Evolutionary many-objective optimisation: Many once or one many?

Multi-objective evolutionary algorithms are widely established and well developed for problems with two or three objectives. However, it is known that for many-objective optimisation, where there are typically more than three objectives, the algorithms applying Pareto optimality as a ranking metric may loose their effectiveness. This paper compares three different approaches to generating Pareto surfaces on both multi and many objective problems. The first approach is using an established Pareto ranking method (NSGA II), the second combines multiple single objective optimisations in a single run (MSOPS), and the third uses multiple runs of a single objective optimiser. The results demonstrate that much can be gained by generating the entire Pareto set in a single run, when compared to repeated single objective optimisations. It is also clear that NSGA II loses its effectiveness as the problem dimensionality increases - it is more effective to use many single objective optimisations than a Pareto-ranking based optimiser on many-objective problems. Ultimately though, "many once or once many" is dependent on algorithm choice, not problem scale