Kriging model based many-objective optimization with efficient calculation of expected hypervolume improvement

The many-objective optimization performance of using expected hypervolume improvement (EHVI) as the updating criterion of the Kriging surrogate model is investigated, and compared with those of using expected improvement (EI) and estimation (EST) updating criteria in this paper. An exact algorithm to calculate hypervolume is used for the problems with less than six objectives. On the other hand, in order to improve the efficiency of hypervolume calculation, an approximate algorithm to calculate hypervolume based on Monte Carlo sampling is adopted for the problems with more objectives. Numerical experiments are conducted in 3 to 12-objective DTLZ1, DTLZ2, DTLZ3 and DTLZ4 problems. The results show that, in DTLZ3 problem, EHVI always obtains better convergence and diversity performances than EI and EST for any number of objectives. In DTLZ2 and DTLZ4 problems, the advantage of EHVI is shown gradually as the number of objectives increases. The present results suggest that EHVI will be a highly competitive updating criterion for the many-objective optimization with the Kriging model.