Exploiting Cycle Structures in Max-SAT

Li, Chu Min; Manyà, Felip; Mohamedou, Nouredine Ould; Planes, Jordi

doi:10.1007/978-3-642-02777-2_43

Cited by 47 publications

(35 citation statements)

References 9 publications

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“…Note that Pwbo2.0 is a parallel solver incorporating a satisfiability-based search into an unsatisfiability-based approach. Akmaxsat1.1 [31] and WmaxSatz [32] are branch and bound solvers. The evaluation results of these MaxSAT solvers are shown in Table 1.…”

Section: Discussionmentioning

confidence: 99%

Extending MaxSAT to Solve the Coalition Structure Generation Problem with Externalities Based on Agent Relations

Liao

Koshimura

Fujita

et al. 2014

IEICE Trans. Inf. & Syst.

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SUMMARYCoalition Structure Generation (CSG) means partitioning agents into exhaustive and disjoint coalitions so that the sum of values of all the coalitions is maximized. Solving this problem could be facilitated by employing some compact representation schemes, such as marginal contribution network (MC-net). In MC-net, the CSG problem is represented by a set of rules where each rule is associated with a real-valued weights, and the goal is to maximize the sum of weights of rules under some constraints. This naturally leads to a combinatorial optimization problem that could be solved with weighted partial MaxSAT (WPM). In general, WPM deals with only positive weights while the weights involved in a CSG problem could be either positive or negative. With this in mind, in this paper, we propose an extension of WPM to handle negative weights and take advantage of the extended WPM to solve the MC-net-based CSG problem. Specifically, we encode the relations between each pair of agents and reform the MC-net as a set of Boolean formulas. Thus, the CSG problem is encoded as an optimization problem for WPM solvers. Furthermore, we apply this agent relation-based WPM with minor revision to solve the extended CSG problem where the value of a coalition is affected by the formation of other coalitions, a coalition known as externality. Experiments demonstrate that, compared to the previous encoding, our proposed method speeds up the process of solving the CSG problem significantly, as it generates fewer number of Boolean variables and clauses that need to be examined by WPM solver.

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Section: Discussionmentioning

confidence: 99%

Extending MaxSAT to Solve the Coalition Structure Generation Problem with Externalities Based on Agent Relations

Liao

Koshimura

Fujita

et al. 2014

IEICE Trans. Inf. & Syst.

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“…It proposes a new unsatisfiability-based algorithm which can be orders of magnitude more efficient that existing algorithms. Besides WBO, there are some other efficient Max-SAT solvers, such as SAT4J [SAT4J 2004], MaxSolver [Xing and Zhang 2005], IncWMaxSatz [Darras et al 2007], W-MaxSatz [Li et al 2006;Li et al 2009], and Clone [Pipatsrisawat and Darwiche 2007].…”

Section: Sat Solversmentioning

confidence: 99%

A SAT-based approach to cost-sensitive temporally expressive planning

Lü

Huang

Chen

et al. 2013

ACM Trans. Intell. Syst. Technol.

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Complex features, such as temporal dependencies and numerical cost constraints, are hallmarks of real-world planning problems. In this paper, we consider the challenging problem of cost-sensitive temporally expressive (CSTE) planning, which requires concurrency of durative actions and optimization of action costs. We first propose a scheme to translate a CSTE planning problem to a minimum cost (MinCost) satisfiability (SAT) problem and to integrate with a relaxed parallel planning semantics for handling true temporal expressiveness. Our scheme finds solution plans that optimize temporal makespan, and also minimize total action costs at the optimal makespan. We propose two approaches for solving MinCost SAT. The first is based on a transformation of a MinCost SAT problem to a weighted partial Max-SAT (WPMax-SAT), and the second, called BB-CDCL, is an integration of the branch-and-bound technique and the conflict driven clause learning (CDCL) method. We also develop a CSTE customized variable branching scheme for BB-CDCL which can significantly improve the search efficiency. Our experiments on the existing CSTE benchmark domains show that our planner compares favorably to the state-of-the-art temporally expressive planners in both efficiency and quality.

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“…Hence, min(wt ((x)), wt ((¬x)) can be added to the lower bound. More powerful inference methods are used to handle more complex cases [7,11]. However, as mentioned above, all of these inferences must be undone on backtrack.…”

Section: Solution Methodsmentioning

confidence: 99%

“…Our approach does not currently achieve state-of-the-art performance, although we are pursuing a number of ideas aimed at improving its performance. Furthermore, much recent research has focused on ways of improving existing bounding techniques, e.g., by exploiting cyclic structures [11]. Our approach offers a completely new way of producing improved bounds through finding specialized ways of learning new clauses.…”

Section: Introductionmentioning

confidence: 99%

Using Learnt Clauses in maxsat

Davies

Cho

Bacchus

2010

Principles and Practice of Constraint Programming – CP 2010

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Abstract. maxsat is an optimization version of SAT capable of expressing a variety of practical problems. maxsat solvers have been designed to take advantage of many of the successful techniques of SAT solvers. However, the most important technique of modern SAT solvers, clause learning, has not been utilized since learnt clauses cannot be soundly added to a maxsat theory. In this paper we present a new method that allows SAT clause learning to be exploited in a maxsat solver without losing soundness. We present techniques for learning clauses during a branch and bound (B&B) maxsat search, a process that is more complicated than standard clause learning. To exploit these learnt clauses we develop a connection between them and bounds that can be used during B&B. This connection involves formulating a hitting set problem and finding bounds on its optimal solution. We present some new techniques for generating useful hitting set bounds and also show how linear and integer programs can be exploited for this purpose, opening the door for a hybrid approach to solving maxsat.

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Exploiting Cycle Structures in Max-SAT

Cited by 47 publications

References 9 publications

Extending MaxSAT to Solve the Coalition Structure Generation Problem with Externalities Based on Agent Relations

Extending MaxSAT to Solve the Coalition Structure Generation Problem with Externalities Based on Agent Relations

A SAT-based approach to cost-sensitive temporally expressive planning

Using Learnt Clauses in maxsat

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