Configuration automatique d’un solveur générique intégrant des techniques de décomposition arborescente pour la résolution de problèmes de satisfaction de contraintes

Abstract : Constraint programming integrates generic solving algorithms within declarative languages based on constraints : these languages allow us to describe combinatorial problems as a set of variables which have to take their values in domains while satisfying constraints. Numerous real-life problems can be modelled in such a way, as for instance, planification problems, scheduling problems, . . . These problems are NP-complete in the general case of finite domains. We introduce in this work a generic solving algorithm parameterized by : — a strategy for exploring the search space, to be chosen from the following six, chronological backtracking, conflict directed backjumping, conflict directed backjumping with reordering, dynamic backtracking, decision repair, and backtracking with tree decomposition ; — a variable ordering heuristic, to be chosen from the following two, min-domain/ddeg and min-domain/wdeg ; — a constraint propagation technique, to be chosen from the following two, forward checking and maintaining arc consistency. Thus, this algorithm leads to 24 different configurations ; some corresponding to already known algorithms, others being new. These 24 configurations have been com- pared experimentally on a benchmark of more than a thousand instances, each configuration being executed several times to take into account the non-determinism of the executions, and a statistical test has been used to compare performances. This experimental evaluation allowed us to better understand the complementarity of the different solving mechanisms, with a focus on the ability to exploit the structure of the instances to speed up the solving process. We identify 13 complementary configurations such that every instance of our benchmark is well solved by at least one of the 13 configurations. A second contribution of this work is to introduce a selector able to choose automatically the best configuration of our generic solver for each new instance to be solved : we describe each instance by a set of features and we use machine learning techniques to build a model to choose a configuration based on these features. Knowing that the learning process is generally harder when there are many configurations to choose from, we state the problem of choosing a subset of configurations that can be picked as a set covering problem and we compare two criterion : the first one aims to maximize the number of instances solved by at least one configuration and the second one aims to maximize the number of instances for which there is a good configuration available. We show experimentally that the second strategy obtains generally better results and that the selector obtains better performances than each of the 24 initial configurations.
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Loïc Blet. Configuration automatique d’un solveur générique intégrant des techniques de décomposition arborescente pour la résolution de problèmes de satisfaction de contraintes. Intelligence artificielle [cs.AI]. INSA de Lyon, 2015. Français. ⟨NNT : 2015ISAL0085⟩. ⟨tel-01214086v2⟩

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