High Dimensional Many Objective Optimisation through Diverse Creation and Categorisation of Reference Vectors

Predefined reference vectors (RVs) are utilised in decomposition-based algorithms to solve many-objective optimisation problems (MaOPs). Two commonly used creation methods are those proposed by Das and Dennis and Deb and Jain. The former method generates many RVs at lower-order boundaries to create sufficient RVs in the intermediate area. The latter solves this challenge by adopting a layered creation of RVs but often fails in creating RVs on higher-order boundaries. To address these challenges, RVs in this study proposed to be created and categorised in clusters in the intermediate area of the m-dimensional space and the boundaries of various kinds independently. Diverse combinations of RV groups, with a manageable number of vectors each, can be utilised in optimisation. Pareto front in various subregions can be investigated with the desired number of approximations. A separate analysis in each subregion can be performed if needed. The approximations can be combined to form the final PF. The method is readily implemented into existing decomposition-based MaOP algorithms.