Cost-based filtering algorithms for a Capacitated Lot Sizing Problem and the Constrained Arborescence Problem

Constraint Programming (CP) is a paradigm derived from artificial intelligence, operational research, and algorithmics that can be used to solve combinatorial problems. CP solves problems by interleaving search (assign a value to an unassigned variable) and propagation. Constraint propagation aims at removing/filtering inconsistent values from the domains of the variables in order to reduce the search space of the problem. In this thesis, we develop filtering algorithms for two complex combinatorial optimization problems: a Capacitated Lot Sizing Problem (CLSP) and the Constrained Arborescence Problem (CAP). Each of these problems has many variants and practical applications.