L2R: Learning to Reduce Search Space for Generalizable Neural Routing Solver

2025-03-05

AI Summary

Existing neural combinatorial optimization (NCO) methods exhibit poor generalization to large-scale routing problems, primarily due to high computational complexity and insufficient modeling of structural patterns. To address this, we propose a learnable search-space reduction mechanism that dynamically selects high-potential candidate nodes at each step of constructive neural solving. Our core contribution is a trainable, adaptive candidate selection model—replacing fixed heuristic constraints—with deep priority modeling of nodes, reinforcement learning–driven constructive decisions, and distributionally robust training. Trained solely on 100-node uniformly distributed instances, our method generalizes across scales: to million-node uniform instances and over 80,000-node instances under diverse spatial distributions. On TSP and CVRP benchmarks, it achieves state-of-the-art solution quality and inference efficiency.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant challenges in generalizing to large-scale problems due to high computational complexity and inefficient capture of structural patterns. To address this issue, we propose a novel learning-based search space reduction method that adaptively selects a small set of promising candidate nodes at each step of the constructive NCO process. Unlike traditional methods that rely on fixed heuristics, our selection model dynamically prioritizes nodes based on learned patterns, significantly reducing the search space while maintaining solution quality. Experimental results demonstrate that our method, trained solely on 100-node instances from uniform distribution, generalizes remarkably well to large-scale Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) instances with up to 1 million nodes from the uniform distribution and over 80K nodes from other distributions.

Problem

• Reduces search space in neural combinatorial optimization
• Improves generalization to large-scale routing problems
• Dynamically selects promising nodes using learned patterns

Innovation

• Learning-based search space reduction method
• Dynamic node prioritization via learned patterns
• Generalizes to large-scale TSP and CVRP instances