Extending the Delaunay triangulation based density measurement to many-objective optimization

This paper investigates the scalability of the Delaunay triangulation (DT) based diversity preservation technique for solving many-objective optimization problems (MaOPs). Following the NSGA-II algorithm, the proposed optimizer with DT based density measurement (NSGAII-DT) determines the density of individuals according to the DT mesh built on the population in the objective space. To reduce the computing time, the population is projected onto a plane before building the DT mesh. Experimental results show that NSGA-II-DT outperforms NSGA-II on WFG problems with 4, 5 and 6 objectives. Two projection strategies using a unit plane and a least-squares plane in the objective space are investigated and compared. Our results also show that the former is more effective than the latter.