Effects of the number of design variables on performances in Kriging-model-based many-objective optimization

The effects of the number of design variables on the optimization performances in Kriging-model-based many-objective optimizations, which use expected hypervolume improvement (EHVI), expected improvement (EI), and estimation (EST) as the criteria for updating the Kriging model, are investigated based on four independent performance metrics in this paper. Numerical experiments are conducted in 3 to 15-objective DTLZ1 and DTLZ7 problems. The results indicate that the advantages of EHVI over EI and EST are more obvious when the number of design variables increases, and EHVI is more suitable for the problems with a large number of design variables. In addition, the comparison results show that, EHVI obtains faster IGD reduction than EI and EST in most test problems. The advantage of EHVI over EI and EST is mainly shown on the convergence performance. The spread performance is better in both EHVI and EI considering estimation errors than EST without considering estimation errors. However, the uniformity of EHVI is weak, especially for the problems with a large number of objectives.