Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs

Filip Rydin, Attila Lischka, Jiaming Wu, Morteza Haghir Chehreghani, Balázs Kulcsár

TL;DR

Two graph neural network-based methods to address multi-objective routing on multigraphs by operating directly on the multigraph by autoregressively selecting edges until a tour is completed are proposed.

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.

Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs

TL;DR

Two graph neural network-based methods to address multi-objective routing on multigraphs by operating directly on the multigraph by autoregressively selecting edges until a tour is completed are proposed.

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.

Paper Structure

This paper contains 44 sections, 1 theorem, 27 equations, 7 figures, 17 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Learning for Routing
  4. Routing on Multigraphs
  5. Problem Formulation
  6. GNN-Based Multigraph Solver
  7. Edge-Based GMS
  8. Dual Head GMS
  9. Training Algorithm
  10. Experimental Studies
  11. Performance on Benchmark Problems
  12. Zero-Shot Generalization
  13. A Difficult Multigraph Problem
  14. Conclusion
  15. Extended Related Work
  16. ...and 29 more sections

Key Result

Proposition 1

Let $f_\lambda(\pi)$ denote the linearly scalarized cost and let $\Pi(\lambda) \subset \Pi$ be the set of feasible tours on the pruned graph $G(\lambda)$. Then, the optimal value of the scalarized subproblem is preserved:

Figures (7)

  • Figure 1: Edge-based GMS and its most important components.
  • Figure 2: Dual head GMS and its most important components
  • Figure 3: Two possible graph transformations to convert multigraphs into simple graphs. For simplicity, we show both transformations on a graph that is not fully connected.
  • Figure 4: MatNet-Based Model (MBM).
  • Figure 5: HV as percentage of best performance for models during training. GMS-EB and GMS-DH reach close to their final performance quickly and are more sample-efficient than MBM.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Proposition 1