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...

This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously considering α-approximations for all closed convex...

We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for multiobjective maximization problems, only...

We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for multiobjective maximization problems, only...

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...

We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or negative. We present the first fully polynomial-time...