On the Complexity of Optimization Problems based on Compiled NNF Representations

Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard. Fortunately, in many problems, the set of feasible solutions does not often change and is independent from the user's request. In such cases, compiling the set of constraints describing the set of feasible solutions during an off-line phase makes sense, if this compilation step renders computationally easier the generation of a non-dominated, yet feasible solution matching the user's requirements and preferences (which are only known at the on-line step). In this article, we focus on propositional constraints. The subsets L of the NNF language analyzed in Darwiche and Marquis' knowledge compilation map are considered. A number of families F of representations of objective functions over propositional variables, including linear pseudo-Boolean functions and more sophisticated ones, are considered. For each language L and each family F, the complexity of generating an optimal solution when the constraints are compiled into L and optimality is to be considered w.r.t. a function from F is identified

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

Optimisation multicritère pour la gestion de dépendances logicielles : utilisation de la norme de Tchebycheff

Session "Posters"National audienceLe problème de gestion de dépendances logicielles concerne l'installation d'applications informatiques modulaires. Il s'agit de programmes ayant la faculté d'être configurés par l'utilisateur, qui peut choisir à tout moment les modules qu'il souhaite installer ou enlever. Un module peut nécessiter la présence d'autres modules pour fonctionner, il peut entrer en conflit avec certains modules, et parfois il peut recommander l'installation de modules spécifiques pour pouvoir être utilisé au meilleur de ses capacités. Il existe généralement plusieurs solutions (listes de paquets à installer et à enlever) pour passer d'une configuration courante à une configuration souhaitée. On peut se donner des critères pour ordonner ces solutions, passant alors d'un problème de décision (" est-ce que je peux ajouter tous ces modules ? ") à un problème d'optimisation (" quelle est la meilleure solution pour ajouter tous ces modules ? "). Dans de nombreux cas, il faut prendre en compte plusieurs critères. Cet article se concentre sur des méthodes algorithmiques capables de calculer des solutions équilibrées en utilisant la norme de Tchebycheff comme méthode d'agrégation de critères. Cette approche est ensuite évaluée sur des problèmes de gestion de dépendances entre paquets GNU/Linux

Reasoning on Feature Models: Compilation-Based vs. Direct Approaches

Analyzing a Feature Model (FM) and reasoning on the corresponding configuration space is a central task in Software Product Line (SPL) engineering. Problems such as deciding the satisfiability of the FM and eliminating inconsistent parts of the FM have been well resolved by translating the FM into a conjunctive normal form (CNF) formula, and then feeding the CNF to a SAT solver. However, this approach has some limits for other important reasoning issues about the FM, such as counting or enumerating configurations. Two mainstream approaches have been investigated in this direction: (i) direct approaches, using tools based on the CNF representation of the FM at hand, or (ii) compilation-based approaches, where the CNF representation of the FM has first been translated into another representation for which the reasoning queries are easier to address. Our contribution is twofold. First, we evaluate how both approaches compare when dealing with common reasoning operations on FM, namely counting configurations, pointing out one or several configurations, sampling configurations, and finding optimal configurations regarding a utility function. Our experimental results show that the compilation-based is efficient enough to possibly compete with the direct approaches and that the cost of translation (i.e., the compilation time) can be balanced when addressing sufficiently many complex reasoning operations on large configuration spaces. Second, we provide a Java-based automated reasoner that supports these operations for both approaches, thus eliminating the burden of selecting the appropriate tool and approach depending on the operation one wants to perform

Multiobjective boolean optimization

L’aide à la décision a pour but d’assister un opérateur humain dans ses choix. La nécessité d’employer de telles techniques s’est imposée avec la volonté de traiter des problèmes dépendant d’une quantité de données toujours plus importante. L’intérêt de l’aide à la décision est encore plus manifeste lorsqu’on souhaite obtenir non pas une solution quelconque, mais une des meilleures solutions d’un problème combinatoire selon un critère donné. On passe alors d’un problème de décision (déterminer l’existence d’une solution) à un problème d’optimisation monocritère (déterminer une des meilleures solutions possibles selon un critère). Un décideur peut aussi souhaiter considérer plusieurs critères, et ainsi faire passer le problème de décision initial à un problème d’optimisation multicritère. La difficulté de ce type de problèmes provient du fait que les critères considérés sont généralement antagonistes, et qu’il n’existe donc pas de solution meilleure que les autres pour l’ensemble des critères. Dans ce cas, il s’agit plutôt de déterminer une solution qui offre un bon compromis entre les critères. Dans cette thèse, nous étudions dans un premier temps la complexité théorique de tâches d’optimisation complexes sur les langages de la logique propositionnelle, puis nous étudions leur résolution pratique via le recours à des logiciels bâtis pour résoudre de manière efficace en pratique des problèmes de décision combinatoires, les prouveurs SAT.Decision aiding aims at helping a decision-maker to pick up a solution among several others. The usefulness of such approaches is as prominent as the size of the problems under consideration increases. The need of decision aiding techniques is salient when the problem does not just consist in deciding whether a solutions exists, but to find one of the best solutions according to a given criterion. In this case, the problem goes from a decision problem (decide whether a solution exists) to a single criterion optimization problem (find one of the best solutions according to a criterion). A decision-maker may even want to consider multiple criteria, which turns the initial decision problem into a multicriteria optimization problem. The main issue arising in such cases lies in the fact that the criteria under consideration are often antagonistic, which implies that there is no solution which is the best for each of the objectives. In this case, a good compromise solution is looked for. In this thesis, we first focus on the complexity of optimization requests based on a set of propositional languages. We then study the practical aspects of the resolution of such problems, using pieces of software designed for dealing with combinatorial decision problems, namely SAT solvers

Artificial Intelligence Conferences Closeness

International audienceWe study the evolution of Artificial Intelligence conference closeness, using the coscinus tool. coscinus computes the closeness between publication supports using the co-publication habits of authors: the more authors publish in two conferences, the closer these two conferences. In this paper we perform an analysis of the main Artificial Intelligence conferences based on principal components analysis and clustering performed on this closeness relation

Leveraging Decision-DNNF Compilation for Enumerating Disjoint Partial Models

International audienceThe All-Solution Satisfiability Problem (AllSAT) extends SAT by requiring the identification of all possible solutions for a propositional formula.In practice, enumerating all complete models is often infeasible, making the identification of partial models essential for generating a concise representation of the solution set.Deterministic Decomposable Negation Normal Form (d-DNNF) serves as a language for representation known to offer polynomial-time algorithms for model enumeration.Specifically, when a propositional formula is encoded in d-DNNF, it enables iterative model enumeration with polynomial delay between models.However, despite the existence of theoretical algorithms for this purpose, no available implementations are currently accessible.Furthermore, these theoretical approaches are nearly impractical as they solely yield complete models.We introduce a novel algorithm that maintains a polynomial delay between partial models while significantly enhancing efficiency compared to baseline approaches.Furthermore, through experimental validation, we demonstrate the superiority of compiling a CNF formula Σ into a d-DNNF formula Σ′ and subsequently enumerating models of Σ′ over existing state-of-the-art methodologies for CNF partial model enumeration

Calcul de solutions équilibrées Pareto-optimales : application au problème de gestion de dépendances logicielles

National audienceOur work deals with software dependency management problems. In this article, we present some improvements of the approaches presented in [2] for computing balanced solutions in this context. More precisely, our aim is to to compute Pareto optimal balanced solutions. We compare some encodings using Boolean variables, implemented on top of the Sat4j solver, and an encoding using integer variables, implemented on top of the CPLEX solver.Notre travail se situe dans le cadre de la gestion de dépendances logicielles. Nous présentons dans cet article des améliorations de l'approche décrite dans [2] concernant le calcul de solutions équilibrées dans ce contexte. Plus précisément, nous nous intéressons ici au calcul de solutions équilibrées Pareto-optimales. Nous comparons plusieurs codages de ce problème à base de variables booléennes, dont la résolution est confiée au prouveur Sat4j, et un codage utilisant une variable entière, dont la résolution est confiée au prouveur CPLEX

Proceedings of the 2022 XCSP3 Competition

arXiv admin note: text overlap with arXiv:1901.01830This 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

Réutiliser ou adapter les prouveurs SAT pour l'optimisation booléenne

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