Dual-Core AMD Opteron 2214 PC with 4GB RAM. The best performing (pure) EA from [4] has been reimplemented as proposed in this original work and described in Section 5.
7.1 Algorithms Settings
The population size of the EA and MA was set to 100. In the MA local search is applied to all new incumbent solutions until 100 consecutive non-improving moves have been tried. Due to space limitations, we present here only results for the MA with simple progressive search, which proved to generally outperform the variants where only a single neighborhood structure is considered. As mentioned earlier,the initial solution for the standalone VNS is the tree with highest TreeRank score of the input collection. HybB is performing the VND on all new incumbents limiting runtime per call to at most 5% of the overall time limit. In case of HybS the EA and the VNS are given 50% of the computation time each, thus it basically corresponds to HybI1.The intertwined EA/VNS hybrid HybI was applied with = 4 alterations, thus in the following denoted by HybI4.For Hyb I we basically combine the settings of the best performing MA with SPS and of HybI4 and call it Hyb
I4.7.2 Test Instances We test the algorithms on three types of instances:trees resulting from three simple agglomerative clusterings (single-link and complete-link [14] as well as average-link,also known as unweighted pair group method with arithmetic mean [21]), trees resulting from several runs of the scatter search approach in [5], and new articial trees. The
latter are created by generating one initial random tree and deriving the actual input trees out of it by copying it and
applying a series of perturbations in the neighborhoods described in Section 3: Random Step, Swap, Rotate, and SPRr
moves are equally likely performed. In order to be able to control the similarity of the resulting input trees in a good
way, we dened minimum and maximum pairwise TreeRank scores and performed the perturbations until a derived tree
achieves a pairwise score w.r.t. the initial tree within these limits. If the actual score is less than the lower bound, the
previous move is undone and the process continues. Note that the initial tree is nally discarded and not included in
the input tree collection. A schematic presentation of this process is shown in Figure 7. An advantage of these arti-
cially generated instances is that the known initial tree,although not necessarily the best possible consensus tree,
lends itself as a reference solution.