My research area is multi-objective optimization for (especially) discrete problems. My dissertation work investigated several methodological aspects of this subject with the idea of handling situations not limited to the bi-objective case. In particular, the efficient representation of the search region, i.e. the part of the objective space not dominated by a given set of feasible points, is not a trivial task beyond the bi-objective case. It is nevertheless crucial since it is used in many exact and approximate iterative solution methods to locate remaining Pareto optimal points. I bridged this subject with the state-of- the-art in Computational Geometry, studied some properties of the representation of the search region by local bounds and proposed a new approach to compute these bounds. Besides, I considered the whole solution process and proposed to hybridize Branch&Bound and ranking or k-best algorithms to propose a new method to solve multi-objective combinatorial optimization problems. This method was instantiated on the multiobjective minimum spanning tree problem and much work was dedicated to the efficient implementation, espe cially regarding algorithms and data structures specific to the problem, and testing of the method.
My current research projects focus on exploiting the studied properties of the search region to (1) define and exploit a neighborhood structure on the search region to increase in certain cases the efficiency of its update and (2) propose a new practically and theoretically efficient approach to compute the hypervolume indicator, a widely used measure to compare the quality of approximations of the Pareto front. More generally, my interests for future research project concern exact and approximation algorithms with a priori guarantee, algorithmic and complexity aspects of metaheuristics and evolutionary algorithms, relations between computational geometry and multi-objective optimization, and taking into account multiple conflicting objectives in decision problems.