A Fast Heuristic for Stochastic Steiner Tree Problems

TL;DR

This work shows how to leverage an existing STP heuristic in building a novel method for solving its stochastic variant, the SSTP, with considerably faster computation times.

Abstract

Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem, there are considerably more state-of-the-art heuristics for its deterministic variant, the Steiner Tree Problem (STP). In this work, we show how to leverage an existing STP heuristic in building a novel method for solving its stochastic variant, the SSTP. This approach is a powerful, yet simple and easy-to-implement way of solving this complex problem. We test our method using benchmark instances from the literature. Numerical results show considerably faster computation times compared to the state-of-the-art, with a gap of approximately 5%.

Figures (6)

• Figure 1: First stage.
• Figure 2: 2nd stage, $s=1$.
• Figure 3: 2nd stage, $s=2$.
• Figure 4: Optimal solution.
• Figure 6: Instance.