Semi‐labeled unrooted binary tree optimization subject to nonnegativity

Let Dn×n denote the distance matrix of n objects, and let T be an unrooted binary tree in which the leaves denote those n objects. We want to find such a tree with the constraint that the edge weights are nonnegative where the distances between the leaves best estimate their corresponding values in D. Accordingly, we have adopted the residual sum of squares (RSS) criterion to minimize the discrepancy between the distance between leaves in the tree and their corresponding distance in D. For this optimization problem, we have designed an iterated local search (ILS) scheme based on the nearest neighbor interchange (NNI) operation to search the neighborhood.