Reference Points Generated on Unit Hypersurfaces for MaOEAs

This paper proposes a method to uniformly generate reference points on a hypersurface for many-objective optimization evolutionary algorithms (MaOEAs). Recently, MaOEAs have been proposed to obtain selection pressure in a multidimensional objective space by using a reference point set, but there is no method for generating a reference point set that is supposed to incorporate user orientation. This paper proposes a method for generating uniform reference points on unit hyperspheres and unit hyperplanes in a multidimensional objective space. The proposed method is applied to the multi-objective genetic programming (GP) problem by non-dominated sorting genetic algorithm-III (NSGA-III) and to the multi-objective combinatorial optimization problem by multiobjective evolutionary algorithm based on decomposition (MOEA/D). As a result, we confirm that the proposed method gives non-inferior results compared to conventional methods. Since the proposed method can easily incorporate user orientation, this shows the effectiveness of the proposed method.