Gap-free computation of Pareto-points by quadratic scalarizations
The paper deals with a multicriteria optimum design method where several objectives have to be minimized simultaneously. For these kind of problems, approximation of the whole solution set are of particular importance to decision makers. Usually, approximating this set involves solving a family of parametrized optimization problems. It was the aim of this paper to argue in favour of parameterised quadratic objective functions, in contrast to a standard weighting approach in which parametrised linear objective functions was used. These arguments were rest on the favourable numerical properties of these quadratic scalarizations, which were investigated in detail. Moreover, it was shown which parameter sets can be used to recover all solutions of an original multicriteria problem where the ordering in the image space was induced by an arbitrary convex cone. The paper is addressed to researches and engineers working in the area of Pareto optimization.
scientific article; zbMATH DE number 2101618