59 research outputs found

    Octagonal Domains for Continuous Constraints

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    International audienceDomains in Continuous Constraint Programming (CP) are generally represented with intervals whose nn-ary Cartesian product (box) approximates the solution space. This paper proposes a new representation for continuous variable domains based on octagons. We generalize local consistency and split to this octagon representation, and we propose an octagonal-based branch and prune algorithm. Preliminary experimental results show promising performance improvements on several classical benchmarks

    Un modÚle markovien pour GSAT et WalkSAT résultats préliminaires

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    National audienceLes algorithmes GSAT et WalkSAT ont un comportement, bien connu expĂ©rimentalement, mais relativement peu Ă©tudiĂ© thĂ©oriquement. Nous Ă©tudions ici un modĂšle de GSAT et WalkSAT sous la forme de chaĂźnes de Markov, modĂšle exact pour la partie gloutonne, approchĂ© pour la version avec random restart. Les rĂ©sultats classiques sur les chaĂźnes de Markov permettent d'en dĂ©duire deux nouvelles majorations de l'espĂ©rance du temps de calcul de WalkSAT sans random restart, en fonction des valeurs propres de la matrice de transition associĂ©e. Nous montrons expĂ©rimentalement sur de petites instances que cette borne permet de retrouver le paramĂ©trage optimal observĂ© dans la littĂ©rature. Nous donnons ensuite deux rĂ©sultats sur l'espĂ©rance de GSAT ou Walk-SAT avec random restart en fonction du nombre d'itĂ©rations avant random restart (entre autres). MĂȘme si les rĂ©sultats restent Ă  approfondir, ce modĂšle donne une piste vers une Ă©tude thĂ©orique du paramĂ©trage optimal et, au delĂ , du comportement de ces algorithmes

    Modular Constraint Solver Cooperation via Abstract Interpretation

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    Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i) interval propagators completion that allows abstract domains to exchange bound constraints, and (ii) delayed product which exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logic programming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose the shared product to combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem. Under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 17 pages. v2: Fix an example in Section 3.2 (improved closure

    Solution Sampling with Random Table Constraints

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    International audienceConstraint programming provides generic techniques to efficiently solve combinatorial problems. In this paper, we tackle the natural question of using constraint solvers to sample combinatorial problems in a generic way. We propose an algorithm, inspired from Meel's ApproxMC algorithm on SAT, to add hashing constraints to a CP model in order to split the search space into small cells. By uniformly sampling the solutions in one cell, we can generate random solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables, which keeps the cost of the hashing process tractable. We implemented this solving method using the constraint solver Choco-solver. The quality of the randomness and the running time of our approach are experimentally compared to a random branching strategy. We show that our approach improves the randomness while being in the same order of magnitude in terms of running time. We also use our algorithm with an other, more powerful, set of hashing constraints: linear modular equalities. We experimentally show that the resulting sampling is uniform, at the cost of a longer running time

    Revisiting Counting Solutions for the Global Cardinality Constraint

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    International audienceCounting solutions for a combinatorial problem has been identified as an important concern within the Artificial Intelligence field. It is indeed very helpful when exploring the structure of the solution space. In this context, this paper revisits the computation process to count solutions for the global cardinality constraint in the context of counting-based search. It first highlights an error and then presents a way to correct the upper bound on the number of solutions for this constraint

    Estimer le nombre de solutions des contraintes de cardinalité grâce à leur décomposition range et roots

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    National audienceEn programmation par contraintes, le choix d’une heuristique de recherche plutôt qu’une autre dépend souvent du problème. Cependant il existe des heuristiques génériques utilisant plutôt des indicateurs sur la structure combinatoire du problème. Les heuristiques "Counting- Based", introduites par Pesant et al., font des choix basés sur une estimation du nombre de solutions restantes dans tel ou tel sous-arbre de l’arbre de recherche. Un inconvénient de ces heuristiques est qu’elles nécessitent des algorithmes de dénombrement spécifiques à chaque contrainte. Cette étude s’intéresse aux contraintes de cardinalité, dont alldifferent, atmost, nvalue, etc... Nous proposons une méthode de comptage de solutions pour les contraintes range et roots, introduites par Bessiere et al. Grâce à la décomposition des contraintes de cardinalité en contraintes range et roots, nous dérivons une méthode systématique de dénombrement de solutions pour la plupart de ces contraintes

    Un solveur de contraintes basé sur les domaines abstraits

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    International audienceDans cet article, nous utilisons des techniques de l'interpréation abstraite (une théorie d'approximation des sémantiques) dans le cadre de la programmation par contraintes (basée sur la logique du premier ordre qui permet de résoudre des problÚmes combinatoires). Nous mettons en évidence certains liens et différences entre ces domaines de recherches : tous deux calculent itérativement des points fixes mais emploient des extrapolations et stratégies de raffinement différentes. De plus, nous pouvons mettre en correspondance les consistances en programmation par contraintes et les domaines abstraits non relationnels. Nous utilisons ensuite ces correspondances pour construire un solveur de contraintes abstrait qui s'appuie sur des techniques d'interprétation abstraite (comme les domaines relationnels) pour aller au-delà des solveurs classiques. Les résultats expérimentaux obtenus avec notre prototype sont encourageants

    Estimating parallel runtimes for randomized algorithms in constraint solving

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    International audienceThis paper presents a detailed analysis of the scalability and par-allelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of a Constraint-Based Local Search solver (Adaptive Search), two SAT Local Search solvers (namely Sparrow and CCASAT), and a propagation-based constraint solver (Gecode, with a random labeling heuristic). We compare the performance predicted by our model to actual parallel implementations of those methods using up to 384 processes. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of problems, we observe that the experimented solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal. Our results show that the proposed framework estimates the runtime of the parallel algorithm with an average discrepancy of 21% w.r.t. the empirical data across all the experiments with the maximum allowed number of processors for each technique

    Cerebellar dysfunction in multiple sclerosis

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    International audienceThe optimization of a palladium-catalyzed Heck Matsuda reaction using an optimization algorithm is presented. We modified and implemented the Nelder-Mead method in order to perform constrained optimizations in a multidimensional space. We illustrated the power of our modified algorithm through the optimization of a multivariable reaction involving the arylation of a deactivated olefin with an arenediazonium salt. The great flexibility of our optimization method allows to fine-tune experimental conditions according to three different objective functions: maximum yield, highest throughput, and lowest production cost. The beneficial properties of flow reactors associated with the power of intelligent algorithms for the fine-tuning of experimental parameters allowed the reaction to proceed in astonishingly simple conditions unable to promote the coupling through traditional batch chemistry
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