The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

This paper investigates the Steiner Tree Problem with Delays (STPD), a variation of the classical Steiner Tree problem that arises in multicast routing. We propose an exact solution approach that is based on a polynomial-size formulation for this challenging NP-hard problem. The LP relaxation of this formulation is enhanced through the derivation of new lifted Miller–Tucker–Zemlin subtour elimination constraints. Furthermore, we present several preprocessing techniques for both reducing the problem size and tightening the LP relaxation. Finally, we report the results of extensive computational experiments on instances with up to 1000 nodes. These results attest to the efficacy of the combination of the enhanced formulation and reduction techniques.

► We consider the Steiner Tree Problem with Delays for multicast routing. ► We propose an exact solution approach using a polynomial-size formulation. ► We enhance the formulation with lifted MTZ subtour elimination constraints. ► We present preprocessing techniques. ► Computational results attest to the efficacy of the proposed solution method.