Algorithms for Weighted Boolean Optimization

Manquinho, Vasco; Marques-Silva, João; Planes, Jordi

doi:10.1007/978-3-642-02777-2_45

Cited by 105 publications

(100 citation statements)

References 34 publications

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“…We ran experiments with all available Maxsat solvers that use a sequence of SAT problem approach: Msuncore, WBO [12], PM2, WPM1, WPM2 [1,2], SAT4J [4], and Qmaxsat [10].…”

Section: Resultsmentioning

confidence: 99%

“…The main prior works utilizing a sequence of SAT tests to solve Maxsat began with the work of Fu and Malik [6], and include SAT4J [4], WPM1, PM2, and WPM2 [1,2], and Msuncore [12]. As mentioned above there has also been work on branch and bound based solvers but such solvers are not directly comparable with the sequence of SAT solvers: each type of solver is best suited for different types of problems.…”

Section: Related Workmentioning

confidence: 99%

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Solving MAXSAT by Solving a Sequence of Simpler SAT Instances

Davies

Bacchus

2011

Lecture Notes in Computer Science

101

103

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Abstract.Maxsat is an optimization version of Satisfiability aimed at finding a truth assignment that maximizes the satisfaction of the theory. The technique of solving a sequence of SAT decision problems has been quite successful for solving larger, more industrially focused Maxsat instances, particularly when only a small number of clauses need to be falsified. The SAT decision problems, however, become more and more complicated as the minimal number of clauses that must be falsified increases. This can significantly degrade the performance of the approach. 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. In this paper we introduce a new Maxsat algorithm that avoids these problems. Our algorithm also solves a sequence of SAT instances. However, these SAT instances are always simplifications of the initial Maxsat formula, and thus are relatively easy for modern SAT solvers. This is accomplished by moving all of the arithmetic reasoning into a separate hitting set problem which can then be solved with techniques better suited to numeric reasoning, e.g., techniques from mathematical programming. As a result the performance of our algorithm is unaffected by the addition of clause weights. Our algorithm can, however, require solving more SAT instances than previous approaches. Nevertheless, the approach is simpler than previous methods and displays superior performance on some benchmarks.

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“…We ran experiments with all available Maxsat solvers that use a sequence of SAT problem approach: Msuncore, WBO [12], PM2, WPM1, WPM2 [1,2], SAT4J [4], and Qmaxsat [10].…”

Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Solving MAXSAT by Solving a Sequence of Simpler SAT Instances

Davies

Bacchus

2011

Lecture Notes in Computer Science

101

103

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show abstract

“…We performed an empirical study of nine existing maxsat solvers: cplex (version 12.2), wpm1 (with the latest 2012 improvements [1]), wpm2 (version 2 [2]), bincd [10], wbo [15], minimaxsat [9], sat4j [4], akmaxsat [13], and maxhsOrig [7]. All of these solvers are able to solve maxsat in its most general form, i.e., weighted partial maxsat, and thus have the widest range of applicability.…”

Section: Empirical Evaluation Of Current Maxsat Solversmentioning

confidence: 99%

Exploiting the Power of mip Solvers in maxsat

Davies

Bacchus

2013

Theory and Applications of Satisfiability Testing – SAT 2013

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Abstract. maxsat is an optimization version of satisfiability. Since many practical problems involve optimization, there are a wide range of potential applications for effective maxsat solvers. In this paper we present an extensive empirical evaluation of a number of maxsat solvers. 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 solving optimization problems and are also theoretically more powerful than sat solvers. In fact, we show that cplex is quite effective on a range of maxsat instances. Based on these observations we extend a previously developed hybrid approach for solving maxsat, that utilizes both a sat solver and a mip solver. Our extensions aim to take better advantage of the power of the mip solver. The resulting improved hybrid solver is shown to be quite effective.

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“…In particular, we have implemented the WPM1 algorithm from [4,24], which is based on the detection of unsatisfiable cores. These are satisfiability test based algorithms, where the parameter k ranges from 0 to k opt .…”

Section: Wsmt Solving (S1)mentioning

confidence: 99%

“…This algorithm is the weighted version of the FuMalik algorithm [4,24] for partial MaxSAT. In those works, the underlying solver was a SAT solver.…”

Section: Wsmt Solving (S1)mentioning

confidence: 99%

Solving weighted CSPs with meta-constraints by reformulation into satisfiability modulo theories

et al. 2012

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We introduce WSimply, a new framework for modelling and solving Weighted Constraint Satisfaction Problems (WCSP) using Satisfiability Modulo Theories (SMT) technology. In contrast to other well-known approaches designed for extensional representation of goods or no-goods, and with few declarative facilities, our approach aims to follow an intensional and declarative syntax style. In addition, our language has built-in support for some meta-constraints, such as priority and homogeneity, which allows the user to easily specify rich requirements on the desired solutions, such as preferences and fairness.We propose two alternative strategies for solving these WCSP instances using SMT. The first is the reformulation into Weighted SMT (WSMT) and the application of satisfiability test based algorithms from recent contributions in the Weighted Maximum Satisfiability field. The second one is the reformulation into an operation research-like style which involves an optimisation variable or objective function and the application of optimisation SMT solvers.We present experimental results of two well-known problems: the Nurse Rostering Problem (NRP) and a variant of the Balanced Academic Curriculum Problem (BACP), and provide some insights into the impact of the addition of metaconstraints on the quality of the solutions and the solving time.

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Algorithms for Weighted Boolean Optimization

Cited by 105 publications

References 34 publications

Solving MAXSAT by Solving a Sequence of Simpler SAT Instances

Solving MAXSAT by Solving a Sequence of Simpler SAT Instances

Exploiting the Power of mip Solvers in maxsat

Solving weighted CSPs with meta-constraints by reformulation into satisfiability modulo theories

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