Using Restarts in Constraint Programming over Finite Domains - An Experimental Evaluation

The use of restart techniques in complete Satisfiability (SAT) algorithms has made solving hard real world instances possible. Without restarts such algorithms could not solve those instances, in practice. State of the art algorithms for SAT use restart techniques, conflict clause recording (nogoods), heuristics based on activity variable in conflict clauses, among others. Algorithms for SAT and Constraint problems share many techniques; however, the use of restart techniques in constraint programming with finite domains (CP(FD)) is not widely used as it is in SAT. We believe that the use of restarts in CP(FD) algorithms could also be the key to efficiently solve hard combinatorial problems. In this PhD thesis we study restarts and associated techniques in CP(FD) solvers. In particular, we propose to including in a CP(FD) solver restarts, nogoods and heuristics based in nogoods as this should improve search algorithms, and, consequently, efficiently solve hard combinatorial problems. We thus intend to: a) implement restart techniques (successfully used in SAT) to solve constraint problems with finite domains; b) implement nogoods (learning) and heuristics based on nogoods, already in use in SAT and associated with restarts; and c) evaluate the use of restarts and the interplay with the other implemented techniques. We have conducted the study in the context of domain splitting backtrack search algorithms with restarts. We have defined domain splitting nogoods that are extracted from the last branch of the search algorithm before the restart. And, inspired by SAT solvers, we were able to use information within those nogoods to successfully help the variable selection heuristics. A frequent restart strategy is also necessary, since our approach learns from restarts

Proceedings of the 2022 XCSP3 Competition

This document represents the proceedings of the 2022 XCSP3 Competition. The results of this competition of constraint solvers were presented at FLOC (Federated Logic Conference) 2022 Olympic Games, held in Haifa, Israel from 31th July 2022 to 7th August, 2022.Comment: arXiv admin note: text overlap with arXiv:1901.0183

Towards improving solution dominance with incomparability conditions : a case-study using Generator Itemset Mining

Funding: EPSRC (EP/P015638/1).Finding interesting patterns is a challenging task in data mining. Constraint based mining is a well-known approach to this, and one for which constraint programming has been shown to be a well-suited and generic framework. Dominance programming has been proposed as an extension that can capture an even wider class of constraint-based mining problems, by allowing to compare relations between patterns. In this paper, in addition to specifying a dominance relation, we introduce the ability to specify an incomparability condition. Using these two concepts we devise a generic framework that can do a batch-wise search that avoids checking incomparable solutions. We extend the ESSENCE language and underlying modelling pipeline to support this. We use generator itemset mining problem as a test case and give a declarative specification for that. We also present preliminary experimental results on this specific problem class with a CP solver backend to show that using the incomparability condition during search can improve the efficiency of dominance programming and reduces the need for post-processing to filter dominated solutions.Publisher PD

Symmetry in constraint programming

Constraint programming is an invaluable tool for solving many of the complex NP-complete problems that we need solutions to. These problems can be easily described as Constraint Satisfaction Problems (CSPs) and then passed to constraint solvers: complex pieces of software written to solve general CSPs efficiently. Many of the problems we need solutions to are real world problems: planning (e.g. vehicle routing), scheduling (e.g. job shop schedules) and timetabling problems (e.g. staff rotas) to name but a few. In the real world, we place structure on objects to make them easier to deal with. This manifests itself as symmetry. The symmetry in these real world problems make them easier to deal with for humans. However, they lead to a great deal of redundancy when using computational methods of problem solving. Thus, this thesis examines some of the many aspects of utilising the symmetry of CSPs to reduce the amount of computation needed by constraint solvers. In this thesis we look at the ease of use of previous symmetry breaking methods. We introduce a new and novel method of describing the symmetries of CSPs. We look at previous methods of symmetry breaking and show how we can drastically reduce their computation while still breaking all symmetry. We give the first detailed investigation into the behaviour of breaking only subsets of all symmetry. We look at how this affects the performance of constraint solvers before discovering the properties of a good symmetry. We then present an original method for choosing the best symmetries to use. Finally, we look at areas of redundant computation in constraint solvers that no other research has examined. New ways of dealing with this redundancy are proposed with results of an example implementation which improves efficiency by several orders of magnitude

Proceedings of CSCLP 2007: Annual ERCIM Workshop on Constraint Solving and Constraint Logic Programming

Ce fichier regroupe en un seul document l'ensemble des articles acceptés pour la conférence CSCLP 2007Constraints are a natural way to represent knowledge, and constraint programming is a declarative programming paradigm that has been successfully used to express and solve many practical combinatorial optimization problems. Examples of application domains are scheduling, production planning, resource allocation, communication networks, robotics, and bioinformatics. These proceedings contain the research papers presented at the 12th International Workshop on Constraint Solving and Constraint Logic Programming (CSCLP'07), held on June 7th and 8th 2007, at INRIA Rocquencourt, France. This workshop, open to all, is organized as the twelfth meeting of the working group on Constraints of the European Research Consortium for Informatics and Mathematics (ERCIM). It continues a series of workshops organized since the creation of the working group in 1997, that have led since 2002 to the publication of a series of books entitled ”Recent Advances in Constraints” in the Lecture Notes in Artificial Intelligence, edited by Springer-Verlag. In addition to the contributed papers collected in this volume, two invited talks were given at CSCLP'07, one by Gilles Pesant, Ecole Polytechnique de Montreal, Canada, and one by Jean-Charles R égin, ILOG, France. The editors would like to take the opportunity to thank all the authors who submitted a paper, as well as the reviewers for their helpful work. CSCLP'07 has been made possible thanks to the support of the European Research Consortium for Informatics and Mathematics (ERCIM), the Institut National de la Recherche en Informatique et Automatique (INRIA) and the Association for Constraint programming (ACP)

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances