Application problems can often not be solved adequately by numerical algorithms as several difficulties might arise at the same time. When developing and improving algorithms which hopefully allow to handle those difficulties in the future, good test instances are required. These can then be used to…
Set-optimization has attracted increasing interest in the last years, as for instance uncertain multiobjective optimization problems lead to such problems with a set- valued objective function. Thereby, from a practical point of view, most of all the so-called set approach is of interest. However, optimality…
Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are…
For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which…
In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. As these vector optimization problems are not only of interest in applications but also mathematical challenging,…
DOMINATING SET remains NP-complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.