On the Practical use of Variable Elimination in Constraint Optimization Problems: 'Still-life' as a Case Study

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of finding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algorithm, interleaved with search, and as a source of good quality lower bounds. We show that these techniques are the best known option both theoretically and empirically. In our experiments we have been able to solve the n=20 instance, which is far beyond reach with alternative approaches

Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network

The restricted Maximum k-Satisfiability MAX- kSAT is an enhanced Boolean satisfiability counterpart that has attracted numerous amount of research. Genetic algorithm has been the prominent optimization heuristic algorithm to solve constraint optimization problem. The core motivation of this paper is to introduce Hopfield network incorporated with genetic algorithm in solving MAX-kSAT problem. Genetic algorithm will be integrated with Hopfield network as a single network. The proposed method will be compared with the conventional Hopfield network. The results demonstrate that Hopfield network with genetic algorithm outperforms conventional Hopfield networks. Furthermore, the outcome had provided a solid evidence of the robustness of our proposed algorithms to be used in other satisfiability problem

A Logical Approach to Efficient Max-SAT solving

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the {\em logic} that is behind. In this paper we introduce an original framework for Max-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: {\em search} and {\em inference}. We show that many algorithmic {\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in {\em logic} terms with our framework in a unified manner. Besides, we introduce an original search algorithm that performs a restricted amount of {\em weighted resolution} at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat evaluation ever reported, show that our algorithm is generally orders of magnitude faster than any competitor

An Efficient Algorithm for Maximum Boolean Satisfiability Based on Unit Propagation, Linear Programming, and Dynamic Weighting

Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a logical formula. A branch-and-bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most efficient complete algorithms for solving max-SAT. In this paper, We propose and investigate a number of new strategies for max-SAT. Our first strategy is a set of unit propagation rules for max-SAT. As unit propaga-tion is a very efficient strategy for SAT, we show that it can be extended to max-SAT, and can greatly improve the performance of an extended DPLL-based algorithm. Our second strategy is an effective lookahead heuristic based on linear programming. We show that the LP heuristic can be made effective as the number of clauses increases. Our third strategy is a dynamic-weight variable ordering, which is based on a thorough analysis of two well-known existing branching rules. Based on the analysis of these strategies, we develop an integrated, constrainedness-sensitive max-SAT solver that is able to dynamically adjust strategies ac-cording to problem characteristics. Our experimental results on random max-SAT and some instances from the SATLIB show that our new solver outperforms most of the existing com-plete max-SAT solvers, with orders of magnitude of improvement in many cases

A Branch and Bound Algorithm for Numerical MaxCSP

Abstract. The Constraint Satisfaction Problem (CSP) framework allows users to define problems in a declarative way, quite independently from the solving process. However, when the problem is over-constrained, the answer "no solution" is generally unsatisfactory. A Max-CSP Pm = V, D, C is a triple defining a constraint problem whose solutions maximise constraint satisfaction. In this paper, we focus on numerical CSPs, which are defined on real variables represented as floating point intervals and which constraints are numerical relations defined in extension. Solving such a problem (i.e., exactly characterizing its solution set) is generally undecidable and thus consists in providing approximations. We propose a branch and bound algorithm that computes under and over approximations of its solution set and determines the maximum number mP of satisfied constraints. The technique is applied on three numeric applications and provides promising results

Estudi comparatiu de la publicació científica en l’àmbit de la informàtica a la UPC vs. altres universitats d’àmbit nacional i internacional (2002-2012)

L'estudi analitza la producció científica de la UPC vinculada amb la informàtica i es compara amb la d'altres 16 universitats de l’estat espanyol, europees, dels Estats Units i asiàtiques, amb una notable activitat investigadora en aquest camp.Postprint (author’s final draft