Generalization of HSO algorithm for computing hypervolume for multiobjective optimization problems

A frame of GHSO (generalization of HSO) algorithm is proposed in this paper. One case of the GHSO is HSO (Hypervolume by Slicing Objectives) for computing hypervolume. Another two new cases are CHSO (contribution of a point to the hypervolume by slicing objective) and DHSO (contribution of a point to the hypervolume of deleted set by slicing objective), which are for computing the contribution of a point to the whole hypervolume under different conditions. Compared with the performance of LAHC (Lebesgue Archiving Hillcimber), the CHSO is improved significantly. Thus the CHSO will enable the use of hypervolume as a diversity mechanism with larger population in more objectives.