Okay, but the problem is that you are asking for a single maximised cluster. But by my logic, (and the references I've looked at for 'clustering algorithms'), suggest that that doesn't make much sense, without some heuristic that allows you to exclude a value and improve the 'score' of what remains. Otherwise the best single cluster is the one that contains everything.

For example, this footnote from step 4 of the algorithm description here:

(*) Of course there is no point in having all the N items grouped in a single cluster but, once you have got the complete hierarchical tree, if you want k clusters you just have to cut the k-1 longest links.