Solving the Steiner Tree Problem in Graphs using Physarum-inspired Algorithms

TL;DR

This paper introduces two Physarum-inspired algorithms for solving the Steiner Tree Problem in Graphs, demonstrating their effectiveness and efficiency on various instances, outperforming some existing methods in accuracy and scalability.

Contribution

The paper presents novel Physarum-inspired algorithms specifically designed for the Steiner Tree Problem, with experimental validation showing improved accuracy and scalability over traditional heuristics.

Findings

First PA achieves 0.19% average error on hundreds-vertex instances.

Second PA finds solutions with 3.69% average error on large instances.

PAs outperform some existing algorithms in accuracy and speed on benchmark problems.

Abstract

Some biological experiments show that the tubular structures of Physarum polycephalum are often analogous to those of Steiner trees. Therefore, the emerging Physarum-inspired Algorithms (PAs) have the potential of computing Steiner trees. In this paper, we propose two PAs to solve the Steiner Tree Problem in Graphs (STPG). We apply some widely-used artificial and real-world VLSI design instances to evaluate the performance of our PAs. The experimental results show that: 1) for instances with hundreds of vertices, our first PA can find feasible solutions with an average error of 0.19%, while the Genetic Algorithm (GA), the Discrete Particle Swarm Optimization (DPSO) algorithm and a widely-used Steiner tree approximation algorithm: the Shortest Path Heuristic (SPH) algorithm can only find feasible solutions with an average error above 4.96%; and 2) for larger instances with up to tens of thousands of vertices, where our first PA, GA and DPSO are too slow to be used, our second PA can find feasible solutions with an average error of 3.69%, while SPH can only find feasible solutions with an average error of 6.42%. These experimental results indicate that PAs can compute Steiner trees, and it may be preferable to apply our PAs to solve STPG in some cases.