar to other closely related problemsolving technologies, such as SAT/SMT, QBF, Planning and Scheduling, advancements in ASP solving are assessed in competition events. In this paper, we report about the design and results of the Sixth ASP Competition, which was jointly organized by the University of Calabria (Italy), Aalto University (Finland), and the University of Genoa (Italy), in affiliation with the 13th International Conference on Logic Programming and Non-Monotonic Reasoning. This edition maintained some of the design decisions introduced in 2014, e.g., the conception of sub-tracks, the scoring scheme, and the adherence to a fixed modeling language in order to push the adoption of the ASP-Core-2 standard. On the other hand, it featured also some novelties, like a benchmark selection stage classifying instances according to their empirical hardness, and a "Marathon" track where the topperforming systems are given more time for solving hard benchmarks.

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Section: Results In the Sp Categorymentioning

confidence: 99%

The Sixth Answer Set Programming Competition

Gebser¹,

Maratea²,

Ricca³

2017

jair

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“…Two main types of exact algorithms are developed for MaxSAT: SAT-based MaxSAT solvers (e.g., Morgado, Heras, Liffiton, Planes, & Marques-Silva, 2013;Ansótegui, Bonet, & Levy, 2013;Davies & Bacchus, 2013a;Ansótegui & Gabas, 2013;Morgado, Dodaro, & Marques-Silva, 2014;Martins, Joshi, Manquinho, & Lynce, 2014) that solve a MaxSAT instance by repeatedly calling a CDCL (Conflict-Driven Clause Learning) based SAT solver to solve a sequence of SAT problems, and the BnB MaxSAT solvers (e.g., Li, Manyà, & Planes, 2007;Kügel, 2010). The SAT-based MaxSAT solvers are particularly efficient to solve industrial MaxSAT problems, while the BnB MaxSAT solvers are particular efficient to solve the random MaxSAT problems.…”

Section: Preliminariesmentioning

confidence: 99%

An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Fang¹,

Li²,

Xu³

2016

jair

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Recently, MaxSAT reasoning is shown very effective in computing a tight upper bound for a Maximum Clique (MC) of a (unweighted) graph. In this paper, we apply MaxSAT reasoning to compute a tight upper bound for a Maximum Weight Clique (MWC) of a wighted graph. We first study three usual encodings of MWC into weighted partial MaxSAT dealing with hard clauses, which must be satisfied in all solutions, and soft clauses, which are weighted and can be falsified. The drawbacks of these encodings motivate us to propose an encoding of MWC into a special weighted partial MaxSAT formalism, called LW (Literal-Weighted) encoding and dedicated for upper bounding an MWC, in which both soft clauses and literals in soft clauses are weighted. An optimal solution of the LW MaxSAT instance gives an upper bound for an MWC, instead of an optimal solution for MWC. We then introduce two notions called the Top-k literal failed clause and the Top-k empty clause to extend classical MaxSAT reasoning techniques, as well as two sound transformation rules to transform an LW MaxSAT instance. Successive transformations of an LW MaxSAT instance driven by MaxSAT reasoning give a tight upper bound for the encoded MWC. The approach is implemented in a branch-and-bound algorithm called MWCLQ. Experimental evaluations on the broadly used DIMACS benchmark, BHOSLIB benchmark, random graphs and the benchmark from the winner determination problem show that our approach allows MWCLQ to reduce the search space significantly and to solve MWC instances effectively. Consequently, MWCLQ outperforms state-of-the-art exact algorithms on the vast majority of instances. Moreover, it is surprisingly effective in solving hard and dense instances.

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“…The cost function will be represented as a set of soft clauses, and so this problem is referred to as Quantified MaxSAT (QMaxSAT). Inspired by algorithms for the non-quantified MaxSAT problem [4,5,16,24,31,55], this paper develops two novel approaches for QMaxSAT. The first one consists of relaxing all clauses and performing a linear (or binary) search over the values of the cost function.…”

Section: Introductionmentioning

confidence: 99%

Quantified maximum satisfiability

2015

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In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies an optimization extension of QBF and considers the problem in a quantified MaxSAT setting. More precisely, the general QMaxSAT problem is defined for QBFs with a set of soft clausal constraints and consists in finding the largest subset of the soft constraints such that the remaining QBF is true. Two approaches are investigated. One is based on relaxing the soft clauses and performing an iterative search on the cost function. The other approach, which is the main contribution of the paper, is inspired by recent work on MaxSAT, and exploits the iterative identification of unsatisfiable cores. The paper investigates the application of these approaches to the two concrete problems of computing smallest minimal unsatisfiable subformulas (SMUS) and smallest minimal equivalent subformulas (SMES), decision versions of which are well-known problems in the second level of the polynomial hierarchy. Experimental results, obtained on representative problem instances, indicate that the core-guided approach for the SMUS and SMES problems outperforms the use of iterative search over the values of the cost function. More significantly, Alexey Ignatiev Constraints the core-guided approach to SMUS also outperforms the state-of-the-art SMUS extractor Digger.

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Iterative and core-guided MaxSAT solving: A survey and assessment

Cited by 126 publications

References 87 publications

The Sixth Answer Set Programming Competition

The Sixth Answer Set Programming Competition

An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Quantified maximum satisfiability

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