3.1 Improvements
In order not to waste time on calculating the UpDown
matrix always from scratch when evaluating a neighbor solution,
we derived incremental update schemes for all the
neighborhood structures. Only eventually aected parts of
the UpDown matrix are eciently updated. This strategy
greatly improves the overall run-time. Unfortunately, it does
not seem to be possible to follow this idea further by also
calculating the UpDown distance and the TreeRank score itself
in a signicantly more ecient incremental way. Thus,
these calculations are always completely performed. A second
improvement we consider is to avoid unnecessary moves
that would result in the original tree again: swapping two
adjacent taxa or moving a taxon or subtree to the same relative
position. In this way some calculations of the TreeRank
score can be saved.
4. VNS WITH EMBEDDED VND
A detailed introduction to Variable Neighborhood Descent
(VND) and Variable Neighborhood Search (VNS) is shown
in [12]. The idea of VND is to extend simple local search by
using several neighborhood structures|typically ordered according
to increasing size or evaluation cost|and switching