Computing Gap Free Pareto Fronts

So far, we have discussed the archiver that stores all non-dominated solutions out of the set of candidate solutions, and two archivers that are entirely based on the concept of \(\epsilon \)-dominance. While the applicability of \(ArchiveUpdateP_Q\) is restricted since it stores too many points during the run of the search process, the opposite can happen for the two \(\epsilon \)-dominance based archivers. To see the latter, consider the extreme examples depicted in Fig. 7.1. Both sub-figures show Pareto fronts that contain flat parts and an “approximation” of this set that consists of three elements. Both approximations indeed form \(\epsilon \)-Pareto fronts for relatively small entries of \(\epsilon \) (compared to the length of the entire Pareto front).