The Social Golfer Problem has been extensively used in recent years by the constraint community as an example of highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as the Kirkman's Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, an generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques allows us to improve previous published results by an order of magnitude for CPU time as well as number of backtracks, and to compute the seven unique solutions of the Kirkman's problem in a few seconds.

SAT Competition 2002 held in March--May 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation. In this report

We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of propositional logic facilitates modeling search problems and often results in very concise encodings. We propose two "native" local-search solvers for theories in the extended language.

search problems

We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M , if M C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudo-boolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the one-step provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.

A previous paper showed that adding binary symmetry breaking constraints to a model can degrade local search performance. This paper shows that even unary constraints are not necessarily beneficial because they can transform solutions into local minima. Furthermore, performance can be improved by the reverse of symmetry breaking: using a supersymmetric model with extra symmetry.

Multiple sequence alignment is a central problem in Bioinformatics and a challenging one for optimisation algorithms. An established integer programming approach is to apply branch-and-cut to a graph-theoretical model. The models are exponentially large but are represented intensionally, and violated constraints can be located in polynomial time. This report describes a new integer program formulation that generates polynomial-sized models small enough to be passed to generic solvers. It is a hybrid formulation relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a pseudo-Boolean local search algorithm are competitive with those of state-of-the-art algorithms. Execution times are much longer, but in future work we aim to develop a more efficient specialised algorithm. 1

Abstract. Multiple sequence alignment is a central problem in Bioinformatics. A known integer programming approach is to apply branch-and-cut to exponentially large graph-theoretic models. This paper describes a new integer program formulation that generates models small enough to be passed to generic solvers. The formulation is a hybrid relating the sparse alignment graph with a compact encoding of the alignment matrix via channelling constraints. Alignments obtained with a SAT-based local search algorithm are competitive with those of state-of-the-art algorithms, though execution times are much longer. 1

Combining advantages of different paradigms such as stochastic local search and constraint propagation is a research area of current interest, but implementing such hybrids is a non-trivial task. This paper describes a straightforward combination of existing search and modeling techniques, yielding a local search algorithm that maintains arc-consistency for binary CSPs. On a set of bandwidth graph colouring benchmarks it finds colourings better than those found by an equivalent forward checking algorithm, and almost as good as those found by a specialized colouring algorithm. It is embedded within a more general local search algorithm for integer linear programs, allowing further novel hybrids.

A hybrid algorithm is devised to boost the performance of complete search on under-constrained problems. We suggest to use random variable selection in combination with restarts, augmented by a coarse-grained local search algorithm that learns favorable value heuristics over the course of several restarts. Numerical results show that this method can speedup complete search by orders of magnitude.