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WPM3: An (in)complete algorithm for weighted partial MaxSAT

Carlos Ansótegui, Joel Gabàs
2017 Artificial Intelligence  
We present and implement a Weighted Partial MaxSAT solver based on successive calls to a SAT solver.  ...  We prove the correctness of our algorithm and compare our solver with other Weighted Partial MaxSAT solvers.  ...  The Partial MaxSAT problem is the Weighted Partial MaxSAT problem when the weights of the soft clauses are equal to one.  ... 
doi:10.1016/j.artint.2017.05.003 fatcat:afzeke5nuncovdbvp6nsxdnnrm

Improving SAT-Based Weighted MaxSAT Solvers [chapter]

Carlos Ansótegui, Maria Luisa Bonet, Joel Gabàs, Jordi Levy
2012 Lecture Notes in Computer Science  
In the last few years, there has been a significant effort in designing and developing efficient Weighted MaxSAT solvers.  ...  The Weighted Partial MaxSAT problem for a weighted partial MaxSAT formula ϕ is the problem of finding an optimal assignment.  ...  We also checked the effectiveness of breaking symmetries for Unweighted Partial MaxSAT instances. For industrial instances we improve from 181 to 262 solved instances, and for crafted from 55 to 115.  ... 
doi:10.1007/978-3-642-33558-7_9 fatcat:uc6ctcx5m5btzpgo6rog2jmoyq

Exploiting subproblem optimization in SAT-based MaxSAT algorithms

Carlos Ansótegui, Joel Gabàs, Jordi Levy
2015 Journal of Heuristics  
Among exact MaxSAT algorithms, SAT-based MaxSAT algorithms are the best performing approaches for real-world problems. We have extended the WPM2 algorithm by adding several improvements.  ...  This led WPM2 to achieve the best overall results at the international MaxSAT Evaluation 2013 (MSE13) on industrial instances.  ...  This solver behaves exactly as wpm2 shuc for (Partial) MaxSAT instances, and includes some efficiencies for Weighted (Partial) MaxSAT instances.  ... 
doi:10.1007/s10732-015-9300-7 fatcat:plb3nu6flbcy3em7fyzxt4v47q

SAT-based MaxSAT algorithms

Carlos Ansótegui, Maria Luisa Bonet, Jordi Levy
2013 Artificial Intelligence  
In particular, our solvers won the 2009 partial MaxSAT and the 2011 weighted partial MaxSAT industrial categories of the MaxSAT evaluation. We prove the correctness of all our algorithms.  ...  Many industrial optimization problems can be translated to MaxSAT. Although the general problem is NP hard, like SAT, many practical problems may be solved using modern MaxSAT solvers.  ...  The Weighted Partial MaxSAT problem for a weighted partial MaxSAT formula ϕ is the problem of finding an optimal assignment.  ... 
doi:10.1016/j.artint.2013.01.002 fatcat:qexoazzicfadlkeyimlub3lnpq

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

Antonio Morgado, Federico Heras, Mark Liffiton, Jordi Planes, Joao Marques-Silva
2013 Constraints  
Whereas the mentioned SLS algorithms were initially developed for the SAT problem, they can be directly applied to approximate (unweighted) MaxSAT and for the most general Weighted Partial MaxSAT [28]  ...  Finally, when some soft clauses have a weight greater than 1 and there is a set of hard clauses, it is referred to as weighted partial MaxSAT.  ...  This work is partially supported by SFI grant BEACON (09/PI/I2618).  ... 
doi:10.1007/s10601-013-9146-2 fatcat:6hwa2oxk35exnn7lbdwcmux27a

Solving MAXSAT by Solving a Sequence of Simpler SAT Instances [chapter]

Jessica Davies, Fahiem Bacchus
2011 Lecture Notes in Computer Science  
This technique also has more difficulty with the important generalization where each clause is given a weight: the weights generate SAT decision problems that are harder for SAT solvers to solve.  ...  However, these SAT instances are always simplifications of the initial Maxsat formula, and thus are relatively easy for modern SAT solvers.  ...  WMS) and weighted partial (WPMS) Maxsat.  ... 
doi:10.1007/978-3-642-23786-7_19 fatcat:om2j3jfayfc2nprazkc3dmfabq

Incremental Cardinality Constraints for MaxSAT [chapter]

Ruben Martins, Saurabh Joshi, Vasco Manquinho, Inês Lynce
2014 Lecture Notes in Computer Science  
We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algo- rithms as compared to their non-incremental counterparts.  ...  These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.  ...  From now on, it is assumed that MaxSAT is defined as a minimization problem. MaxSAT has several variants such as partial MaxSAT, weighted MaxSAT and weighted partial MaxSAT [33] .  ... 
doi:10.1007/978-3-319-10428-7_39 fatcat:cjn55eryfvhtpj4dh7sxk66zle

Maximum Satisfiability Using Core-Guided MaxSAT Resolution

Nina Narodytska, Fahiem Bacchus
However, these formulas are constructed using MAXSAT resolution, a sound rule of inference for MAXSAT.  ...  These approaches solve a MAXSAT formula by building a sequence of SAT formulas, where in each formula a greater weight of soft clauses can be relaxed.  ...  First, we proposed a novel algorithm for solving weighted partial MAXSAT problems based on the MAXRES rule.  ... 
doi:10.1609/aaai.v28i1.9124 fatcat:k7p4wmg3kzhqddf5of4i2geh24

Improvements to Core-Guided Binary Search for MaxSAT [chapter]

Antonio Morgado, Federico Heras, Joao Marques-Silva
2012 Lecture Notes in Computer Science  
Maximum Satisfiability (MaxSAT) and its weighted variants are wellknown optimization formulations of Boolean Satisfiability (SAT).  ...  Motivated by practical applications, recent years have seen the development of core-guided algorithms for MaxSAT.  ...  Introduction Maximum Satisfiability (MaxSAT) and its variants, namely (Weighted) (Partial) MaxSAT, find a growing number of practical applications.  ... 
doi:10.1007/978-3-642-31612-8_22 fatcat:wdw33xz4lfab7dgusiguy4hnwq

Relaxation Search: A Simple Way of Managing Optional Clauses

Fahiem Bacchus, Jessica Davies, Maria Tsimpoukelli, George Katsirelos
For example, the soft clauses in a MAXSAT formula are optional—they can be falsified for a cost.  ...  We demonstrate how relaxation search can be used to solve MAXSAT and to compute Minimum Correction Sets.  ...  For the comparison, we experimented with the set of 1343 instances used in (Marques-Silva et al. 2013 ), which consists of a mix of (Weighted Partial) MAXSAT and SAT instances.  ... 
doi:10.1609/aaai.v28i1.8849 fatcat:w5ofpqiwvnhvje64zudeesm75a

Boolean lexicographic optimization: algorithms & applications

Joao Marques-Silva, Josep Argelich, Ana Graça, Inês Lynce
2011 Annals of Mathematics and Artificial Intelligence  
The proposed algorithms build on existing algorithms for either Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO), or Integer Linear Programming (ILP).  ...  This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic.  ...  Well-known variants of the MaxSAT problem include weighted MaxSAT, partial MaxSAT and weighted partial MaxSAT [36] .  ... 
doi:10.1007/s10472-011-9233-2 fatcat:2mhgwr4skbestjaktr7rwxve4y

Exploiting the Power of mip Solvers in maxsat [chapter]

Jessica Davies, Fahiem Bacchus
2013 Lecture Notes in Computer Science  
The resulting improved hybrid solver is shown to be quite effective.  ...  In addition to traditional maxsat solvers, we also evaluate the use of a state-of-the-art Mixed Integer Program (mip) solver, cplex, for solving maxsat. mip solvers are the most popular technology for  ...  We conclude the paper with some ideas for further work. Background In this paper we address weighted partial maxsat problems (WPMS).  ... 
doi:10.1007/978-3-642-39071-5_13 fatcat:r7bme7kvzfg3philjudjei57oe

Postponing Optimization to Speed Up MAXSAT Solving [chapter]

Jessica Davies, Fahiem Bacchus
2013 Lecture Notes in Computer Science  
A recent approach for solving maxsat is to exploit both a sat solver and a Mixed Integer Programming (mip) solver in a hybrid approach.  ...  maxsat is an optimization version of sat that can represent a wide variety of important optimization problems.  ...  This most general version of maxsat is often called weighted partial maxsat (WPMS) and is what we address in this paper.  ... 
doi:10.1007/978-3-642-40627-0_21 fatcat:sqmhw5g7ifguheslfkbznmlppu

On Validating Boolean Optimizers [article]

Antonio Morgado, Joao Marques-Silva
2011 arXiv   pre-print
For example, the issue of confidence is paramount in safety critical settings.  ...  This entails implementing solutions for validating both satisfiable and unsatisfiable answers from the NP oracle.  ...  can be considered, namely partial MaxSAT, weighted MaxSAT and weighted partial MaxSAT.  ... 
arXiv:1109.2752v1 fatcat:yzjboh7g45attpigydap3h3wvi

Solving MaxSAT by Successive Calls to a SAT Solver [chapter]

Mohamed El Halaby
2017 Lecture Notes in Networks and Systems  
Many exact solvers for MaxSAT have been developed during recent years, and many of them were presented in the well-known SAT conference.  ...  Algorithms for MaxSAT generally fall into two categories: (1) branch and bound algorithms and (2) algorithms that use successive calls to a SAT solver (SAT- based), which this paper in on.  ...  Carlos Ansótegui (University of Lleida, Spain) for his advice to include a section on translating pseudo Boolean constraints and his encouraging review of this work.  ... 
doi:10.1007/978-3-319-56994-9_31 fatcat:n3dzcn4skbdgjhxes7szk6fciy
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