An improved CHSO algorithm for multi-objective optimization problem

The CHSO algorithm is a fast algorithm for computing the contribution of a point to the hypervolume of the whole set directly. In this paper an improved CHSO is described. And it is explained by theory why not only the points in the first nondominated front, but also the points in the second nondominated front which are dominated only by one of points in the first nondominated front are considered in CHSO while the points in the first nondominated front are considered in HSO. It is shown by experiment that improved CHSO outperforms basic CHSO with reduction running time of approximately 50%. So improved CHSO can enable hypervolume to be used as diversity or selection mechanism more efficiently.