Analyses of inverted generational distance for many-objective optimisation algorithms

Inverted generational distance is a widely used indicator for evaluating many-objective optimisation algorithms. In the past several years, numerous researchers have paid much attention to the improvement of many-objective optimisation algorithms, while few researchers have mathematically analysed inverted generational distance. In this paper, we present detailed mathematical analyses of inverted generational distance, and then reveal the relation between generational distance and inverted generational distance. The conclusion is drawn that convergence plays different roles in different stages. Experimental results on seven many-objective benchmark problems verify our analyses.