In the paper (p. 3) and the slides presents the formulation of the Steiner problem on graphs via so called Steiner cuts. But according to the definition, the number of Steiner cuts and so the number of constraints grows exponentially with the number of vertices in the graph.
First question: How to solve the problem in this cut-formulation? After all, we have too many constraints? For example, to solve the problem in the formulation through the multi-commodity flow described in the first article, we have only 'number of terminals' * 'number of vertices' constraints, and this can be solved.
Second question: Is there any practical benefit to solve the LP-relaxed problem, and then improve it with metaheuristics? Or is it the same to build a first Steiner tree aproximation with a greedy algorithm and then improve it?