Encodings and Benchmarks for MaxSAT Solving
- Autores: María Alba Cabiscol Teixidó
- Directores de la Tesis: Ramón Béjar Torres (dir. tes.), Felip Manyà Serres (dir. tes.)
- Lectura: En la Universitat de Lleida ( España ) en 2012
- Idioma: inglés
- Tribunal Calificador de la Tesis: Lluis Godo Lacasa (presid.), Carlos Ansótegui Gil (secret.), César Fernández Camón (voc.), Gonzalo Escalada Imaz (voc.), Mateu Villaret Auselle (voc.)
- Materias:
- Enlaces
- Tesis en acceso abierto en: TDX
- Resumen
Problem solving based on the Propositional Satisfiability Problem (SAT) is an active research area in Artificial Intelligence, and has been successfully applied to solve both academic and industrial decision problems. The success of SAT-based problem solving has in turn contributed to explore extensions of SAT such as Satisfiability Modulo Theories, Quantified Boolean Formulas, Many-Valued Satisfiability, Pseudo-Boolean Optimization, and Maximum Satisfiability. In this thesis we focus on the Maximum Satisfiability Problem (MaxSAT), which is an optimization variant of SAT. Given a CNF formula $\phi$, MaxSAT consists in finding a truth assignment that satisfies the maximum number of clauses of $\phi$. Usually, we focus on the MaxSAT extension that associates weights with clauses, and where each clause is declared to be either soft or hard. In this case, known as Weighted Partial MaxSAT, an optimal solution is a truth assignment that satisfies all the hard clauses, and maximizes the sum of the weights of the satisfied soft clauses. Weighted Partial MaxSAT is called Weighted MaxSAT when all the clauses are soft, and Partial MaxSAT when all the soft clauses have the same weight. Given the recent and promising results on MaxSAT, the main objective of this thesis is to contribute to develop appropriate MaxSAT technology for solving challenging NP-hard optimization problems by first reducing them to a MaxSAT formalism, and then finding a solution with a state-of-the-art MaxSAT solver. More specifically, our goal is twofold: firstly, improve the modeling of decision and optimization problems by defining original and efficient encodings from the Constraint Satisfaction Problem (CSP) into SAT, and extending them to map the Maximum Constraint Satisfaction Problem (MaxCSP) into MaxSAT; and secondly, create MaxSAT instances generators of adjustable hardness to help identify potential enhancements and weaknesses of MaxSAT solvers, and assess the impact of individual and combined solving techniques. Concerning encodings from CSP into SAT, we present two new encodings from CSP into SAT: the minimal support encoding and the interval-based support encoding. The minimal support encoding reduces the size of the support encoding, and the interval-based support encoding is the first support encoding containing only regular literals in which the size of the derived encoding does not grow exponentially in the worst case. Concerning encodings from MaxCSP into Partial MaxSAT, we define and analyze a number of novel encodings that extend variants of the direct and support encodings from CSP into SAT. We identify the clauses that must be declared as hard and the clauses that must be declared as soft, and determine whether it is necessary to introduce auxiliary variables for producing encodings in such a way that the minimum number of falsified clauses in the generated Partial MaxSAT encoding is the same as the minimum number of violated constraints in the encoded MaxCSP instance. Concerning the creation of MaxSAT instance generators of adjustable hardness, we describe generators that encode into MaxSAT the following combinatorial optimization problems: Max1+pSAT, Partial Max2SAT, MaxCut, and rectangular bin packing. The conducted empirical investigation provides evidence that the new encodings from CSP into SAT are particularly good for SAT solvers with conflict clause learning, the proposed encodings from MaxCSP into MaxSAT are well-suited for modelling optimization problems, and the created generators produce challenging benchmarks for MaxSAT solvers.
