  NSGA-II and NSGA-III are two of the most popular evolutionary multi-objective
algorithms used in practice. While NSGA-II is used for few objectives such as 2
and 3, NSGA-III is designed to deal with a larger number of objectives. In a
recent breakthrough, Wietheger and Doerr (IJCAI 2023) gave the first runtime
analysis for NSGA-III on the 3-objective OneMinMax problem, showing that this
state-of-the-art algorithm can be analyzed rigorously. We advance this new line
of research by presenting the first runtime analyses of NSGA-III on the popular
many-objective benchmark problems mLOTZ, mOMM, and mCOCZ, for an arbitrary
constant number $m$ of objectives. Our analysis provides ways to set the
important parameters of the algorithm: the number of reference points and the
population size, so that a good performance can be guaranteed. We show how
these parameters should be scaled with the problem dimension, the number of
objectives and the fitness range. To our knowledge, these are the first runtime
analyses for NSGA-III for more than 3 objectives.
