# End-to-end Deep Reinforcement Learning for Stochastic Multi-objective Optimization in C-VRPTW

arXiv: https://arxiv.org/abs/2512.01518 · HTML: https://mlsanity.com/paper/2512.01518/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 15 of 15)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (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)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2004.01608/) (2020)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2310.15196/) (2023)
- [Reasoning About Beliefs and Actions Under Computational Resource Constraints](https://mlsanity.com/paper/1304.2759/) (2013)
- [A concise guide to existing and emerging vehicle routing problem variants](https://mlsanity.com/paper/1906.06750/) (2019)
- [Guidelines for the Computational Testing of Machine Learning approaches to Vehicle Routing Problems](https://mlsanity.com/paper/2109.13983/) (2021)
- [Equity-Transformer: Solving NP-hard Min-Max Routing Problems as Sequential Generation with Equity Context](https://mlsanity.com/paper/2306.02689/) (2023)
- [Multiobjective Vehicle Routing Optimization with Time Windows: A Hybrid Approach Using Deep Reinforcement Learning and NSGA-II](https://mlsanity.com/paper/2407.13113/) (2024)
- [Reinforcement Learning for Solving Stochastic Vehicle Routing Problem](https://mlsanity.com/paper/2311.07708/) (2023)

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

- [Hard Constraints Meet Soft Generation: Guaranteed Feasibility for LLM-based Combinatorial Optimization](https://mlsanity.com/paper/2602.01090/) (2026)

## Abstract (arXiv)

In this work, we consider learning-based applications in routing to solve a Vehicle Routing variant characterized by stochasticity and multiple objectives. Such problems are representative of practical settings where decision-makers have to deal with uncertainty in the operational environment as well as multiple conflicting objectives due to different stakeholders. We specifically consider travel time uncertainty. We also consider two objectives, total travel time and route makespan, that jointly target operational efficiency and labor regulations on shift length, although different objectives could be incorporated. Learning-based methods offer earnest computational advantages as they can repeatedly solve problems with limited interference from the decision-maker. We specifically focus on end-to-end deep learning models that leverage the attention mechanism and multiple solution trajectories. These models have seen several successful applications in routing problems. However, since travel times are not a direct input to these models due to the large dimensions of the travel time matrix, accounting for uncertainty is a challenge, especially in the presence of multiple objectives. In turn, we propose a model that simultaneously addresses stochasticity and multi-objectivity and provide a refined training mechanism for this model through scenario clustering to reduce training time. Our results show that our model is capable of constructing a Pareto Front of good quality within acceptable run times compared to three baselines.