arXiv subjects

Changliang Zhou

Publications and source records attributed to Changliang Zhou.

9 recordsLinked to original sources

arXiv2026

URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization

Multi-task neural routing solvers have emerged as a promising paradigm for their ability to solve multiple vehicle routing problems (VRPs) using a single model. However, existing neural solvers typically rely on predefined problem constraints or require per-problem fine-tuning, which substantially limits their zero-shot generalization ability to unseen VRP variants. To address this critical bottleneck, we propose URS, a unified neural routing solver that achieves zero-shot generalization across a wide range of unseen VRPs with a single model. We propose a unified data representation (UDR) that replaces problem enumeration with data unification, thereby broadening the problem coverage and reducing reliance on domain expertise. In addition, we introduce a mixed bias module (MBM) during encoding to improve node embeddings, which efficiently captures multiple priors inherent to various problems. On top of the UDR, we develop a problem-conditioned parameter generator to further improve zero-shot generalization. Extensive experiments show that URS consistently produces high-quality solutions for 110 VRP variants (including 99 unseen variants) while demonstrating impressive scalability to large-scale instances with up to 7000 nodes. To the best of our knowledge, URS is the first neural solver to handle over 100 VRP variants with a single model. Our code is available at https://github.com/CIAM-Group/URS.

cs.LG↗

arXiv2026

Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solver

In modern intelligent transportation systems (ITS), particularly in freight transportation and logistics, real-time route planning is crucial. It presents unique challenges driven by high uncertainty in service requests, where the number of service customers can vary drastically, ranging from hundreds to thousands. Existing neural methods struggle to maintain performance under such significant variations, which severely limits their practical applicability. To address this crucial shortcoming, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) designed for better large-scale generalization. In particular, we design a simple yet efficient instance-conditioned adaptation function that adjusts the policy based on the specific geometry and density of the current traffic scenario to improve model adaptability with minimal computational overhead. Furthermore, we propose a powerful yet low-complexity instance-conditioned adaptation module to generate better solutions for instances across various scales. Extensive experiments on synthetic, benchmark, and real-world instances demonstrate that ICAM can consistently achieve promising generalization performance across four widely studied large-scale route planning scenarios. Notably, our proposed method delivers high-quality solutions with remarkably fast inference speed, providing a scalable and efficient solution for real-time intelligent transportation operations. Our code is available at https://github.com/CIAM-Group/ICAM.

cs.AI↗

arXiv2026

Learning to Reduce Search Space for Generalizable Neural Routing Solver

Constructive neural combinatorial optimization (NCO) offers a promising paradigm for solving vehicle routing problems (VRPs) by directly learning to construct approximate optimal solutions, thereby reducing reliance on expert knowledge for algorithm design. However, scaling these methods to handle large-scale instances remains challenging due to high computational complexity. While recent dynamic search space reduction (SSR) methods can improve inference efficiency through geometric distance-based pruning, they often struggle on complex instances with non-uniform distributions or when optimal solutions rely heavily on non-spatial constraints. To address this critical issue, we propose Learning to Reduce (L2R), which is the first learning-based dynamic SSR framework. L2R learns to adaptively prioritize nodes by extracting patterns from problem-specific features to prune the search space at each step, enabling efficient and scalable solution construction. Extensive experiments show that our L2R framework generalizes robustly to different problem scales and data distributions on various VRP variants. To the best of our knowledge, L2R is the first neural solver to effectively scale to VRP instances with $10$ million nodes while maintaining high solution quality, which significantly pushes the frontier of NCO in terms of generalization and scalability. Our code is available at https://github.com/CIAM-Group/L2R.

cs.AI↗

arXiv2026

SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver

Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when switching to asymmetric settings due to input inconsistencies or inherent structural differences, substantially limiting their practicality in real-world scenarios that encompass both scenarios. To address this limitation, we define the spatial position of each node based on the relative distances to a specific set of pivots and further propose a Spatial Pivot-Aligned Coordinate-free Embedding (SPACE) framework that unifies node representation and solution generation across symmetric and asymmetric VRPs. Specifically, we construct a bidirectional Frechet representation using a novel furthest pivot sampling strategy to enable invariant node representations across distinct problem settings. Furthermore, we introduce a weight-decomposed adaptive decoding mechanism that decouples geometric perception from problem representations, mitigating the overfitting of constraint decisions to a specific geometry setting. Extensive experiments on 110 VRP variants, comprising 55 symmetric problems and their asymmetric counterparts, demonstrate that SPACE achieves promising zero-shot generalization in both symmetric and asymmetric VRPs.

cs.AI↗

arXiv2026

Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver

Heavy-Encoder-Light-Decoder (HELD) neural routing solvers have emerged as a promising paradigm due to their broad applicability across multiple vehicle routing problems (VRPs). However, they typically struggle with VRP variants with complex constraints. To address this limitation, this paper systematically revisits existing neural solvers from the perspective of the generation mechanism for state embeddings (i.e., query vector prior to compatibility calculation) during decoding. We identify that current mechanisms restrict the observation space during attention computation, introducing a key bottleneck to achieving high-quality solutions. Through detailed empirical analysis, we demonstrate the necessity of preserving a global observation space. To overcome the constraint-agnostic drawback inherent to global observation spaces, we propose a simple yet powerful Constraint-Aware Residual Modulation (CARM) module. By adaptively modulating the context embedding with constraint-relevant variables, CARM effectively enhances constraint awareness, enabling the neural solver to fully leverage the global observation space and generate an efficient state embedding. Extensive experimental results across two single-task and five multi-task neural routing solvers confirm that the CARM module consistently boosts baseline performance. Notably, solvers equipped with our CARM achieve substantial improvements in scaling to large-scale instances and in generalizing to unseen VRP variants. These findings provide valuable insights for the architectural design of neural routing solvers.

cs.AI↗

arXiv2026

Survey on Neural Routing Solvers

Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted counterparts in classic heuristic frameworks, thereby reducing reliance on costly manual design and trial-and-error adjustments. This survey makes two main contributions: (1) The heuristic nature of NRSs is highlighted, and existing NRSs are reviewed from the perspective of heuristics. A hierarchical taxonomy based on heuristic principles is further introduced. (2) A generalization-focused evaluation pipeline is proposed to address limitations of the conventional pipeline. Comparative benchmarking of representative NRSs across both pipelines uncovers a series of previously unreported gaps in current research.

math.OC↗

arXiv2025

UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, often leading to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global instance dividing and a fixed-length sub-path solver for conquering divided sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/UDC-Large-scale-CO-master.

cs.AI↗

arXiv2024

Distilling Autoregressive Models to Obtain High-Performance Non-Autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed

Neural construction models have shown promising performance for Vehicle Routing Problems (VRPs) by adopting either the Autoregressive (AR) or Non-Autoregressive (NAR) learning approach. While AR models produce high-quality solutions, they generally have a high inference latency due to their sequential generation nature. Conversely, NAR models generate solutions in parallel with a low inference latency but generally exhibit inferior performance. In this paper, we propose a generic Guided Non-Autoregressive Knowledge Distillation (GNARKD) method to obtain high-performance NAR models having a low inference latency. GNARKD removes the constraint of sequential generation in AR models while preserving the learned pivotal components in the network architecture to obtain the corresponding NAR models through knowledge distillation. We evaluate GNARKD by applying it to three widely adopted AR models to obtain NAR VRP solvers for both synthesized and real-world instances. The experimental results demonstrate that GNARKD significantly reduces the inference time (4-5 times faster) with acceptable performance drop (2-3\%). To the best of our knowledge, this study is first-of-its-kind to obtain NAR VRP solvers from AR ones through knowledge distillation.

cs.LG↗

arXiv2019

Anisotropic Moser-Trudinger inequality involving $L^n$ norm

The paper is concerned about a sharp form of Anisotropic Moser-Trudinger inequality which involves $L^{n}$ norm. Let \begin{equation*} λ_{1}(Ω) = \inf_{u\in W_0^{1,n}(Ω),u\not\equiv 0} ||F(\nabla u)||_{L^n(Ω)}^n / ||u||_{L^n(Ω)}^n \end{equation*} be the first eigenvalue associated with $n$-Finsler-Laplacian. using blowing up analysis, we obtain that \begin{equation*} \sup_{u\in W_{0}^{1,n}(Ω),||F(\nabla u)||_{L^n(Ω)} = 1} \int_Ωe^{λ_n (1+α||u||_{L^n (Ω)}^n)^{\frac{1}{n-1}} |u|^{\frac{n}{n-1}}}dx \end{equation*} is finite for any $0\leq α<λ_{1}(Ω)$,and the supremum is infinite for any $α\geq λ_{1}(Ω)$, where $λ_{n} = n^{\frac{n}{n-1}} κ_n^{\frac{1}{n-1}}$ ($κ_{n}$ is the volume of the unit wulff ball) and the function $F$ is positive,convex and homogeneous of degree $1$, and its polar $F^o$ represents a Finsler metric on $\mathbb{R}^n$. Furthermore, the supremum is attained for any $0\leq α<λ_{1}(Ω)$.

math.AP↗