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Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problems

Yang Wang, Ya-Hui Jia, Wei-Neng Chen, Yi Mei

TL;DR

A distance-aware attention reshaping method, assisting neural solvers in solving large-scale vehicle routing problems without the need for additional training, utilizing the Euclidean distance information between current nodes to adjust attention scores.

Abstract

Neural solvers based on attention mechanism have demonstrated remarkable effectiveness in solving vehicle routing problems. However, in the generalization process from small scale to large scale, we find a phenomenon of the dispersion of attention scores in existing neural solvers, which leads to poor performance. To address this issue, this paper proposes a distance-aware attention reshaping method, assisting neural solvers in solving large-scale vehicle routing problems. Specifically, without the need for additional training, we utilize the Euclidean distance information between current nodes to adjust attention scores. This enables a neural solver trained on small-scale instances to make rational choices when solving a large-scale problem. Experimental results show that the proposed method significantly outperforms existing state-of-the-art neural solvers on the large-scale CVRPLib dataset.

Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problems

TL;DR

A distance-aware attention reshaping method, assisting neural solvers in solving large-scale vehicle routing problems without the need for additional training, utilizing the Euclidean distance information between current nodes to adjust attention scores.

Abstract

Neural solvers based on attention mechanism have demonstrated remarkable effectiveness in solving vehicle routing problems. However, in the generalization process from small scale to large scale, we find a phenomenon of the dispersion of attention scores in existing neural solvers, which leads to poor performance. To address this issue, this paper proposes a distance-aware attention reshaping method, assisting neural solvers in solving large-scale vehicle routing problems. Specifically, without the need for additional training, we utilize the Euclidean distance information between current nodes to adjust attention scores. This enables a neural solver trained on small-scale instances to make rational choices when solving a large-scale problem. Experimental results show that the proposed method significantly outperforms existing state-of-the-art neural solvers on the large-scale CVRPLib dataset.
Paper Structure (18 sections, 12 equations, 5 figures, 4 tables)

This paper contains 18 sections, 12 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Vehicle Routing Problem and Neural Combinatorial Optimization
  4. Related Works
  5. Proposed Method
  6. Attention Dispersion Analysis
  7. DAR Method
  8. Reinforcement Learning Training
  9. Experiments
  10. Datasets
  11. Training Setting
  12. Inference Setting
  13. Baselines
  14. Generalization Performance on CVRPLib
  15. Generalized performance details of CVRPLib Set-XXL
  16. ...and 3 more sections

Figures (5)

  • Figure 1: The distribution of attention scores when an NS trained on instances with 100 nodes tries to solve VRPs with 100 and 1000 nodes. Red points represents scores larger than -1.
  • Figure 2: The schematic diagrams of ELG and our model.
  • Figure 3: The emergence of attention dispersion when generalize an NS from small to large.
  • Figure 4: The pipeline of our model.
  • Figure 5: Case Ghent1 attention score.