# Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization

arXiv: https://arxiv.org/abs/2402.16891 · HTML: https://mlsanity.com/paper/2402.16891/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [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)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Zero-Shot Task Generalization with Multi-Task Deep Reinforcement Learning](https://mlsanity.com/paper/1706.05064/) (2017)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [Simulation-guided Beam Search for Neural Combinatorial Optimization](https://mlsanity.com/paper/2207.06190/) (2022)
- [Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy](https://mlsanity.com/paper/2308.14104/) (2023)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Independent Prototype Propagation for Zero-Shot Compositionality](https://mlsanity.com/paper/2106.00305/) (2021)
- [Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness](https://mlsanity.com/paper/2110.10942/) (2021)
- [Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2110.02629/) (2021)
- [Learning to Solve Routing Problems via Distributionally Robust Optimization](https://mlsanity.com/paper/2202.07241/) (2022)
- [On the Generalization of Neural Combinatorial Optimization Heuristics](https://mlsanity.com/paper/2206.00787/) (2022)
- [Analytics and Machine Learning in Vehicle Routing Research](https://mlsanity.com/paper/2102.10012/) (2021)
- [A concise guide to existing and emerging vehicle routing problem variants](https://mlsanity.com/paper/1906.06750/) (2019)

## Built on by (most cited first, 30 of 50)

- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [Graph Neural Networks for Job Shop Scheduling Problems: A Survey](https://mlsanity.com/paper/2406.14096/) (2024)
- [Learning to Reduce Search Space for Generalizable Neural Routing Solver](https://mlsanity.com/paper/2503.03137/) (2025)
- [ARS: Automatic Routing Solver with Large Language Models](https://mlsanity.com/paper/2502.15359/) (2025)
- [FlexiReg: Flexible Urban Region Representation Learning](https://mlsanity.com/paper/2503.09128/) (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)
- [RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization](https://mlsanity.com/paper/2503.16159/) (2025)
- [Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solver](https://mlsanity.com/paper/2405.01906/) (2024)
- [Collaboration! Towards Robust Neural Methods for Routing Problems](https://mlsanity.com/paper/2410.04968/) (2024)
- [Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimization](https://mlsanity.com/paper/2408.12214/) (2024)
- [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)
- [PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization](https://mlsanity.com/paper/2409.03811/) (2024)
- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [Fine-tuning Large Language Model for Automated Algorithm Design](https://mlsanity.com/paper/2507.10614/) (2025)
- [Survey on Neural Routing Solvers](https://mlsanity.com/paper/2602.21761/) (2026)
- [Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers](https://mlsanity.com/paper/2411.09238/) (2024)
- [Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM](https://mlsanity.com/paper/2510.11121/) (2025)
- [RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains](https://mlsanity.com/paper/2511.02331/) (2025)
- [Towards Efficient Constraint Handling in Neural Solvers for Routing Problems](https://mlsanity.com/paper/2602.16012/) (2026)
- [TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problems](https://mlsanity.com/paper/2503.12662/) (2025)
- [Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs](https://mlsanity.com/paper/2603.01667/) (2026)
- [SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver](https://mlsanity.com/paper/2605.24484/) (2026)
- [RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs](https://mlsanity.com/paper/2411.19517/) (2024)
- [USPR: Learning a Unified Solver for Profiled Routing](https://mlsanity.com/paper/2505.05119/) (2025)
- [Hierarchical Optimization via LLM-Guided Objective Evolution for Mobility-on-Demand Systems](https://mlsanity.com/paper/2510.10644/) (2025)

## Abstract (arXiv)

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a learning-based model to solve VRPs without manual algorithm design has gained substantial attention. However, current NCO methods typically require building one model for each routing problem, which significantly hinders their practical application for real-world industry problems with diverse attributes. In this work, we make the first attempt to tackle the crucial challenge of cross-problem generalization. In particular, we formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. Extensive experiments are conducted on eleven VRP variants, benchmark datasets, and industry logistic scenarios. The results show that the unified model demonstrates superior performance in the eleven VRPs, reducing the average gap to around 5% from over 20% in the existing approach and achieving a significant performance boost on benchmark datasets as well as a real-world logistics application. The source code is included in https://github.com/FeiLiu36/MTNCO.