Journal of Classification 11:209-232 (1994) A Tree 9 A Window 9 A Hill; Generalization of Nearest- Neighbor Interchange in Phylogenetic Optimization

The method of nearest-neighbor interchange effects local improvements in a binary tree by replacing a 4-subtree by one of its two alternatives if this improves the objective function. We extend this to k-subtrees to reduce the number of local optima. Possible sequences of k-subtrees to be examined are produced by moving a window over the tree, incorporating one edge at a time while deactivating another. The direction of this movement is chosen according to a hill-climbing strategy. The algorithm includes a backtracking component. Series of simulations of molecular evolution data/parsimony analysis are carded out, for k = 4 . . . . ,8, contrasting the hill-climbing strategy to one based on a random choice of next window, and comparing two stopping rules. Increasing window size k is found to be the most effective way of improving the local optimum, followed by the choice of hill-climbing over the random strategy. A suggestion for achieving higher values of k is based on a recursive use of the hill-climbing strategy.