A Bi-Criteria Approach for Steiner’s Tree Problems in Communication Networks

In this paper, an improved version of a previously proposed heuristic that finds ‘good’ compromise solutions for a bi-criteria Steiner trees problem is presented. This bi-criteria formulation of the Steiner’s tree problem is well suited for application in telecommunication networks whenever it is important to find the minimum amount of resources to connect a given subset of network nodes. In fact there are some (additive) metrics that may not lead to a tree with the minimum number of Steiner nodes when used in the single criterion Steiner’s tree problem. In this case it can be advantageous to consider also the minimisation of the hop count as a second criteria in the problem formulation. The performance of the new heuristic is evaluated and compared with the previous version by recurring to reference networks from a library of Steiner’s tree problems.