Algorithms for degree-constrained Euclidean Steiner minimal tree

A new problem of degree-constrained Euclidean Steiner minimal tree is discussed,which is quite useful in several fields.Although it is slightly different from the traditional degree-constrained minimal spanning tree,it is aho NP-hard.Two intelligent algorithms are proposed in an attempt to solve this difficult problem.Series of numerical examples are tested,which demonstrate that the algorithms also work well in practice.