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Destroy and Repair Using Hyper Graphs for Routing

Ke Li, Fei Liu, Zhengkun Wang, Qingfu Zhang

TL;DR

The paper tackles large-scale routing problems by addressing limitations of existing neural combinatorial optimization methods. It introduces Destroy and Repair by Hyper-Graphs (DRHG), a framework that condenses destroyed segments into fixed hyper-edges, enabling learning on reduced hyper-graphs and enabling large-neighborhood search via a supervised repair process. DRHG combines a lightweight encoder with a multi-layer linear-attention decoder to predict the next node, trained with clustering-based destruction and distribution-aligned preprocessing. Empirical results show state-of-the-art performance on TSP up to 10K nodes and strong generalization to real-world TSPLib and CVRPLib instances, with competitive CVRP performance and robust applicability to large-scale problems. The work offers a scalable, generalizable approach to routing optimization that can extend to additional problems and destruction strategies in future research.

Abstract

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in this domain has explored two primary categories of methods: iterative and non-iterative. While non-iterative methods struggle to generate near-optimal solutions directly, iterative methods simplify the task by learning local search steps. However, existing iterative methods are often limited by restricted neighborhood searches, leading to suboptimal results. To address this limitation, we propose a novel approach that extends the search to larger neighborhoods by learning a destroy-and-repair strategy. Specifically, we introduce a Destroy-and-Repair framework based on Hyper-Graphs (DRHG). This framework reduces consecutive intact edges to hyper-edges, allowing the model to pay more attention to the destroyed part and decrease the complexity of encoding all nodes. Experiments demonstrate that DRHG achieves stateof-the-art performance on TSP with up to 10,000 nodes and shows strong generalization to real-world TSPLib and CVRPLib problems.

Destroy and Repair Using Hyper Graphs for Routing

TL;DR

The paper tackles large-scale routing problems by addressing limitations of existing neural combinatorial optimization methods. It introduces Destroy and Repair by Hyper-Graphs (DRHG), a framework that condenses destroyed segments into fixed hyper-edges, enabling learning on reduced hyper-graphs and enabling large-neighborhood search via a supervised repair process. DRHG combines a lightweight encoder with a multi-layer linear-attention decoder to predict the next node, trained with clustering-based destruction and distribution-aligned preprocessing. Empirical results show state-of-the-art performance on TSP up to 10K nodes and strong generalization to real-world TSPLib and CVRPLib instances, with competitive CVRP performance and robust applicability to large-scale problems. The work offers a scalable, generalizable approach to routing optimization that can extend to additional problems and destruction strategies in future research.

Abstract

Recent advancements in Neural Combinatorial Optimization (NCO) have shown promise in solving routing problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) without handcrafted designs. Research in this domain has explored two primary categories of methods: iterative and non-iterative. While non-iterative methods struggle to generate near-optimal solutions directly, iterative methods simplify the task by learning local search steps. However, existing iterative methods are often limited by restricted neighborhood searches, leading to suboptimal results. To address this limitation, we propose a novel approach that extends the search to larger neighborhoods by learning a destroy-and-repair strategy. Specifically, we introduce a Destroy-and-Repair framework based on Hyper-Graphs (DRHG). This framework reduces consecutive intact edges to hyper-edges, allowing the model to pay more attention to the destroyed part and decrease the complexity of encoding all nodes. Experiments demonstrate that DRHG achieves stateof-the-art performance on TSP with up to 10,000 nodes and shows strong generalization to real-world TSPLib and CVRPLib problems.

Paper Structure

This paper contains 32 sections, 12 equations, 7 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Non-iterative NCO Routing Solvers
  4. One-shot Constructive Solvers
  5. Heatmap-based Solvers
  6. Iterative NCO Routing Solvers
  7. Methodology
  8. DRHG Framework
  9. Hyper-graph Representation
  10. Model Structure
  11. Encoder
  12. Decoder
  13. Training Scheme
  14. Experiments
  15. Experiment Setup
  16. ...and 17 more sections

Figures (7)

  • Figure 1: Pipeline of Destroy-and-Repair using Hyper-Graphs
  • Figure 2: Model structure of DRHG
  • Figure 3: Non-optimal rate on 10k TSP100 instances
  • Figure 4: Linear attention module
  • Figure 5: Node emergence in hyper-graph following additional node destruction
  • ...and 2 more figures