Carlos Ansótegui

A gender-based genetic algorithm for the automatic configuration of algorithms

A problem that is inherent to the development and efficient use of solvers is that of tuning parameters. The CP community has a long history of addressing this task automatically. We propose a robust, inherently parallel genetic algorithm for the problem of configuring solvers automatically. In order to cope with the high costs of evaluating the fitness of individuals, we introduce a gender separation whereby we apply different selection pressure on both genders. Experimental results on a selection of SAT solvers show significant performance and robustness gains over the current state-of-the-art in automatic algorithm configuration.

Solving (Weighted) Partial MaxSAT through Satisfiability Testing

Recently, Fu and Malik described an unweighted Partial MaxSAT solver based on successive calls to a SAT solver. At the k th iteration the SAT solver tries to certify that there exist an assignment that satisfies all but k clauses. Later Marques-Silva and Planes implemented and extended these ideas. In this paper we present and implement two Partial MaxSAT solvers and the weighted variant of one of them. Both are based on Fu and Malik ideas. We prove the correctness of our algorithm and compare our solver with other (Weighted) MaxSAT and (Weighted) Partial MaxSAT solvers.

SAT-based MaxSAT 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. In this paper we present several algorithms specially designed to deal with industrial or real problems. All of them are based on the idea of solving MaxSAT through successive calls to a SAT solver. We show that this SAT-based technique is efficient in solving industrial problems. In fact, all state-of-the-art MaxSAT solvers that perform well in industrial instances are based on this technique. 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. We also present a complete experimental study comparing the performance of our algorithms with latest MaxSAT solvers.

Mapping problems with finite-domain variables to problems with boolean variables

We define a collection of mappings that transform many-valued clausal forms into satisfiability equivalent Boolean clausal forms, analyze their complexity and evaluate them empirically on a set of benchmarks with state-of-the-art SAT solvers. Our results provide empirical evidence that encoding combinatorial problems with the mappings defined here can lead to substantial performance improvements in complete SAT solvers.

The community structure of SAT formulas

The research community on complex networks has developed techniques of analysis and algorithms that can be used by the SAT community to improve our knowledge about the structure of industrial SAT instances. It is often argued that modern SAT solvers are able to exploit this hidden structure, without a precise definition of this notion. In this paper, we show that most industrial SAT instances have a high modularity that is not present in random instances. We also show that successful techniques, like learning, (indirectly) take into account this community structure. Our experimental study reveal that most learnt clauses are local on one of those modules or communities.

Improving SAT-Based weighted MaxSAT solvers

In the last few years, there has been a significant effort in designing and developing efficient Weighted MaxSAT solvers. We study in detail the WPM1 algorithm identifying some weaknesses and proposing solutions to mitigate them. Basically, WPM1 is based on iteratively calling a SAT solver and adding blocking variables and cardinality constraints to relax the unsatisfiable cores returned by the SAT solver. We firstly identify and study how to break the symmetries introduced by the blocking variables and cardinality constraints. Secondly, we study how to prioritize the discovery of higher quality cores. We present an extensive experimental investigation comparing the new algorithm with state-of-the-art solvers showing that our approach makes WPM1 much more competitive.

Improving WPM2 for (Weighted) Partial MaxSAT

Weighted Partial MaxSAT (WPMS) is an optimization variant of the Satisfiability (SAT) problem. Several combinatorial optimization problems can be translated into WPMS. In this paper we extend the state-of-the-art WPM2 algorithm by adding several improvements, and implement it on top of an SMT solver. In particular, we show that by focusing search on solving to optimality subformulas of the original WPMS instance we increase the efficiency of WPM2. From the experimental evaluation we conducted on the PMS and WPMS instances at the 2012 MaxSAT Evaluation, we can conclude that the new approach is both the best performing for industrial instances, and for the union of industrial and crafted instances. This research has been partially founded by the CICYT research projects TASSAT (TIN2010-20967-C04-01/03/04) and ARINF (TIN2009-14704-C03-01).

On the structure of industrial SAT instances

During this decade, it has been observed that many realworld graphs, like the web and some social and metabolic networks, have a scale-free structure. These graphs are characterized by a big variability in the arity of nodes, that seems to follow a power-law distribution. This came as a big surprise to researchers steeped in the tradition of classical random networks. SAT instances can also be seen as (bi-partite) graphs. In this paper we study many families of industrial SAT instances used in SAT competitions, and show that most of them also present this scale-free structure. On the contrary, random SAT instances, viewed as graphs, are closer to the classical random graph model, where arity of nodes follows a Poisson distribution with small variability. This would explain their distinct nature. We also analyze what happens when we instantiate a fraction of the variables, at random or using some heuristics, and how the scale-free structure is modified by these instantiations. Finally, we study how the structure is modified during the execution of a SAT solver, concluding that the scale-free structure is preserved.

Building Automated Theorem Provers for Infinitely-Valued Logics with Satisfiability Modulo Theory Solvers

There is a relatively large number of papers dealing with complexity and proof theory issues of infinitely-valued logics. Nevertheless, little attention has been paid so far to the development of efficient solvers for such logics. In this paper we show how the technology of Satisfiability Modulo Theories (SMT) can be used to build efficient automated theorem provers for relevant infinitely-valued logics, including Lukasiewicz, Gödel and Product logics. Moreover, we define a test suite for those logics, and report on an experimental investigation that evaluates the practical complexity of Lukasiewicz and Gödel logics, and provides empirical evidence of the good performance of SMT technology for automated theorem proving on infinitely-valued logics.

Boosting Chaff's performance by incorporating CSP heuristics

Identifying CSP variables in SAT encodings of combinatorial problems allows one to incorporate CSP-like variable selection heuristics into SAT solvers. We show that such heuristics turn out to be more powerful than the best performing state-of-the-art variable selection heuristics for SAT. In particular, we define five novel CSP-like variable selection heuristics for Chaff —one of the most modern, powerful and robust SAT solvers— and provide experimental evidence that Chaff augmented with those heuristics outperforms the original Chaff solver one order of magnitude on difficult SAT-encoded problems like random binary CSPs, pigeon hole, and graph coloring. Research partially supported by project CICYT TIC2001-1577-C03-03 funded by the Ministerio de Ciencia y Tecnologia.