Destroy and Repair Using Hyper Graphs for Routing

TL;DR

This paper introduces a novel destroy-and-repair framework using hyper-graphs for neural combinatorial optimization, significantly improving routing solutions for large-scale TSP and CVRP problems.

Contribution

It presents the DRHG framework that extends neighborhood search capabilities by leveraging hyper-graphs, enabling better solutions for large and real-world routing problems.

Findings

Achieves state-of-the-art results on TSP with up to 10,000 nodes.

Demonstrates strong generalization to real-world TSP and CVRP datasets.

Outperforms existing iterative methods in solution quality.

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.