It is well known that, under very weak assumptions, multiobjective optimization problems admit (1+ε,⋯,1+ε)-approximation sets (also called ε-Pareto sets ) of polynomial cardinality (in the size of the instance and in 1ε). While an approximation guarantee of 1+εfor any ε0is the best one...

It is well known that, under very weak assumptions, multiobjective optimization problems admit (1+ε,⋯,1+ε)-approximation sets (also called ε-Pareto sets ) of polynomial cardinality (in the size of the instance and in 1ε). While an approximation guarantee of 1+εfor any ε0is the best one...

The goal of this thesis is to propose new general methods to get around the intractability of multi-objective optimization problems.First, we try to give some insight on this intractability by determining an, easily computable, upper bound on the number of nondominated points, knowing the number...

Graph Theory with path-breaking contributions on the theory of flows in networks and project scheduling, Multiple Criteria Decision Aiding with the invention of the family of ELECTRE methods and methodological contribution to decision-aiding which lead to the creation of Multi-Criteria Decision...

This thesis deals with several aspects related to solving multi-objective problems, without restriction to the bi-objective case. We consider exact solving, which generates the nondominated set, and approximate solving, which computes an approximation of the nondominated set with a priori...

We consider the the two-machine ow-shop serial-batching scheduling problem where the batches have limited size. Two criteria are considered here. The rst criterion is to minimize the number of batches. This criterion re ects situations where processing of any batch induces a xed cost, which...

Our aim in this thesis is to propose efficient algorithms for solving difficult combinatorial optimization problems. Our algorithms are based on a generic method of ordered enumeration. Initially, we describe the principle of ordered enumeration which consists in generating in a specific order...