XCSP3-core: A Format for Representing Constraint Satisfaction/Optimization Problems

In this document, we introduce XCSP3-core, a subset of XCSP3 that allows us to represent constraint satisfaction/optimization problems. The interest of XCSP3-core is multiple: (i) focusing on the most popular frameworks (CSP and COP) and constraints, (ii) facilitating the parsing process by means of dedicated XCSP3-core parsers written in Java and C++ (using callback functions), (iii) and defining a core format for comparisons (competitions) of constraint solvers.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0339

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Parallélisme en programmation par contraintes

We study the search procedure parallelization in Constraint Programming (CP). After giving an overview on various existing methods of the state-of-the-art, we present a new method, named Embarrassinqly Parallel Search (EPS). This method is based on the decomposition of a problem into many disjoint subproblems which are then solved in parallel by computing units with little or without communication. The principle of EPS is to have a resolution times balancing for each computing unit in a statistical sense to obtain a goodDépôt de thèse – Données complémentaireswell-balanced workload. We assume that the amount of resolution times of all subproblems is comparable to the resolution time of the entire problem. This property is checked with CP and allows us to have a simple and efficient method in practice. In our experiments, we are interested in enumerating all solutions of a problem, and proving that a problem has no solution and finding an optimal solution of an optimization problem. We observe that the decomposition has to generate at least 30 subproblems per computing unit to get equivalent workloads per computing unit. Then, we evaluate our approach on different architectures (multicore machine, cluster and cloud computing) and we observe a substantially linear speedup. A comparison with current methods such as work stealing or portfolio shows that EPS gets better results.Nous étudions la parallélisation de la procédure de recherche de solution d’un problème en Programmation Par Contraintes (PPC). Après une étude de l’état de l’art, nous présentons une nouvelle méthode, nommée Embarrassingly Parallel Search (EPS). Cette méthode est basée sur la décomposition d’un problème en un très grand nombre de sous-problèmes disjoints qui sont ensuite résolus en parallèle par des unités de calcul avec très peu, voire aucune communication. Le principe d’EPS est d’arriver statistiquement à un équilibrage des temps de résolution de chaque unité de calcul afin d’obtenir une bonne répartition de la charge de travail. EPS s’appuie sur la propriété suivante : la somme des temps de résolution de chacun des sous-problèmes est comparable au temps de résolution du problème en entier. Cette propriété est vérifiée en PPC, ce qui nous permet de disposer d’une méthode simple et efficace en pratique. Dans nos expérimentations, nous nous intéressons à la recherche de toutes les solutions d’un problème en PPC, à prouver qu’un problème n’a pas de solution et à la recherche d’une solution optimale d’un problème d’optimisation. Les résultats montrent que la décomposition doit générer au moins 30 sous-problèmes par unité de calcul pour obtenir des charges de travail par unité de calcul équivalentes. Nous évaluons notre approche sur différentes architectures (machine multi-coeurs, centre de calcul et cloud computing) et montrons qu’elle obtient un gain pratiquement linéaire en fonction du nombre d’unités de calcul. Une comparaison avec les méthodes actuelles telles que le work stealing ou le portfolio montre qu’EPS obtient de meilleurs résultats

Designing and Optimizing Representations for Non-Binary Constraints

Ph.DDOCTOR OF PHILOSOPH

A path-optimal GAC algorithm for table constraints

10.3233/978-1-61499-098-7-510Frontiers in Artificial Intelligence and Applications242510-51