Neural Cluster First, Route Second: One-Shot Capacitated Vehicle Routing via Differentiable Optimal Transport

2026-05-09

AI Summary

This work addresses key limitations of existing neural combinatorial optimization methods for the Capacitated Vehicle Routing Problem (CVRP)—namely, sequential decoding bottlenecks, sensitivity to spatial symmetries, and poor out-of-distribution generalization—by introducing the first purely non-autoregressive, one-shot solution framework based on a “cluster-then-route” paradigm. The approach globally enforces fleet capacity constraints via a differentiable entropy-regularized optimal transport layer, integrates an exact assignment solver to produce high-quality solutions, and inherently eliminates three types of symmetry: E(2) spatial invariance, inter-route permutations, and intra-route traversal directions. Despite its lightweight architecture comprising only a single network layer, the method achieves a 2.73% optimality gap on standard benchmarks and maintains sub-4% gaps on out-of-distribution instances with up to 1,000 nodes, demonstrating significantly enhanced zero-shot generalization capability.

Abstract

The Capacitated Vehicle Routing Problem (CVRP) underpins modern last-mile logistics. Current Neural Combinatorial Optimization (NCO) methods construct CVRP solutions autoregressively, inheriting sequential decoding bottlenecks, sensitivity to spatial symmetries, and brittle out-of-distribution behavior. We revisit the classical Cluster-First-Route-Second (CFRS) paradigm -- long known to be asymptotically optimal but largely overlooked by NCO -- and argue that it is structurally aligned with the core strengths of deep learning: similarity and assignment over global context, rather than the construction of long sequential tours. We introduce Neural CFRS, the first purely non-autoregressive one-shot neural CFRS framework for the CVRP. It enforces global fleet-capacity constraints end-to-end via a differentiable entropic Optimal Transport layer, producing a continuous transport plan to sparsify an exact capacitated assignment solver. We provide formal theoretical guarantees that our architecture intrinsically abstracts away $E(2)$ spatial, inter-route permutation, and intra-route traversal symmetries. By equipping the framework with a pre-trained spatial vocabulary, we unlock extreme parameter efficiency and zero-shot scaling. Designed primarily for real-world spatial distributions under a constant capacity setting, Neural CFRS scales robustly to out-of-distribution $N=1000$ instances with a < 4% gap -- retaining an approximate 5% gap at this scale even as an ultra-lightweight, single-layer architecture. Furthermore, when deployed out-of-the-box on standard benchmarks, we achieve a highly competitive 2.73% optimality gap on size-100 problems.

Problem

• Capacitated Vehicle Routing Problem
• Neural Combinatorial Optimization
• spatial symmetries
• out-of-distribution generalization
• sequential decoding

Innovation

• Differentiable Optimal Transport
• Non-autoregressive Neural Solver
• Cluster-First-Route-Second
• Symmetry Invariance
• Zero-shot Scaling