Learning to Reduce Search Space for Generalizable Neural Routing Solver

TL;DR

This work introduces Learning to Reduce (L2R), a reinforcement learning based framework that adaptively reduces the search space in constructive neural routing solvers. By combining static graph pruning with a lightweight embedding and attention based reduction plus a local solution constructor, L2R achieves scalable generalization to large scale TSP and CVRP instances while maintaining solution quality. Extensive experiments show strong cross size and cross distribution generalization, with state of the art performance among neural solvers on up to 1 million nodes, and practical speed advantages over classical solvers on large instances. The approach addresses fundamental limitations of distance based SSR by leveraging learned patterns to select promising candidate nodes, enabling robust real world routing applications.

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.

Figures (7)

• Figure 1: Different Search Space Reduction (SSR) Methods: (a) Static Search Space Reduction prunes the whole search space only once at the beginning of optimization process; (b) Dynamic Search Space Reduction reduces the search space to a small set of candidate nodes based on the distance to the last visited node at each construction step; (c) Learning to Reduce (Ours) builds reinforcement learning based model to adaptively reduce the search space and then select the next node for solution construction.
• Figure 2: Impacts of distance-based search space reduction on solution optimality. (a)-(d) Optimal solutions for TSP1K instances under four distribution patterns: uniform, cluster, explosion, and implosion. Restricting the search space to the k-nearest neighbors ($k = 20$) will lead to suboptimal routes. The red, green, and blue nodes indicate the current node, the next visiting node, and $k$ nearest neighbors, respectively.
• Figure 3: The pipeline of our proposed L2R framework for solving large-scale vehicle routing problem instances.
• Figure 4: The effect of distance-based search space reduction on the gap in diverse constructive NCO architectures (Left: LEHD luo2023lehd; Right: POMO kwon2020pomo). Here $\Delta Gap=Gap_{\text{reduced}}-Gap_{\text{original}}$.
• Figure 5: The solution visualizations of TSPLIB instances under different levels of search space. All solutions are obtained by the LKH-3 algorithm LKH3.