# Lifelong Learning with Behavior Consolidation for Vehicle Routing

arXiv: https://arxiv.org/abs/2509.21765 · HTML: https://mlsanity.com/paper/2509.21765/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 37)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [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)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [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)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Adversarial Continual Learning](https://mlsanity.com/paper/2003.09553/) (2020)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [Towards Omni-generalizable Neural Methods for Vehicle Routing Problems](https://mlsanity.com/paper/2305.19587/) (2023)
- [Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2404.02657/) (2024)
- [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)
- [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)
- [Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences](https://mlsanity.com/paper/2107.08285/) (2021)
- [Policy Consolidation for Continual Reinforcement Learning](https://mlsanity.com/paper/1902.00255/) (2019)
- [Incremental Learning via Rate Reduction](https://mlsanity.com/paper/2011.14593/) (2020)
- [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)
- [RKLD: Reverse KL-Divergence-based Knowledge Distillation for Unlearning Personal Information in Large Language Models](https://mlsanity.com/paper/2406.01983/) (2024)

## Built on by (most cited first, 1 of 1)

- [Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks](https://mlsanity.com/paper/2601.22509/) (2026)

## Abstract (arXiv)

Recent neural solvers have demonstrated promising performance in learning to solve routing problems. However, existing studies are primarily based on one-off training on one or a set of predefined problem distributions and scales, i.e., tasks. When a new task arises, they typically rely on either zero-shot generalization, which may be poor due to the discrepancies between the new task and the training task(s), or fine-tuning the pretrained solver on the new task, which possibly leads to catastrophic forgetting of knowledge acquired from previous tasks. This paper explores a novel lifelong learning paradigm for neural VRP solvers, where multiple tasks with diverse distributions and scales arise sequentially over time. Solvers are required to effectively and efficiently learn to solve new tasks while maintaining their performance on previously learned tasks. Consequently, a novel framework called Lifelong Learning Router with Behavior Consolidation (LLR-BC) is proposed. LLR-BC consolidates prior knowledge effectively by aligning behaviors of the solver trained on a new task with the buffered ones in a decision-seeking way. To encourage more focus on crucial experiences, LLR-BC assigns greater consolidated weights to decisions with lower confidence. Extensive experiments on capacitated vehicle routing problems and traveling salesman problems demonstrate LLR-BC's effectiveness in training high-performance neural solvers in a lifelong learning setting, addressing the catastrophic forgetting issue, maintaining their plasticity, and improving zero-shot generalization ability.