Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs

TL;DR

This paper introduces two neural network-based methods for multi-objective routing on multigraphs, addressing a gap in existing approaches by handling multiple edges with distinct attributes, and demonstrates their effectiveness through extensive empirical evaluation.

Contribution

It presents novel neural routing models specifically designed for multigraphs, including a scalable pruning-based approach, filling a key gap in current routing methodologies.

Findings

Both models outperform traditional heuristics.

The pruning-based model achieves comparable results with higher scalability.

Models are effective across diverse graph types and problem settings.

Abstract

Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with distinct attributes between node pairs, despite their strong relevance in real-world scenarios. In this paper, we propose two graph neural network-based methods to address multi-objective routing on multigraphs. Our first approach operates directly on the multigraph by autoregressively selecting edges until a tour is completed. The second model, which is more scalable, first simplifies the multigraph via a learned pruning strategy and then performs autoregressive routing on the resulting simple graph. We evaluate both models empirically, across a wide range of problems and graph distributions, and demonstrate their competitive performance compared to strong heuristics and neural baselines.