Un schéma générique d'algorithmes énumératifs avec (no)good recording pour la résolution bornée de CSP

Ce papier présente un schéma générique d'algorithmes énumératifs pour la résolution de CSP. Ce schéma exploite des propriétés sémantiques et topologiques du réseau de contraintes afin de produire des goods et des nogoods. Il repose sur un ensemble de séparateurs du graphe de contraintes et plusieurs fonctions et procédures paramétrables de sorte à exploiter des heuristiques, des méthodes de filtrage, des techniques de retour en arrière intelligent, d'enregistrement de nogoods classiques ou de (no)goods structurels et des bornes de complexité théorique héritées des méthodes basées sur les décompositions de graphes. Selon les choix effectués, nous obtenons une famille d'algorithmes dont la complexité en temps est comprise entre $O(exp(w+1))$ et $O(exp(n))$ avec $w$ la largeur d'arbre du graphe de contraintes et $n$ le nombre de variables

Dynamic Heuristics for Backtrack Search on Tree-Decomposition of CSPs

This paper deals with methods exploiting tree-decomposition approaches for solving constraint networks. We consider here the practical efficiency of these approaches by defining five classes of variable orders more and more dynamic which preserve the time complexity bound. For that, we define extensions of this theoretical time complexity bound to increase the dynamic aspect of these orders. We define a constant k allowing us to extend the classical bound from O(exp(w + 1)) firstly to O(exp(w + k + 1)), and finally to O(exp(2(w + k+1)−s −)), with w the ”tree-width ” of a CSP and s − the minimum size of its separators. Finally, we assess the defined theoretical extension of the time complexity bound from a practical viewpoint

Stochastic Constraint Programming

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial Intelligenc

Managing Complex Scheduling Problems with Dynamic and Hybrid Constraints.

The task of scheduling can often be a difficult one because of the inherent complexity of real-world problems. In the field of Artificial Intelligence, many representations and algorithms have been developed to automate the scheduling process. Many state of the art scheduling systems deal with this complexity by making assumptions that simplify the algorithms, but in doing so, miss some opportunities to improve performance. Scheduling problems are temporal in nature, and so they often contain constraints that change over time. Many scheduling systems assume that the problems they are solving are all independent, and so they ignore the similarities between subsequent sets of scheduling constraints. Additionally, scheduling problems often contain a mixture of finite-domain and temporal constraints. Many of the systems that can solve problems of this type do so by creating finite-domain variables to represent the constraints, but then ignore the distinction between the different types of variables when searching for a solution. In this dissertation, I identify opportunities to improve performance by exploiting structure where it has previously been overlooked. Following this approach, I develop a set of techniques that apply to a wide variety of situations that can arise in real-world scheduling problems. First, I consider dynamic scheduling problems with constraints that change over time. To address such problems, I introduce a new representation called the Dynamic Disjunctive Temporal Problem, along with several techniques to improve both efficiency and stability when solving one. Second, I consider scheduling problems in which a mixture of finite-domain and temporal variables can interact through hybrid constraints. I introduce the Hybrid Scheduling Problem to represent such problems, and I present a set of techniques that capitalize on the distinction between variable types to improve efficiency across the problem space. Finally, I conclude by proposing several ways that the dynamic and hybrid representations and techniques can be combined. To compare many of the techniques presented throughout this dissertation in the context of structured, real-world problems, I use them to solve scheduling problems based on actual air traffic control constraints recorded from the Dallas/Fort Worth International Airport.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57625/2/pschwart_1.pd

Filtering, Decomposition and Search Space Reduction for Optimal Sequential Planning

International audienceWe present in this paper a hybrid planning system which combines constraint satisfaction techniques and planning heuris-tics to produce optimal sequential plans. It integrates its own consistency rules and filtering and decomposition mechanisms suitable for planning. Given a fixed bound on the plan length, our planner works directly on a structure related to Graphplan's planning graph. This structure is incrementally built: Each time it is extended, a sequential plan is searched. Different search strategies may be employed. Currently, it is a forward chaining search based on problem decomposition with action sets partitioning. Various techniques are used to reduce the search space, such as memorizing nogood states or estimating goals reachability. In addition, the planner implements two different techniques to avoid enumerating some equivalent action sequences. Empirical evaluation shows that our system is very competitive on many problems, especially compared to other optimal sequential planners

Quantum Computing and Phase Transitions in Combinatorial Search

We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem structure as used by classical backtrack methods to avoid unproductive search choices. This quantum algorithm is much more likely to find solutions than the simple direct use of quantum parallelism. Furthermore, empirical evaluation on small problems shows this quantum algorithm displays the same phase transition behavior, and at the same location, as seen in many previously studied classical search methods. Specifically, difficult problem instances are concentrated near the abrupt change from underconstrained to overconstrained problems.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl