Vehicle Routing

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7 papers in the last four weeks, down 22% on the four weeks before. 0.1% of all new papers.

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Latest papers 77

Sep 30, 2026cs.RO

HALO: Heterogeneous Allocation Via Localized Observations for the Vehicle Routing Problem

Scalable robotic fleets have become increasingly popular for various applications such as package delivery, warehouse management, and military operations. Prior fleet control algorithms solve centralized routing problems with up to

1{,}000

tasks in controlled environments, yet they fail to consider realistic constraints such as limited observation and communication ranges typical of decentralized fleets. Thus, deploying existing fleet control algorithms into real-world settings is currently infeasible. To tackle this, we propose Heterogeneous Allocation via Localized Observations (HALO) to solve the Vehicle Routing Problem (VRP). HALO is a hybrid method that splits the VRP into allocation and routing portions to provide onboard, real-time solutions to robots in dynamic environments. During the allocation phase, HALO utilizes a heterogeneous graph neural network framework with unique message passing layers to explicitly separate the learning of spatial distributions and task-to-robot compatibility. Evaluation results on a partially observable, online variant of the VRP show HALO significantly outperforms the heuristic baseline while maintaining similar solution quality to an all-knowing offline variant of HALO. While HALO is explicitly designed for partially observable environments, it imposes no strict upper bound on the observation space allowing us to test HALO on the traditional static, single-depot VRP. Here, HALO outperforms state-of-the-art architectures strictly optimized for the static variant of the VRP by up to

14.06\%

. Throughout all testing, this framework maintains the quickest execution times which emphasizes its potential for large-scale, real-time deployment.

Andrew Meighan, Hyungsub Kim, Or Dantsker

Department of Intelligent Systems Engineering, Indiana University Bloomington · Department of Computer Science, Indiana University Bloomington

Vehicle Routing Multi-Robot Coordination Multi-Robot Task Allocation

Sep 28, 2026cs.AI

Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimization

Large-scale routing problems are difficult to solve efficiently as their search spaces grow rapidly with problem size. Existing approaches primarily improve the optimization procedure itself, often at increasing computational cost. We instead shift the focus to a useful initialization that can be refined into a high-quality solution with limited downstream refinement. We propose Just Initialize, a training-free and solver-agnostic initialization component for large-scale routing optimization. Just Initialize compresses a large routing instance into a compact surrogate space, optimizes its global routing structure, and recovers the resulting solution as an optimization-friendly starting point in the original space. Extensive experiments on Traveling Salesman Problems (TSPs), Capacitated Vehicle Routing Problems (CVRPs), Vehicle Routing Problems with Time Windows (VRPTWs), and Prize-Collecting Traveling Salesman Problems (PCTSPs) demonstrate that Just Initialize achieves high-quality solutions comparable to or better than state-of-the-art methods while substantially reducing computational cost across instances ranging from 1K to 100K nodes, including an average speedup of approximately 70

\times

, sub-second runtimes on 10K-node instances, and runtimes within tens of seconds on 100K-node instances.

Jiale Zhao, Sirui Mao, Zimu Chen +5

School of Automation Science and Electrical Engineering, Beihang University, Beijing, China · School of Computer Science and Engineering, Beihang University, Beijing, China · School of Cyber Science and Technology, Beihang University, Beijing, China +1

Traveling Salesperson Problem Combinatorial Optimization Vehicle Routing

Sep 28, 2026cs.LG

Depot-Closed Multi-Component Construction for Neural Vehicle Routing

Most neural constructive solvers for the vehicle routing problem (VRP) use route-by-route construction, extending one route until completion before starting the next. This commits route membership early and hinders global coordination across routes. We propose multi-component construction, which maintains many route components simultaneously and merges them in an arbitrary order. This removes the depot-return cue that route-by-route construction obtains from the remaining capacity; to compensate, we introduce an interpretation in which every component is treated as an implicitly depot-closed route. Under this depot-closed interpretation, every intermediate state of standard CVRP construction is a complete feasible solution, and the exact cost reduction of a merge is the Clarke-Wright saving. The neural policy combines this CW-saving signal with the evolving component state to learn what to connect and when to connect. A policy trained only on CVRP100 outperforms the reported results of representative neural solvers on CVRP100-500 with greedy inference and, reused for ruin-and-reconstruct, performs strongly at all evaluated sizes up to CVRP1000. In a zero-shot Constraint Tightness evaluation with capacities from

C=10

to

500

, it outperforms the reported neural solvers at every capacity. Controlled analyses show that robustness persists without CW grounding and point to learned route-closing behavior as a plausible contributor to the tight-regime degradation of learned route-by-route solvers.

Shinichiro Hamada, Hisashi Kashima

Core Technology, R&D Division Panasonic Connect Co., Ltd. · Graduate School of Informatics Kyoto University

Vehicle Routing Neural Combinatorial Optimization

Sep 21, 2026cs.NE

DCL-GPGLS: Dynamic Curriculum Learning for Genetic Programming Guided Local Search in Large-Scale Vehicle Routing

Genetic Programming Guided Local Search (GPGLS) uses genetic programming to evolve utility functions for guided local search in large-scale vehicle routing problems (LSVRPs). Evaluating every GP individual on every training instance at every generation is expensive, so GPGLS is usually trained on small instance batches. Existing curriculum-based GPGLS orders these batches mainly by instance size. Adaptive Curriculum Learning GPGLS (ACL-GPGLS) improves training efficiency by adapting when the search moves between fixed curriculum stages, but the instance difficulty order remains predefined. We propose DCL-GPGLS, which estimates the difficulty of each training instance from the current population's solution quality and updates the estimates during evolution. Each generation then receives a batch near a scheduled difficulty level, with a correction that limits repeated selection of the same instances. Experiments on a fixed training-test split of the CVRPLIB X set show that DCL-GPGLS achieves the best observed average rank and mean test cost among six training policies. It obtains the lowest mean cost on 36 of 65 unseen test instances and is significantly better than the static feedback-derived curriculum, matched in total evaluator calls, on 6 instances, with no significant difference on the remaining 59.

Saining Liu, Yi Mei, Mengjie Zhang

School of Engineering and Computer Science, Victoria University of Wellington, Wellington, New Zealand

Metaheuristic Optimization Genetic Programming Vehicle Routing Curriculum Learning

Sep 21, 2026cs.NE

Genetic Programming with Behaviour-based Niching for Learning Guided Local Search in Vehicle Routing Problems

Genetic Programming Guided Local Search (GPGLS) learns utility functions that guide local search for vehicle routing. Its evolving programs can have similar fitness while inducing different search behaviour, making fitness alone an incomplete basis for population diversity management. We propose GPGLS with Behaviour-based Niching (BN-GPGLS), which characterises programs through six operator-level descriptors collected during local search. A current-generation archive selects fitness-competitive, compact representatives from strata of a behaviour score. Fixed policies use archive parents continuously, whereas adaptive policies activate them using training-fitness and standardised behaviour-dispersion signals, optionally with a tree-size condition. We compare four behaviour-based variants with a no-archive GPGLS control and fitness-based niching over 30 seed-matched runs on generated 200-customer instances. BN-Adaptive achieves the best descriptive average rank on a separate 90-instance monitoring set; aggregate routing-cost differences are small. All five archive policies produce lower final-population median tree sizes than the GPGLS control, with paired Wilcoxon comparisons remaining significant after Holm adjustment. These results identify useful solution-quality and program-size trade-offs within the evaluated setting, without attributing the size reductions to behaviour representation alone.

Saining Liu, Yi Mei, Mengjie Zhang

School of Engineering and Computer Science, Victoria University of Wellington, Wellington, New Zealand

Automated Heuristic Design Metaheuristic Optimization Genetic Programming Vehicle Routing

Sep 12, 2026cs.AI

RouteRepair: Instance-Level Failure Diagnosis and Targeted Repair in LLM-Based Automated Heuristic Design for Routing Optimization

Efficient routing optimization is essential to freight transportation, urban logistics, and shared mobility, where high-quality heuristics are often required under limited computational budgets. Recent large language model (LLM)-based automated heuristic design methods can generate effective routing rules, but aggregate evaluation may mask recurrent failures on particular instance structures. To address this limitation, this study develops RouteRepair, which diagnoses parent-specific weaknesses from instance-level performance and applies targeted modifications to the corresponding heuristic components while protecting behavior that already performs well. Routing evidence, solver behavior, and program context are combined to define bounded repair objectives, and each intervention is validated through matched parent-child evaluation of failure recovery and collateral degradation. Experiments on the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) span constructive search, guided local search, and ant colony optimization. RouteRepair-GLS reduces the mean TSP optimality gap from 1.7476% to 0.7587%, while the constructive CVRP heuristic lowers average route cost by 1.91% relative to the savings heuristic; the generated ACO priors also outperform matched hand-designed priors. These results show that failure-aware, evidence-constrained refinement can improve routing heuristics on difficult instances while preserving performance on cases they already solve well.

Binghao Ji, Di Huang, Jiahui Fang +1

Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing, China, 211189.

Automated Program Repair Automated Heuristic Design Metaheuristic Optimization Large Language Model-Guided Optimization Vehicle Routing

Sep 9, 2026cs.RO

HiRAD: A Flexible Large-Scale AGV Routing System

Automatic Guided Vehicles (AGVs) substantially boost warehouse throughput, but routing large-scale AGV fleets remains challenging. Classical Multi-Agent Pathfinding solvers suffer from exploding combinatorial complexity and super-quadratic runtime, while relying on idealized grid or piecewise-linear motion models that mismatch real-world kinematics. Recent Reinforcement Learning (RL) solutions improve flexibility via decentralized agent policies but depend on discretized spatiotemporal representations, require millions of episodes to converge, and incur full-map observation at every step, which leads to large models, slow convergence, and high inference latency that violates real-time industrial control constraints. To address these bottlenecks, we propose HiRAD, a hierarchical RL framework for continuous-space AGV routing with real-time guarantees: (1) a step-level spatiotemporal representation that translates continuous motion into a differentiable RL problem, (2) a hierarchical strategy that splits heading choice from velocity control to reduce the action space, and (3) an asynchronous event-driven decision pipeline that lowers inference complexity from O(n^2) to O(n) and cuts per-step latency by as much as 71 percent. Across random graphs and two warehouse maps, HiRAD reduces makespan by 45 percent to 63 percent and shortens end-to-end runtime.

Yunjie Huang, Ruizhong Wu, Mengxuan Zhang +3

Hierarchical RL Vehicle Routing Robot Motion Planning Multi-Agent Path Finding

Sep 4, 2026cs.LG

GNN-Guided Graph Coarsening and Adaptive QUBO Penalties for the Capacitated Vehicle Routing Problem with Time Windows on a Quantum Annealer

Graph coarsening reduces the large Quadratic Unconstrained Binary Optimization (QUBO) formulations arising when vehicle-routing problems are solved by quantum annealing. Nearby customers with compatible time windows are merged into super-nodes, the reduced problem is solved, and the solution is expanded to the original graph. For the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), existing coarsening heuristics require family-specific tuning and remain unreliable on random instances. We address these limitations on the Solomon benchmark using simulated annealing and a D-Wave Advantage2 processor. We first introduce adaptive penalty calibration. Uniform penalty scaling has little effect, whereas controlling the internal coefficient range substantially improves raw samples. Removing non-binding constraints, normalising binding ones, and scaling the remaining penalties reduces mean raw constraint violations from 33.0 to 0.06 at the same solver budget (p=3.7e-11, n=56). A variable-count-preserving control attributes this gain to conditioning rather than problem size. Second, we replace the hand-tuned merge score with a graph neural network (GNN) using one configuration across all families. At N=10, it achieves 100% feasibility across all Solomon families, including R-type (100% vs. 80% for the tuned heuristic). Across N=10,...,100, feasibility is 83% vs. 69%, with the GNN better or tied on 85/90 instance-size pairs. At N=80,100, the difference is significant (p=0.002; 25/25 pairs), while the QUBO remains approximately 5-6 times smaller. Finally, hardware experiments reproduce the conditioning effect at fixed logical variable count: feasible samples increase from 0.02% to 39% across 13 instances. Classical repair with local search remains a reference bound for end-to-end solution cost.

Youssef Kamel Rezk, Paweł Gora

Alamein International University, Alamein, Egypt · Jagiellonian University, Kraków, Poland · Fundacja Quantum AI, Warsaw, Poland

Quantum Annealing Graph Coarsening Vehicle Routing Quadratic Unconstrained Binary Optimization

Sep 2, 2026cs.NE

LLM-Driven Joint Evolution of Coupled Heuristics Components for Routing Optimization

Heuristic design for combinatorial optimization remains heavily reliant on expert knowledge, while existing large language model (LLM)-enhanced evolutionary methods typically evolve isolated algorithmic components, even when one determines the search state on which another operates. This paper proposes LLM-driven Heuristic Components Joint Generation (LLM-HCJG), a population-based framework that jointly generates and co-evolves interdependent heuristic components under a shared design blueprint. Applied to guided local search (GLS), LLM-HCJG couples solution initialization with penalty construction and embeds the generated pair into an enhanced online search mechanism. The resulting form is further transferred from the traveling salesman problem (TSP) to the capacitated vehicle routing problem (CVRP). Theoretical analysis establishes the non-separable state-transition effects between the two components and the advantage in generation consistency. Across synthetic instances and 41 public TSPLIB/CVRPLIB benchmarks, LLM-HCJG attains consistently low optimality gaps, including best or tied-best results on 28 of 29 TSPLIB instances and all 12 CVRPLIB instances. Ablation and structural analyses further indicate that these gains are associated with cross-component compatibility and alignment rather than isolated-component recombination. These results support effective cross-instance transfer within the evaluated routing settings under limited-sample, modest-cost training.

Juntao Wei, Yangming Zhou, Zhibin Jiang +1

Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China · Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai 200240, China

Automated Heuristic Design Evolutionary Optimization Local Search Vehicle Routing Traveling Salesperson Problem

Sep 2, 2026cs.MA

RideSkill: A Hierarchical Algorithm for Generalized Ride Sharing with LLM-Driven Automatic Evolution

Ride-sharing, which allows multiple passengers with different origin-destination (OD) pairs to share a single vehicle, is a challenging operational problem, as it requires orders with different OD pairs to be efficiently bundled and assigned to vehicles under uncertain and varying scenarios. Although multi-agent reinforcement learning (MARL) solutions have achieved promising performance, they suffer from limited generalization (adapting to different environmental scenarios), low transferability (adapting to different platform objectives), and training difficulties in large-scale systems, such as the curse of dimensionality. Recently, motivated by the scaling of large language models (LLMs), several works have incorporated LLMs into ride-hailing systems, either by employing LLMs directly as decision-making agents or using them for automatic algorithm design. However, none of these approaches support vehicle sharing, which complicates the problem by expanding both the state and action spaces exponentially. Moreover, most of them require frequent LLM calls at inference time, making them infeasible for real-time deployment. To address these issues, we propose RideSkill, a hierarchical method for ride-sharing that leverages LLM-assisted automatic algorithmic design. RideSkill consists of a combiner that assigns appropriate skills to each vehicle from a learned skill repository, enabling adaptive dispatch under varying scenarios and objectives, and a repositioner that sequentially relocates idle vehicles to emerging regions, avoiding conflicts among vehicles. Crucially, the skill repository, combiner, and repositioner are all trained by an LLM-based automatic evolutionary method, eliminating the need for LLM calls during deployment and thus ensuring high real-time performance.

Zijian Zhao, Sen Li, Xialiang Tong +1

The Hong Kong University of Science and Technology · Noah’s Ark Lab, Huawei · The Hong Kong University of Science and Technology (Guangzhou)

Vehicle Routing Hierarchical Planning

Sep 1, 2026cs.AI

Reinforcement Learning Enhanced LLM Agents for Complex Vehicle Routing Problems

Vehicle Routing Problems (VRPs) are fundamental combinatorial optimization problems with widespread applications in various scenarios. The advanced optimization solvers can effectively solve such problems. However, modeling complex VRP variants for solvers often requires substantial domain expertise, which limits the accessibility of advanced optimization technologies. In this paper, we propose Reinforcement Learning Enhanced LLMAgents(RLEA), a multi-agent framework designed to automate the modeling of complex VRPs. RLEA introduces a lightweight neural Planner trained with Soft Q-learning to efficiently orchestrate the actions of LLM-based agents. In addition, we equip the system with an evolutionary memory module and retrieval-augmented generation, enabling the agent to leverage both accumulated experience and external solver knowledge during program generation and refinement for solving VRPs. We evaluated 48 distinct VRP variants across various solvers. The experimental results demonstrate that RLEA outperforms the previous state-of-the-ar method, achieving a 16.67% higher success rate while significantly reducing runtime errors. These results validate that integrating reinforcement learning with LLM-based reasoning is highly effective for automated optimization modeling. The appendix is available at: https://doi.org/10.5281/zenodo.19134435.

Yi Chen, Zikang Yu, Jiahai Wang +3

School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China · Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore

Multi-Agent System Optimization LLM-Guided RL Vehicle Routing Natural Language to Optimization Modeling

Sep 1, 2026cs.LG

GeoPAR: Large-Scale Multi-Agent Combinatorial Optimization with Geometry-Guided Parallel Autoregressive Learning

Multi-agent combinatorial optimization problems are notoriously challenging due to their NP-hard nature. Recent parallel autoregressive neural solvers improve inference efficiency by allowing agents to make decisions simultaneously, but their performance often degrades on large-scale instances. This is largely attributable to weak modeling of local geometric structures and the fact that conflicting task selections are handled only after action generation. To address these limitations, we propose GeoPAR, a geometry-guided parallel autoregressive reinforcement learning framework for scalable multi-agent combinatorial optimization. GeoPAR integrates three key components: (1) a projection-window sparse geometry mechanism that builds lightweight local candidate neighborhoods through multi-directional projections, (2) sparse edge-biased attention that injects these geometric relations into node representations, and (3) cache-guided conflict-aware assignment that reuses the geometric cache during decoding to suppress duplicate selections of exclusive tasks. Experiments on heterogeneous vehicle routing and open multi-depot pickup-and-delivery problems show that GeoPAR improves large-scale zero-shot generalization while substantially reducing rollout steps and maintaining efficient inference.

Wenjian Wu, Zesheng Jia, Jiaying Tang +2

School of Future Science and Engineering, Soochow University, Suzhou, China

Combinatorial Optimization Vehicle Routing Autoregressive Decoding RL for Combinatorial Optimization Neural Combinatorial Optimization

Aug 31, 2026cs.LG

A hybrid quantum-classical neural network for learning to route

This work studies hybrid quantum-classical neural networks for learning routing heuristics. Specifically, this paper asks whether small quantum neural networks can replace parameter-heavy modules inside a competitive attention-based routing model while maintaining solution quality. For the capacitated vehicle routing problem, encoder feed-forward replacement emerges as the most promising design: it reduces the number of model parameters by 56.6% while keeping the hybrid model close to the classical neural baseline at small and medium instance sizes, although the gap grows for larger instances. This work also compares to classical routing algorithms, which remain highly competitive and often superior on the fixed Euclidean test sets. Our results therefore do not indicate quantum advantage or solver dominance, but identify encoder feed-forward replacement as a viable hybrid-module compression strategy for neural combinatorial optimization.

Marcus Rolf Peter Ritt, Alexsandro Santos da Rosa Júnior, Marcos Vinicius Reballo +2

Instituto de Pesquisas Eldorado – Porto Alegre – RS – Brazil · Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis 88040-900, SC, Brazil

Hybrid Quantum-Classical ML Vehicle Routing Neural Combinatorial Optimization Neural Network Compression Quantum Neural Networks

Aug 31, 2026cs.AI

Learning-Assisted Congestion-Aware Route Scheduling for Semiconductor Fab Material Control Systems

Automated material handling systems in semiconductor fabs are operated by a material control system (MCS) that must schedule a relay route for every transport command online, before execution. This is a data-driven scheduling problem in which route cost is dominated in the upper tail by queueing at heterogeneous, partially observable relay equipment, so route selection requires estimating both delivery time and congestion risk at the decision moment. This paper proposes a transport-network-aware dynamic congestion representation (TN-DCR). Built on a static directed transport graph induced by historically observed relay segments, TN-DCR combines structural route priors, multi-window network-wide congestion context, route-level bottleneck exposure, and an inductive graph-aware route embedding, all constructed under a prediction-time-safety invariant that admits only information observed strictly before the prediction moment. The representation feeds separate queue- and transfer-time regressors and an ordinal multi-label classifier producing calibrated multi-threshold exceedance scores, with an empirical-Bayes stock-key residual correction reducing systematic queue-time underprediction. The predictions serve as costs in a risk-constrained route-scheduling rule that minimizes predicted delivery time subject to a bound on extreme-congestion probability, embedding the learned predictors within a lightweight operations-research decision model. In a controlled closed-loop evaluation, mean delivery time falls by 16.4% and internal resource waiting time by 22.6% while throughput remains essentially unchanged.

Hao Yin, Meiqi Tu, Anbang Liu +2

Department of Data and Systems Engineering, The University of Hong Kong · The Research Center for Digital Production and Smart Logistics, Tsinghua University

Real-Time Scheduling Semiconductor Manufacturing Vehicle Routing Traffic Forecasting

Aug 31, 2026cs.LG

Trajectory-Initialized Neural Double Q-Routing for Large-Scale Overhead Hoist Transport Systems

Large-scale industrial robot fleets share constrained physical infrastructure, making vehicle travel times dependent on safety separation, intersection access, downstream blocking, and station contention. We study this problem in overhead hoist transport (OHT) systems, a representative ceiling-mounted material-handling system used in semiconductor fabs. Static shortest-path routing cannot account for these time-varying traffic costs, whereas tabular Q-routing adapts online but learns each destination--node--action value independently, limiting information sharing across sparsely visited routing contexts and making startup behavior sensitive to inaccurate value estimates. We propose Neural Double Q-routing, which replaces destination-indexed tables with a shared state--action value network. The network is warm-started through return-to-go regression on mixed simulator-generated routing trajectories and then refined online using Double-Q updates, local congestion correction, and event-stratified structured replay. Across nine matched fleet-size--arrival-rate settings with 100, 150, and 200 OHTs, the proposed framework reduces mean completion time relative to tabular Double Q-routing by

0.8\%

--

8.8\%

. It achieves the lowest mean completion time among all compared methods in the six 150- and 200-OHT settings, whereas Dijkstra remains best in the three 100-OHT settings. Completed-task counts remain within

1\%

of tabular Double Q-routing in eight of nine settings, and 95th-percentile completion time decreases in eight settings. In two matched startup scenarios, offline initialization increases the number of completed tasks by up to

23\%

and reduces tail completion time by up to

15\%

.

Cheng Gu, Qiusheng Zhao, Anbang Liu +2

Department of Data and Systems Engineering, The University of Hong Kong, Hong Kong · College of Engineering, University of California, Berkeley, CA, USA

Q-Learning Vehicle Routing Industrial Robotics

Aug 12, 2026eess.SY

Energy-Aware Wind-Resilient Routing for Truck-Assisted Multi-UAV Delivery under Wind Uncertainty

Energy feasibility under wind uncertainty is a critical safety issue for low-altitude air-ground delivery. In truck-UAV systems, UAVs complete assigned deliveries and safely return to a mobile truck or depot, while wind-induced propulsion costs vary online and are only partially observable. Existing routing methods often rely on static or deterministic energy models, which may underestimate headwind, crosswind, battery-voltage, and return-feasibility risks. This paper proposes Energy-Aware Wind-Resilient Routing (EWR), an online risk-sensitive planning framework for wind-aware and energy-safe UAV routing. The delivery environment is represented as a time-dependent directed energy graph whose edge costs are updated using delayed noisy wind estimates, payload states, and conservative uncertainty margins. Experiments using synthetic delivery graphs with replayed wind logs from a public truck-UAV delivery dataset show that EWR improves mission success rates and reduces wind-induced return failures.

Tianshun Li, Yanggang Sheng, Hongliang Lu +3

The Hong Kong University of Science and Technology (Guangzhou), China · Southern University of Science and Technology, China · Intelligent Transportation Thrust, Systems Hub, The Hong Kong University of Science and Technology (Guangzhou), China

UAV Navigation Vehicle Routing

Aug 7, 2026cs.MA

Per-Shipment Multi-Agent Reinforcement Learning for Intermodal Freight Routing Under Hurricane Disruption

Intermodal freight networks face growing disruption risk from climate extremes that degrade multiple corridors simultaneously. To address this, we formulate freight routing as a Dec-POMDP with per-shipment action granularity and train Independent PPO (IPPO) under Centralized Training with Decentralized Execution, comparing against two heuristic baselines with privileged state access on a 15-hub network under hurricane disruption. Across 30 matched episodes, no single policy dominates: IPPO achieves the highest throughput (

+12.7\%

) and delivery rate while a capacity-aware heuristic leads on Resilience Index (RI) and delay. Under demand surge (2.9:1 capacity ratio), IPPO's RI advantage grows to

+6.4\%

, suggesting learned routing is most valuable when capacity is scarce. A Multi-Agent PPO (MAPPO) variant collapses under train-eval queue mismatch (

\mathrm{RI} = 0.811

); retraining recovers RI to

1.018

but IPPO still leads on throughput, pointing to residual limitations in centralized critics under per-shipment dispatch.

Aliza Sharmin, Xudong Wang, Mustafa Can Camur +1

Department of Industrial and Systems Engineering University of Tennessee Knoxville, TN 37996

Vehicle Routing Proximal Policy Optimization Supply Chain Management Multi-Agent Reinforcement Learning

Aug 7, 2026cs.AI

Vehicle routing problem using deep reinforcement learning - A case study about truck planning in the industry

As an important component of the supply chain industry, transportation has experienced rapid development in the past decade with the assistance of digital platforms and intelligent algorithms. Within the field of transportation research, Vehicle Routing Problem (VRP) has remained a persistent and enduring challenge. In the realm of management science, experts, and scholars from both the industrial and academic sectors have continuously explored optimization models and algorithms to effectively address routing problems, from the classical Traveling Salesman Problem to the more general Vehicle Routing Problem. These models and algorithms are applied in real-world industrial scenarios to achieve cost optimization and reduce carbon footprints. However, due to the complexity of real-world problems, numerous specific constraints are often added, and challenges such as information opacity, uncertainty, and irrational human behavior may arise. Therefore, deploying and optimizing mathematical models for VRP in practical scenarios while maintaining optimal results poses numerous challenges. This paper discusses and provides solutions for three different logistic use cases involving external truck network design. Through these industrial case study, the paper introduces how deep reinforcement learning-based vehicle routing optimization has been implemented. As a result, it can be observed that the routes optimized by reinforcement learning agent have over 10% total cost compared to baseline results. Furthermore, the paper proposes that in future research, DRL algorithms for vehicle routing problems could be generalized into more variations of VRP.

Siliang Lu, Dan Hu, Lili Wu

Bosch Center for Artificial Intelligence Shanghai, China · School of Electronic Information and Electrical Engineering Shanghai, China · School of Computer Science, Macau University of Science and Technology Macau, China

Vehicle Routing Supply Chain Management RL for Combinatorial Optimization

Jul 27, 2026cs.LG

MobiWave: Dispatch-Oriented Graph Wavelets and Drift-Guided Selective Optimization for Autonomous Fleet Rebalancing

Autonomous fleets enable mobility platforms to coordinate idle vehicles directly, making fleet-wide rebalancing possible. However, two obstacles limit reliable deployment: overlapping regional and local traffic patterns can hide roads that remain useful for dispatch, and mobility drift can make a trained policy unreliable. Existing spatial aggregation mixes these patterns, while updating all parameters from limited recent data is costly and can damage stable knowledge. We propose \name, a framework that connects a dispatch-oriented multi-scale graph wavelet module with Drift-Guided Layer-Selective Optimization (DGLS). The first module addresses the representation challenge by separating graph-frequency patterns and weighting each scale according to its value for demand prediction and feasible rebalancing. DGLS addresses the adaptation challenge by measuring Dispatch-weighted Spectral Drift, selecting affected layers within a resource budget, and separating short shocks from persistent changes through a drift-aware fast--slow update. Candidate validation further rejects updates that fail to improve held-out dispatch reward without worsening monitored service or safety constraints. Experiments on both real-world datasets and simluated environments demonstrate the effectiveness of \name\ in comparing with state-of-the-art methods. The source code and datasets are available at https://anonymous.4open.science/r/MobiWave-40F8/.

Xiao Han, Pinbo Wang, Yuanshao Zhu +2

Graph Neural Networks Concept Drift Vehicle Routing Selective Fine-Tuning

Jul 27, 2026cs.AI

Unequal Trips, Unequal Places: Diagnosing and Mitigating Delay Inequity in Autonomous Vehicle Fleet Coordination

City-scale autonomous vehicle fleet coordinators are typically optimized for aggregate travel time, yet fleet averages conceal how delay is distributed across trips and regions. We conduct a distributional audit on three real-city road-network and taxi-demand datasets from Manhattan, Chicago, and San Francisco. The audit reveals pervasive trip-length inequity whose direction depends on the city and coordinator. After accounting for trip length, spatial inequity becomes more pronounced as demand grows and is consistently stronger when trips are grouped by origin rather than destination. These findings motivate SPatially Aware RErouting (SPARE), a budgeted online coordination framework that assigns limited replanning capacity to delayed vehicles and redirects them using recently observed waiting pressure. SPARE provides a per-review decision guarantee and explicitly bounds online route updates. Experiments on all three datasets against six representative baselines show that SPARE delivers the strongest joint efficiency-fairness performance while retaining city-scale scalability. The results demonstrate that bounded congestion-responsive rerouting improves performance and equity without full-fleet replanning.

Nicole Hu, Mingtao Zhang, Haoyang LI +2

School of Hotel and Tourism Management The Hong Kong Polytechnic University Hong Kong SAR, China · Department of Computing The Hong Kong Polytechnic University Hong Kong SAR, China · School of Hotel and Tourism Management & Computing The Hong Kong Polytechnic University Hong Kong SAR, China

Algorithmic Fairness Vehicle Routing Multi-Robot Coordination Autonomous Driving Planning

Jul 26, 2026cs.AI

SpecAHD: Localize to Specialize for Automated Heuristic Design in Large-Scale Routing Problems

LLM-based automated heuristic design (AHD) typically scores executable programs on complete instances or within fixed solver components. In large-scale routing problems, localized reconstruction reduces the size of each optimization task, but repair regions within the same incumbent can exhibit substantially different structures. One construction rule must therefore compromise across them. In this paper, we propose SpecAHD, a coupled bilevel framework for within-instance specialization. An upper-level search learns where to expose bounded repair regions, while a lower-level search evolves a complementary repertoire of executable heuristics for the induced repair tasks. The upper-level program determines the repair tasks seen by the lower level, while checked repair outcomes determine how upper-level programs are evaluated. The lower-level objective favors heuristics that perform well on average or solve tasks that the current repertoire handles poorly. For the repair tasks induced by a fixed upper-level program and a fixed lower-level candidate pool, this objective is monotone submodular, allowing greedy repertoire selection with a (1-1/e) approximation guarantee. Across four routing problems and multiple LLM backbones, SpecAHD reduces held-out objective cost by up to 57.7% against the strongest competing AHD baseline and outperforms the per-instance baseline envelope on most public instances.

Kezhao Lai, Yutao Lai, Hai-Lin Liu

School of Mathematics and Statistics, Guangdong University of Technology, China

Automated Heuristic Design Large Language Model-Guided Optimization Combinatorial Optimization Vehicle Routing Bilevel Optimization

Jul 25, 2026math.OC

KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering

Time-dependent routing recognizes that the same journey can take a different time depending on when it begins. Under duration minimization, even the departure time of each vehicle becomes a decision. Exact methods for this setting exist in the literature, but researchers and practitioners have lacked a ready-to-use open solver that combines rich piecewise-linear travel times, early feasible solutions and optimality claims. KAYROS fills this gap with two modes on one checker-consistent engine: an Iterated Local Search that streams improving solutions and a Branch-Price-and-Cut method that can issue computational optimality certificates under explicit arithmetic and search assumptions. It installs with one command and has no proprietary dependency. The public MAMUT-routing store currently contains 704 KAYROS certificates under a four-solve publication protocol, which has also led to the retraction and repair of invalid earlier claims. The report presents two complementary benchmark contributions to MAMUT-routing. The first integrates Blauth2024, a benchmark from the literature whose travel times derive from measured Uber speeds, for which KAYROS provides new best-known solutions on all 40 instances. The second proposes Poryos2026, a new benchmark of 1,080 paired static and time-dependent instances built from OpenStreetMap road networks and controlled synthetic traffic. Finally, the report describes the intensive human-AI collaboration behind this work and the verification practices that kept its outputs independently verifiable.

Florian Rascoussier

IMT Atlantique, Lab-STICC, CNRS, UMR 6285 (équipe DECIDE) and INSA Lyon, Inria, CITI, UR3720, 69621 Villeurbanne, France.

Metaheuristic Optimization Vehicle Routing

Jul 24, 2026cs.LG

Integrated Order Dispatching and Routing for Last-Mile Pickup via Deep Reinforcement Learning

In recent years, the growing complexity of last-mile pickup operations has increased the need for fast and accurate decision-making on logistics platforms. This challenge is fundamentally driven by two key and tightly coupled decision-making processes: order dispatching and routing. Solving them separately overlooks their interdependence, while fully end-to-end learning can be unstable and costly on large, variable-scale instances due to sparse rewards. To solve this problem, we propose an integrated optimization framework which couples a learned routing oracle with real-time dispatching heuristics. For the routing subproblem, we develop a Dynamic-Residual Graph Attention Network encoder with a Look-Ahead Courier-Personalized decoder. For the dispatching subproblem, we develop a routing-oracle-guided dispatching heuristic with local search, where the oracle provides near-optimal solutions to select candidate couriers while retaining real-time scalability. Extensive experiments on real-world datasets from Cainiao Logistics are used to test the performance of our approach, including an offline evaluation and an online rolling-horizon simulation. The experimental results show that our approach outperforms other benchmarks regarding solution quality and solving time, indicating it can effectively support logistics companies in solving real-time and large-scale last-mile pickup problems.

Yida Xu, Zhaofang Mao, Yuheng Miao +2

College of Management and Economics, Tianjin University, Tianjin 300072, China · Laboratory of Computation and Analytics of Complex Management Systems (CACMS), Tianjin University, Tianjin 300072, China

Vehicle Routing Supply Chain Management RL for Combinatorial Optimization Neural Combinatorial Optimization

Jul 20, 2026cs.AI

LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers

Multi-task neural solvers aim to handle multiple Vehicle Routing Problem (VRP) variants within a unified model, avoiding separate training for each constraint combination. However, VRP variants differ in optimization difficulty, while existing methods lack stage-wise feedback on their training status, making the model biased to some specific variants. Although meta-learning can support adaptive training, it typically requires bi-level optimization and additional gradient updates, increasing computational cost. To address this limitation, we propose LLM-as-Trainer (LaT), a plug-and-play training paradigm that uses a pretrained large language model as an external trainer. LaT periodically analyzes cross-task validation metrics to generate a stage-wise guidance vector. This vector is combined with the current task's constraint vector and injected into each encoder layer, providing the neural solver with additional training information during subsequent policy optimization. Experiments on 16 VRP variants show that LaT improves the solution quality of several state-of-the-art multi-task neural solvers on both trained and unseen variants, supporting the effectiveness and generality of the proposed training paradigm.

Yang Wang, Ya-Hui Jia, Wei-Neng Chen +3

School of Future Technology, South China University of Technology, China · School of Computer Science and Engineering, South China University of Technology, China · School of Engineering and Computer Science, Victoria University of Wellington, New Zealand +2

Large Language Model-Guided Optimization Multi-Task Learning Vehicle Routing Neural Combinatorial Optimization

Jul 18, 2026cs.LG

Certified-Gap Dual-Price Policies for Real-Time Truckload Bid Acceptance with Relocating, Clock-Constrained Resources

A truckload carrier must accept or reject each load tender within seconds. The decision depends on fleet state, hours-of-service (HOS) clocks, and appointment windows. We model this as a weakly coupled dynamic program in which the resources relocate and carry clocks: serving a request moves the truck to a new market and depletes its clocks, and whether a truck can serve a request depends on its state. Occupancy-based reusable-resource models do not cover this setting. We build a real-time dual-price policy from the same Lagrangian relaxation that gives the problem's upper bound. Policy and bound come from one object, so every run reports a certified optimality gap. We prove three things. First, the certificate is valid for any duals, any discretization, and any surrogate quality. Second, the policy's same-time spatial-gradient rule is exactly fluid complementary slackness, and the policy is asymptotically optimal in the subcritical fluid regime; the fitted prices are also portable across sample paths, by linear-programming basis stability. Third, certificates have limits: per-resource Lagrangian slack can stay bounded away from zero at every fleet size. We exhibit a three-truck kernel with an exact rational certificate and a replication lemma. On a public closed-loop benchmark with thirty paired seeds, the policy -- which needs no rollout labels, only one offline dual solve -- beats a rollout-trained surrogate on two of three scenarios (tight: +2.0 pp, 95% CI [+0.5, +3.6], Wilcoxon p = 0.023; mild: +3.5 pp, CI [+2.4, +4.5]) and ties the third. It decides in 0.04-0.09 ms, three orders of magnitude faster than the Monte Carlo rollout teacher. Its certificates are stable across ten bounded instances per scenario, at 57-64% of optimal, within 3-6 points of what the 1000x-slower teacher certifies.

Aswin Chandrasekaran

Bubba AI

Real-Time Scheduling Intelligent Transportation Systems Vehicle Routing Constrained Optimization Online Resource Allocation Real-Time Bidding

Jul 18, 2026math.OC

A Deep Reinforcement Learning Algorithm for the Vehicle Routing Problem with Stochastic Demands and Outsourcing

We introduce the vehicle routing problem with stochastic demands and outsourcing options (VRP-SDO), in which a logistics service provider partitions customer requests into customers outsourced to a common carrier and customers committed to its fixed fleet. The latter induces a vehicle routing problem with stochastic demands (VRP-SD), solved dynamically. Demands are revealed upon visit; residual demand may be served by other vehicles or after restocking at the depot. Work beyond the regular shift incurs overtime costs, and the unit outsourcing cost decreases with the expected outsourced demand. The objective is to minimize expected travel, overtime, and outsourcing costs. We propose an iterative two-level methodology whose first level partitions customers into committed and outsourced subsets, while the second level estimates the expected VRP-SD routing cost. To avoid solving this problem from scratch at every iteration, we learn an offline routing policy that estimates costs almost instantly for any committed subset. An iterated local search establishes the first-level partitions. We formulate the second level as a Markov decision process and solve it with a deep Q-network whose state is represented by a graph attention network aggregating customer and vehicle information by relevance to the acting vehicle. Trained offline on instances with variable customer cardinality and locations, the policy applies to any daily customer realization; online fine-tuning improves the cost approximation. Experiments show that our policy reduces routing costs by 19.6% relative to a state-of-the-art method and by at least 29.6% over classical heuristics. Our overall algorithm saves 13.7% on average over the version without the attention-based representation and generates high-quality decisions within minutes, whereas benchmarks without an offline-trained estimator require over an hour.

Mohsen Dastpak, Fausto Errico, Ola Jabali

aDepartment de génie de la construction, École de technologie supérieure, , Montréal, H3C 1K3, QC, Canada · bGERAD, , Montréal, H3T 1J4, QC, Canada · cCIRRELT, , Montréal, H3C 3J7, QC, Canada +1

Vehicle Routing RL for Combinatorial Optimization

Jul 16, 2026cs.MA

Randomized routing strategies of fleets of CAVs may prove market efficient

In future cities every driver may own a vehicle which could be either independently driven (HDV), or autonomously routed and piloted (CAV). The autonomous operations could be handled by a few competing companies. What is the market structure which would make this market aligned with city goals? In this paper we discuss a variant of the emerging market of collectively routed fleets of CAVs, where revenue for fleet operators is proportional to market share. We provide benchmark scenarios to compare the routing algorithms. We present several routing algorithms and demonstrate that, when the attitudes of human drivers towards CAVs exhibit significant diversity, randomised CAV routing, resulting in unpredictable travel times for HDVs, is more efficient than routing proportional to system optimum/user equilibrium. Based on this, we propose to improve the design of the market by augmenting the market-share objective with mean systemwide travel time in order to limit antisocial randomised strategies of fleet operators and drive the competition towards social welfare oriented cooperation.

Grzegorz Jamróz, Łukasz Gorczyca, Rafał Kucharski

Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

Intelligent Transportation Systems Vehicle Routing Autonomous Driving Planning

Jul 15, 2026cs.RO

Dynamical Vehicle Orienteering Problem for Multi-Rotor Unmanned Aerial Vehicles

This paper introduces the Dynamical Vehicle Orienteering Problem (DVOP), a generalization of the Orienteering Problem (OP). The OP maximizes the reward collected from spatial targets under a limited travel budget; the DVOP extends it by accounting for both external and vehicle-actuated forces. We study the DVOP in the context of multi-rotor Unmanned Aerial Vehicle (UAV) flight planning, using a three-dimensional Point-Mass Model (PMM) constrained by maximum velocity and acceleration magnitudes and subject to gravitational acceleration, with the travel budget expressed as a maximum flight time. Because the DVOP couples reward maximization with time-optimal trajectory planning, it cannot be formulated as a simple graph problem and solved exactly without relaxing or under-actuating the vehicle dynamics. We therefore propose two solution approaches: a Branch-and-Bound (BnB) procedure that combines Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP) to provide high-quality solutions, and a Large Neighborhood Search (LNS) metaheuristic that supplies an initial reward bound and scales to instances intractable for the BnB. The BnB relies on a novel MILP formulation of travel costs based on minimum-time trajectory primitives through target triplets, yielding a tight reward upper bound, while the LNS uses limited thrust decomposition to compute fast, high-quality PMM trajectories. Experiments on benchmark instances show improvements of up to 37 % over state-of-the-art solutions for the Kinematic Orienteering Problem, and a real-world deployment on a multi-rotor UAV verifies the proposed PMM solution trajectories.

František Nekovář, Matej Novosad, Martin Saska +1

Faculty of Electrical Engineering, Czech Technical University, Technicka 2, 166 27, Prague, Czech Republic

Trajectory Optimization Branch and Bound UAV Navigation Combinatorial Optimization Vehicle Routing UAV Trajectory Optimization+1

Jul 15, 2026math.OC

Learned Pairwise Deep Dual-Optimal Inequalities for Stabilizing Column Generation

Column generation (CG) is central to many large-scale optimization algorithms, including branch-price-and-cut methods for vehicle routing problems, but unstable dual solutions can substantially slow its convergence. Existing deep dual-optimal inequalities can reduce this instability by restricting the dual space. Their construction, however, typically relies on problem-specific exchange arguments that are difficult to establish for routing problems with capacity limits, time windows, and other resource constraints. We introduce learned pairwise deep dual-optimal inequalities (L-PDDOIs), a learning framework that predicts pairwise orderings between dual variables and incorporates their primal counterparts directly into the master problem. To construct training labels, the framework samples optimal dual solutions and selects pairwise order relations that hold simultaneously on a sufficiently large common subset of the samples. A classifier then assigns a score to each candidate relation. Because conflicts and redundancies among the predicted relations can impair performance, graph-based postprocessing filters and compresses the candidate set before deployment. We further introduce a recovery procedure that selectively relaxes learned inequalities and provides a certificate when the baseline CG bound has been restored. On the main test sets for the capacitated vehicle routing problem and the vehicle routing problem with time windows, direct deployment of L-PDDOIs reduces the geometric mean root CG time by 89.7% and 93.9%, respectively, while incurring mean bound losses of only 1.3% and 0.5%. The recovery procedure retains corresponding time reductions of 54.8% and 83.1%, respectively, while guaranteeing no loss in the CG bound.

Zhengzhong Ricky You, Bo Tang, Haoran Liu +1

Department of Civil Engineering, Tsinghua University, Beijing 100084, China · MIT Sloan School of Management, Massachusetts Institute of Technology, 100 Main Street, Cambridge, MA 02142, USA · Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA

Primal-Dual Optimization Combinatorial Optimization Vehicle Routing

Jul 11, 2026cs.MA

RideGym: A Standardized Interface for Real-World Large-Scale Ride-Sharing System

Ride-sharing has become an essential component of modern urban transportation and has attracted significant attention across computer science, transportation, and management science. While the field spans a broad range of problems, such as driver relocation, dynamic pricing, and vehicle charging or fueling dispatch, the core challenge remains order assignment and trip bundling, which directly affect urban traffic efficiency and carbon emissions. Despite its importance, existing simulation platforms are typically tailored to specific operational studies or tightly coupled to a particular dispatch algorithm, and rarely expose a standardized, learning-friendly interface. As a result, most researchers still build customized environments from scratch, raising serious concerns about reproducibility and fair comparison, and incurring substantial redundant effort. To address this gap, we present RideGym, the first open-source, standardized Gym-style interface tailored to MARL-based order dispatch in real-world ride-sharing systems. By fully decoupling the environment from the dispatch algorithm, RideGym enables diverse learning-based and model-based methods to be developed and compared under identical, fully specified conditions. It supports efficient, large-scale city-level simulations on real road networks, and offers flexible configurations for vehicle attributes, order specifications, and automatic shortest-path routing. We validate RideGym by reproducing several baselines, and demonstrate its high efficiency, with a one-hour simulation involving thousands of vehicles and tens of thousands of orders completed within one minute across all methods. Moreover, we reveal that the choice of exploration noise can significantly affect both the performance and the relative ranking of MARL solutions, an aspect often overlooked in prior work.

Zijian Zhao, Yulong Hu, Sen Li

The Hong Kong University of Science and Technology Hong Kong, China

Vehicle Routing AI Agent Benchmarks