In this paper, the author uses CH (Caliński–Harabasz index) and SIL (Silhouette index) methods to decide the number of clusters. However, instead of selecting the highest values, it applies a L-method on these index, choosing its knee (elbow) points.
In this link there are many subquestions, in which one is about why the authors use the maximal 'stability' of CH to define the number of clusters. However, there wasn't a answer for this subquestion that has explained that decision.
The maximal 'stability' on that question is related with the L-method as they chose points where the changes start to be the smallest.
What could be the reason for using the L-method (or the maximal stability) with CH and SIL indexes, which usually are wanted to me maximized? (I would understand if they would be using the within sum of squares, for instance)