A Robust and Scalable Algorithm for the Steiner Problem in Graphs

TL;DR

This paper introduces a robust, scalable heuristic for the Steiner Problem in Graphs, combining multistart strategies, elite solution merging, and a fast dual ascent implementation to improve solution quality and efficiency.

Contribution

It presents a novel heuristic integrating fast local searches and dual ascent techniques, enhancing robustness and scalability for solving the Steiner Problem in Graphs.

Findings

Competitive with previous methods in solution quality and runtime

Able to improve or match best published results on open instances

Effective for various graph classes and scalable with longer runs

Abstract

We present an effective heuristic for the Steiner Problem in Graphs. Its main elements are a multistart algorithm coupled with aggressive combination of elite solutions, both leveraging recently-proposed fast local searches. We also propose a fast implementation of a well-known dual ascent algorithm that not only makes our heuristics more robust (by quickly dealing with easier cases), but can also be used as a building block of an exact (branch-and-bound) algorithm that is quite effective for some inputs. On all graph classes we consider, our heuristic is competitive with (and sometimes more effective than) any previous approach with similar running times. It is also scalable: with long runs, we could improve or match the best published results for most open instances in the literature.