Research

My research interests are in operations research, combinatorial optimization, mathematical programming, graph theory, and algorithm complexity. These branches of optimization have undergone considerable development over the past three decades. Several methods developed in them have proven effective in modeling, analyzing, and approaching combinatorial problems (whose underlying structure is generally a graph) from various fields such as transportation, production, telecommunications, biology, etc. In particular, polyhedral techniques in combinatorial optimization have been successfully used to solve difficult (NP-hard) problems. They now constitute the basic tool for the practical resolution of these problems. These methods make it possible to reduce a combinatorial optimization problem to the resolution of a linear program by the complete description of the polyhedron of solutions by a system of linear inequalities. Such a description is generally difficult to obtain. However, a partial characterization of the polyhedron, used within the framework of a Branch & Cut (Branch & Bound) method, can sometimes be sufficient to optimally solve the problem. Indeed, these approaches have made it possible in recent years to solve previously intractable large-scale problems, such as the famous traveling salesman problem. They have also been effectively applied to solve practical operations research problems such as routing problems and telecommunications network design problems.
My work falls within this line of research. It concerns the modeling and polyhedral and algorithmic study of operations research and combinatorial optimization problems, the development of Branch & Cut-type solution methods for these problems, and the implementation of these methods.