Experiments with graph convolutional networks for solving the vertex $p$-center problem

TL;DR

This paper explores the application of graph convolutional networks to the vertex p-center problem, highlighting challenges in transferability from similar problems like TSP and proposing PCP as a new benchmark for GCN development.

Contribution

The study investigates adapting GCN models from TSP to PCP, revealing difficulties and suggesting PCP as a new benchmark for GCN research in combinatorial optimization.

Findings

Direct transfer of TSP-based GCN models to PCP is ineffective.

PCP presents unique challenges due to its min-max objective and symmetry.

PCP could serve as a new benchmark for GCN advancements.

Abstract

In the last few years, graph convolutional networks (GCN) have become a popular research direction in the machine learning community to tackle NP-hard combinatorial optimization problems (COPs) defined on graphs. While the obtained results are usually still not competitive with problem-specific solution approaches from the operations research community, GCNs often lead to improvements compared to previous machine learning approaches for classical COPs such as the traveling salesperson problem (TSP). In this work we present a preliminary study on using GCNs for solving the vertex p-center problem (PCP), which is another classic COP on graphs. In particular, we investigate whether a successful model based on end-to-end training for the TSP can be adapted to a PCP, which is defined on a similar 2D Euclidean graph input as the usually used version of the TSP. However, the objective of the PCP has a min-max structure which could lead to many symmetric optimal, i.e., ground-truth solutions and other potential difficulties for learning. Our obtained preliminary results show that indeed a direct transfer of network architecture ideas does not seem to work too well. Thus we think that the PCP could be an interesting benchmark problem for new ideas and developments in the area of GCNs.