Iterated local search algorithms for the Euclidean Steiner tree problem in n dimensions

We propose algorithmic frameworks based on the iterated local search (ILS) metaheuristic to obtain good‐quality solutions for the Euclidean Steiner tree problem (ESTP) in n dimensions. This problem consists in finding a tree with minimal total length that spans p points given in an n‐dimensional Euclidean space and, eventually, also some additional points whose insertion contributes to reduce the total length of the tree. These ILS approaches make use of both the tree enumeration structure, called topology‐describing vector, and the exact minimization step of a well‐known branch‐and‐bound method for the ESTP. Computational results are provided.