scholarly journals Relaxed Survey Propagation for The Weighted Maximum Satisfiability Problem

2009 ◽  
Vol 36 ◽  
pp. 229-266 ◽  
Author(s):  
H.L. Chieu ◽  
W.S. Lee
Keyword(s):  
Phase Transition ◽  
State Of The Art ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Sat Problem ◽  
Sat Solvers ◽  
Minimal Weight ◽  
Survey Propagation ◽  
Max Sat

The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y algorithm generalizes SP to work on the maximum satisfiability (Max-SAT) problem, but the cover interpretation of SP does not generalize to SP-y. In this paper, we formulate the relaxed survey propagation (RSP) algorithm, which extends the SP algorithm to apply to the weighted Max-SAT problem. We show that RSP has an interpretation of estimating marginals over covers violating a set of clauses with minimal weight. This naturally generalizes the cover interpretation of SP. Empirically, we show that RSP outperforms SP-y and other state-of-the-art Max-SAT solvers on random Max-SAT instances. RSP also outperforms state-of-the-art weighted Max-SAT solvers on random weighted Max-SAT instances.

scholarly journals Improved Exact Solver for the Weighted MAX-SAT Problem

10.29007/38lm ◽  
2018 ◽  
Author(s):  
Adrian Kuegel
Keyword(s):  
Data Structure ◽  
Lower Bound ◽  
Branch And Bound ◽  
State Of The Art ◽  
Branch And Bound Algorithm ◽  
Sat Problem ◽  
Sat Solvers ◽  
Propagation Algorithm ◽  
Max Sat ◽  
Unit Propagation

Many exact Max-SAT solvers use a branch and bound algorithm, where the lower bound is calculated with a combination of Max-SAT resolution and detection of disjoint inconsistent subformulas. We propose a propagation algorithm which improves the detection of disjoint inconsistent subformulas compared to algorithms previously used in Max-SAT solvers. We implemented this algorithm in our new solver akmaxsat and compared our solver with three solvers using unit propagation and restricted failed literal detection; these solvers are currently state-of-the-art on random Max-SAT instances. We also developed a lazy deletion data structure for our solver which speeds up lower bound calculation on instances with a high clauses-to-variables ratio. Our experiments show that our solver runs faster than the previously best solvers on randomly generated instances with a high clauses-to-variables ratio.

Unsatisfiable Core Analysis and Aggregates for Optimum Stable Model Search

2020 ◽  
Vol 176 (3-4) ◽  
pp. 271-297
Author(s):  
Mario Alviano ◽  
Carmine Dodaro
Keyword(s):  
State Of The Art ◽  
Answer Set Programming ◽  
Efficient Algorithms ◽  
Satisfiability Problem ◽  
Core Analysis ◽  
Stable Model ◽  
Maximum Satisfiability ◽  
Model Search ◽  
Unsatisfiable Core ◽  
Stable Models

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.

scholarly journals Reduced Cost Fixing for Maximum Satisfiability

2018 ◽  
Author(s):  
Fahiem Bacchus ◽  
Antti Hyttinen ◽  
Matti Järvisalo ◽  
Paul Saikko
Keyword(s):  
Integer Programming ◽  
Real World ◽  
Recent Trend ◽  
Optimization Problems ◽  
State Of The Art ◽  
Boolean Satisfiability ◽  
Maximum Satisfiability ◽  
Hitting Set ◽  
Sat Solvers ◽  
Speed Up

Maximum satisfiability (MaxSAT) offers a competitive approach to solving NP-hard real-world optimization problems. While state-of-the-art MaxSAT solvers rely heavily on Boolean satisfiability (SAT) solvers, a recent trend, brought on by MaxSAT solvers implementing the so-called implicit hitting set (IHS) approach, is to integrate techniques from the realm of integer programming (IP) into the solving process. This allows for making use of additional IP solving techniques to further speed up MaxSAT solving. In this line of work, we investigate the integration of the technique of reduced cost fixing from the IP realm into IHS solvers, and empirically show that reduced cost fixing considerable speeds up a state-of-the-art MaxSAT solver implementing the IHS approach.

scholarly journals Analysis of comparative effectiveness of state-of-the-art heuristics for CDCL SAT solvers

2021 ◽  
Author(s):  
S. Kochemazov
Keyword(s):  
Comparative Effectiveness ◽  
Major Part ◽  
State Of The Art ◽  
Learning Algorithms ◽  
Boolean Satisfiability ◽  
Satisfiability Problem ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Clause Learning ◽  
Good For

The Conflict-Driven Clause Learning algorithms for solving the Boolean satisfiability problem comprise the major part of the methods used to solve various instances of the problems that arise in industry and science. In recent years there have been proposed several major heuristics for these algorithms which are assumed to be de facto good for the solvers’ performance over diverse sets of benchmarks. The goal of this paper is to evaluate the contribution of each separate heuristic to the performance of a state-of-the-art solver, see the extent to which they are beneficial, and figure out if the heuristics have any particular features that need to be taken into account.

scholarly journals MAX-SAT Problem using Hybrid Harmony Search Algorithm

2018 ◽  
Vol 27 (4) ◽  
pp. 643-658 ◽  
Author(s):  
Iyad Abu Doush ◽  
Amal Lutfi Quran ◽  
Mohammed Azmi Al-Betar ◽  
Mohammed A. Awadallah
Keyword(s):  
Search Algorithm ◽  
Harmony Search ◽  
Harmony Search Algorithm ◽  
Satisfiability Problem ◽  
Boolean Formula ◽  
Stochastic Local Search ◽  
Boolean Variable ◽  
Sat Problem ◽  
Max Sat ◽  
The Impact

Abstract Maximum Satisfiability problem is an optimization variant of the Satisfiability problem (SAT) denoted as MAX-SAT. The aim of this problem is to find Boolean variable assignment that maximizes the number of satisfied clauses in the Boolean formula. In case the number of variables per clause is equal or greater than three, then this problem is considered NP-complete. Hence, many researchers have developed techniques to deal with MAX-SAT. In this paper, we investigate the impact of different hybrid versions of binary harmony search (HS) algorithm on solving MAX 3-SAT problem. Therefore, we propose two novel hybrid binary HS algorithms. The first hybridizes Flip heuristic with HS, and the second uses Tabu search combined with Flip heuristic. Furthermore, a distinguished feature of our proposed approaches is using an objective function that is updated dynamically based on the stepwise adaptation of weights (SAW) mechanism to evaluate the MAX-SAT solution using the proposed hybrid versions. The performance of the proposed approaches is evaluated over standard MAX-SAT benchmarks, and the results are compared with six evolutionary algorithms and three stochastic local search algorithms. The obtained results are competitive and show that the proposed novel approaches are effective.

scholarly journals CCEHC: An Efficient Local Search Algorithm for Weighted Partial Maximum Satisfiability (Extended Abstract)

2017 ◽  
Author(s):  
Chuan Luo ◽  
Shaowei Cai ◽  
Kaile Su ◽  
Wenxuan Huang
Keyword(s):  
Local Search ◽  
State Of The Art ◽  
Search Algorithm ◽  
Stochastic Local Search ◽  
Local Search Algorithm ◽  
Maximum Satisfiability ◽  
Biased Random Walk ◽  
Configuration Checking ◽  
Significant Generalization ◽  
Max Sat

Weighted partial maximum satisfiability (WPMS) is a significant generalization of maximum satisfiability (MAX-SAT), with many important applications. Recently, breakthroughs have been made on stochastic local search (SLS) for weighted MAX-SAT and (unweighted) partial MAX-SAT (PMS). However, the performance of SLS for WPMS lags far behind. In this work, we present a new SLS algorithm named CCEHC for WPMS. CCEHC is mainly based on a heuristic emphasizing hard clauses, which has three components: a variable selection mechanism focusing on configuration checking based only on hard clauses, a weighting scheme for hard clauses, and a biased random walk component. Experiments show that CCEHC significantly outperforms its state-of-the-art SLS competitors. Experiments comparing CCEHC with a state-of-the-art complete solver indicate the effectiveness of CCEHC on a number of application WPMS instances.

Algorithms for the maximum satisfiability problem

Computing ◽  
1990 ◽  
Vol 44 (4) ◽  
pp. 279-303 ◽  
Author(s):  
Pierre Hansen ◽  
Brigitte Jaumard
Keyword(s):  
Satisfiability Problem ◽  
Maximum Satisfiability

scholarly journals GASAT: A Genetic Local Search Algorithm for the Satisfiability Problem

2006 ◽  
Vol 14 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Frédéric Lardeux ◽  
Frédéric Saubion ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Local Search ◽  
Hybrid Algorithm ◽  
State Of The Art ◽  
Search Algorithm ◽  
Satisfiability Problem ◽  
Local Search Algorithm ◽  
Overall Performance ◽  
Genetic Local Search ◽  
Search Stage

This paper presents GASAT, a hybrid algorithm for the satisfiability problem (SAT). The main feature of GASAT is that it includes a recombination stage based on a specific crossover and a tabu search stage. We have conducted experiments to evaluate the different components of GASAT and to compare its overall performance with state-of-the-art SAT algorithms. These experiments show that GASAT provides very competitive results.

Boosting branch-and-bound MaxSAT solvers with clause learning

2021 ◽  
pp. 1-21
Author(s):  
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Branch And Bound ◽  
Real World ◽  
Optimization Problems ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Combinatorial Optimization Problems ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document