Novel Presolving Techniques for the Connected Facility Location Problem

We consider the connected facility location problem (ConFLP), a useful model in telecommunication network design. First we introduce the extended connected facility location problem which generalizes the ConFLP by allowing pre-opened and pre-fixed facilities. This new concept is advantageous for applying complex sequences of reduction tests. By such an analysis of the solution space we anticipate solution dependencies in favor of following optimization methods. Besides transferring existing techniques designed for the facility location problem, the Steiner tree problem and the group Steiner tree problem, specific new reduction methods are introduced. The presented concepts based on graph theoretic formulations are also of theoretical interest. Additionally, we propose an efficient self-adaptive presolving strategy based on test dependencies and test impacts respectively. A computational study shows that the number of edges could be reduced up to 85% and the number of nodes up to 36% respectively on instances from the literature.