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

TL;DR

This paper introduces Neural CFRS, a non-autoregressive, one-shot neural framework for the Capacitated Vehicle Routing Problem that leverages differentiable optimal transport and symmetry invariance, achieving high scalability and competitive performance.

Contribution

It presents the first neural CFRS framework that enforces capacity constraints via differentiable optimal transport, with formal symmetry guarantees and zero-shot scalability to large instances.

Findings

Scales robustly to N=1000 instances with less than 4% optimality gap.

Achieves a 2.73% gap on standard size-100 benchmarks.

Provides theoretical guarantees for symmetry invariance.

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.