# Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks

arXiv: https://arxiv.org/abs/2601.22509 · HTML: https://mlsanity.com/paper/2601.22509/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 61 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 34)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Towards Continual Reinforcement Learning: A Review and Perspectives](https://mlsanity.com/paper/2012.13490/) (2020)
- [Selective Experience Replay for Lifelong Learning](https://mlsanity.com/paper/1802.10269/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [Towards Omni-generalizable Neural Methods for Vehicle Routing Problems](https://mlsanity.com/paper/2305.19587/) (2023)
- [Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation](https://mlsanity.com/paper/2210.07686/) (2022)
- [Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy](https://mlsanity.com/paper/2308.14104/) (2023)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer](https://mlsanity.com/paper/2402.02317/) (2024)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [Learning to Solve Routing Problems via Distributionally Robust Optimization](https://mlsanity.com/paper/2202.07241/) (2022)
- [How Good Is Neural Combinatorial Optimization? A Systematic Evaluation on the Traveling Salesman Problem](https://mlsanity.com/paper/2209.10913/) (2022)
- [ASP: Learn a Universal Neural Solver!](https://mlsanity.com/paper/2303.00466/) (2023)
- [Cross-Problem Learning for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2404.11677/) (2024)
- [Concept Drift Adaptation by Exploiting Historical Knowledge](https://mlsanity.com/paper/1702.03500/) (2017)
- [Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problems](https://mlsanity.com/paper/2401.06979/) (2024)
- [Learning to Reduce Search Space for Generalizable Neural Routing Solver](https://mlsanity.com/paper/2503.03137/) (2025)
- [MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver](https://mlsanity.com/paper/2506.02935/) (2025)
- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
- [Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees](https://mlsanity.com/paper/2505.24627/) (2025)
- [URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2509.23413/) (2025)
- [Prompt Learning for Generalized Vehicle Routing](https://mlsanity.com/paper/2405.12262/) (2024)

## Abstract (arXiv)

Existing neural solvers for vehicle routing problems (VRPs) are typically trained either in a one-off manner on a fixed set of pre-defined tasks or in a lifelong manner with tasks arriving sequentially, assuming sufficient training on each task. Both settings overlook a common real-world property: problem patterns may drift continually over time, yielding massive tasks sequentially arising, each with only limited training resources. In this paper, we propose a novel lifelong learning paradigm for neural VRP solvers under continual task drift over time, where each task is locally stationary at one learning time step but receives only insufficient training resources. We empirically demonstrate that such continual drift arises in practice using a real-world logistics dataset. We then propose Dual Replay with Experience Enhancement (DREE), a general framework to improve learning efficiency and mitigate catastrophic forgetting under such drift. Extensive experiments based on both the real-world logistics dataset and commonly used synthetic dataset show that, under such continual drift, DREE effectively learns new tasks, preserves prior knowledge, improves generalization to unseen tasks, and can be applied to various existing neural solvers.