A Fast Algorithm for Computing the Contribution of a Point to the Hypervolume

A fast algorithm, called the contribution of a point to the hypervolume by slicing objective (CHSO) algorithm, is presented for computing the contribution of a point to the hypervolume directly. It is based on the same idea as HSO algorithm by processing the objectives in a front one at a time, rather than the points one at a time as in LAHC algorithm. It is shown that CHSO is much faster than LAHC for randomly generated data and benchmark data in three to eight objectives. So CHSO will enable the use of hypervolume as a diversity mechanism with larger population in more objectives.