Estimating the number of solutions on cardinality constraints

Abstract : The main asset of constraint programming is its wide variety of algorithms that comes from the major areas of artificial intelligence, logic programming and operational research. It offers specialists a limitless range of possible configurations to tackle combinatorial problems, but it becomes an obstacle to the wider diffusion of the paradigm. The current tools are very far from being used as a black-box tool, and it assumes a good knowledge of the field, in particular regarding the parametrization of solvers.In this thesis, we propose to analyze the behavior of cardinality constraints with probabilistic models and counting tools, to automatically parameterize constraint solvers: heuristics of choice of variables and choice of values and search strategies.
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Giovanni Christian Lo Bianco Accou. Estimating the number of solutions on cardinality constraints. Combinatorics [math.CO]. Ecole nationale supérieure Mines-Télécom Atlantique, 2019. English. ⟨NNT : 2019IMTA0155⟩. ⟨tel-02408009⟩

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