Hierarchical Convex Multiobjective Optimization by the Euclidean Reference Point Method

Abstract

In the present article convex multiobjective optimization problems with an arbitrary number of cost functions are considered. Since the weighted sum method has some deficiencies when it comes to approximating the Pareto front equidistantly, the Euclidean reference point method is investigated. However, for this method it is not clear how to choose reference points, i.e., the parameters in the scalarization function, guaranteeing a complete approximation of the Pareto front in the case of more than two cost functions. It is shown that by hierarchically solving subproblems of the original problem, it is possible to get a characterization of these reference points which is also numerically applicable independent of the number of cost functions. The resulting algorithm can thus be used for an arbitrary number of cost functions, which is shown in numerical tests for up to four cost functions.