For the general case of dierent taxa sets in T1 and T2 see
[23]. The TreeRank score is thus a measure of the topological
relationships in T1 that are found to be the same or similar in
T2. It is bounded above by 100% but has no lower bound,
which can be shown by comparing perfectly balanced and
maximal unbalanced trees.
The rst metaheuristic approaches applied to the consensus
tree problem using the TreeRank measure have been
described by Cotta [4]. Therein several evolutionary algorithms
are presented diering in the way of whether applying
mutation or crossover and the adopted evolution model.
Tests on real-world instances indicate that solely applying
the well-known prune-delete-graft recombination operator
[16] in combination with a steady-state model performs best.
This recombination operator selects a subtree of the rst
parent at random, removes its leaves in the second parent
and grafts the subtree therein at a random position. Considering
subtrees as building blocks, they are well preserved,
inherited, and mixed by this operator. Although this operator
was shown to be more destructive to one parent than
to the other [20], it is the de facto standard when dealing
with phylogenetic trees in evolutionary algorithms in general.
The variants utilizing only mutation by scrambling
subtrees or swapping taxa turned out to be inferior. It is
further important to include the given input tree collection
T in the initial population, otherwise the results are signi
cantly worse. As tness function the average TreeRank
score of a candidate solution to the set of input trees is used: