A Fast Heuristic for Stochastic Steiner Tree Problems

TL;DR

This paper introduces a fast, heuristic-based method for solving the stochastic Steiner Tree Problem by leveraging existing deterministic heuristics, resulting in significantly faster solutions with minimal optimality gap.

Contribution

It presents a novel approach that adapts deterministic Steiner Tree heuristics to efficiently solve the stochastic variant, improving computation speed.

Findings

Faster computation times compared to existing methods.

Achieved approximately 5% optimality gap.

Effective on benchmark instances from literature.

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%.