Une Stratégie de Résolution Orientée par la Topologie des CSPs Numériques

http://www710.univ-lyon1.fr/~csolnonLes méthodes classiques de résolution de CSPs numériques sont basées sur un algorithme combinant une technique de bissection et un filtrage par consistance locale. En général, le filtrage est basé sur la Hull-consistance ou la Box-consistance. Les algorithmes de filtrage correspondants identifient souvent des trous dans les domaines, c'est-à-dire des intervalles sur lesquels certaines contraintes ne sont pas satisfaites. Ces trous sont cependant utilisés uniquement pour déterminer le plus petit intervalle englobant les solutions. Ce papier présente une stratégie de recherche, nommée TopSearch (Topological Search), qui exploite les trous identifiés par ces filtrages. TopSearch utilise ces informations pour sélectionner la direction de coupe ainsi que pour définir le point de coupe dans le domaine sélectionné. Si aucun trou n'est identifié une bissection standard est mise en oeuvre. Les premiers résultats expérimentaux montrent que cette heuristique de recherche dont le sur-coût est minime, peut améliorer de manière très significative les performances de la bissection classique

LocFaults: A new flow-driven and constraint-based error localization approach

International audienceWe introduce in this paper LocFaults, a new flow-driven and constraint-based approach for error localization. The input is a faulty program for which a counter-example and a postcondition are provided. To identify helpful informa-tion for error location, we generate a constraint system for the paths of the control flow graph for which at most k con-ditional statements may be erroneous. Then, we calculate Minimal Correction Sets (MCS) of bounded size for each of these paths. The removal of one of these sets of constraints yields a maximal satisfiable subset, in other words, a max-imal subset of constraints satisfying the post condition. To compute the MCS, we extend the algorithm proposed by Liffiton and Sakallah [21] in order to handle programs with numerical statements more efficiently. The main advantage of this flow-driven approach is that the computed sets of suspicious instructions are small, each of them being asso-ciated with an identified path. Moreover, the constraint-programming based framework of LocFaults allows mix-ing Boolean and numerical constraints in an efficient and straightforward way. Preliminary experiments are quite en-couraging. * This work was partially supported by ANR VAC-SIM (ANR-11-INSE-0004), ANR AEOLUS (ANR-10-SEGI-0013), and OSEO ISI PAJERO projects

Revisiting the upper bounding process in a safe Branch and Bound algorithm

Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and inequalities. More precisely, it exploits the optimal solution of a linear relaxation of the problem to compute efficiently a promising upper bound. First experiments on the Coconuts benchmarks demonstrate that this approach is very effective.Comment: Optimization, continuous domains, nonlinear constraint problems, safe constraint based approaches; 14th International Conference on Principles and Practice of Constraint Programming, Sydney : Australie (2008

Constraint Programming and Safe Global Optimization

International audienceWe investigate the capabilities of constraints programming techniques in rigor- ous global optimization methods. We introduce different constraint programming techniques to reduce the gap between efficient but unsafe systems like Baron1, and safe but slow global optimization approaches. We show how constraint program- ming filtering techniques can be used to implement optimality-based reduction in a safe and efficient way, and thus to take advantage of the known bounds of the ob- jective function to reduce the domain of the variables, and to speed up the search of a global optimum. We describe an efficient strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equalities and inequalities to compute efficiently a promising upper bound. Experiments on the COCONUT benchmarks demonstrate that these different techniques drastically improve the performances

Un nouvel algorithme de consistance locale sur les nombres flottants

National audienceSolving constraints over oating-point numbers is a critical issue in numerous applications notably in program veri cation. Capabilities of ltering algorithms over the oating-point numbers have been so far limited to 2b-consistency and its derivatives. Though safe, such ltering techniques su er from the well known pathological problems of local consistencies, e.g., inability to e ciently handle multiple occurrences of the variables. These limitations also take roots in the strongly restricted oating-point arithmetic. To circumvent the poor properties of oating-point arithmetic, we propose in this paper a new ltering algorithm which relies on various relaxations over the reals of the problem over the oats. Safe bounds of the domains are computed with a mixed integer linear programming solver (MILP) on safe linearizations of these relaxations. Preliminary experiments on a relevant set of benchmarks are very promising and show that this approach can be very effective for boosting local consistency algorithms over the floats.La résolution de contraintes sur les nombres a virgule flottante soulève des problèmes critiques dans de nombreuses applications, notamment en vérification de programmes. Jusqu'à maintenant, les algorithmes de filtrage sur les nombres à virgule flottante ont été limités a la 2B{consistance et ses dérivées. Bien que ces filtrages soient conservatifs des solutions, ils souffrent des problèmes bien connus des consistances locales, e.g., leur incapacité à traiter efficacement les occurrences multiples de variables. Leurs limitations proviennent aussi de la pauvret e des propriétés de l'arithmétique des nombres à virgule flottante. Afin de pallier à ces limitations, nous proposons dans cet article un nouvel algorithme de filtrage de contraintes sur les flottants qui repose sur des relaxations successives sur les réels du problème initial sur les flottants. Des bornes conservatives des domaines sont obtenues à l'aide d'un solveur de programme linéaire mixte (MILP) appliquées à des linéarisations conservatives de ces relaxations. Les résultats préliminaires sont prometteurs et montrent que cette approche peut effectivement accélérer les filtrages par consistances locales