# Learning to Solve the Min-Max Mixed-Shelves Picker-Routing Problem via Hierarchical and Parallel Decoding

arXiv: https://arxiv.org/abs/2502.10233 · HTML: https://mlsanity.com/paper/2502.10233/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 14 Feb 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [Matrix Encoding Networks for Neural Combinatorial Optimization](https://mlsanity.com/paper/2106.11113/) (2021)
- [RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark](https://mlsanity.com/paper/2306.17100/) (2023)
- [PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimization](https://mlsanity.com/paper/2402.14048/) (2024)
- [Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvement](https://mlsanity.com/paper/2403.15180/) (2024)
- [Self-Labeling the Job Shop Scheduling Problem](https://mlsanity.com/paper/2401.11849/) (2024)
- [DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems](https://mlsanity.com/paper/2405.17272/) (2024)
- [Equity-Transformer: Solving NP-hard Min-Max Routing Problems as Sequential Generation with Equity Context](https://mlsanity.com/paper/2306.02689/) (2023)
- [CAMP: Collaborative Attention Model with Profiles for Vehicle Routing Problems](https://mlsanity.com/paper/2501.02977/) (2025)
- [Formulating and solving integrated order batching and routing in multi-depot AGV-assisted mixed-shelves warehouses](https://mlsanity.com/paper/2101.11473/) (2021)

## Built on by (most cited first, 2 of 2)

- [Solving the Pod Repositioning Problem with Deep Reinforced Adaptive Large Neighborhood Search](https://mlsanity.com/paper/2506.02746/) (2025)
- [Multi-Action Self-Improvement for Neural Combinatorial Optimization](https://mlsanity.com/paper/2510.12273/) (2025)

## Abstract (arXiv)

The Mixed-Shelves Picker Routing Problem (MSPRP) is a fundamental challenge in warehouse logistics, where pickers must navigate a mixed-shelves environment to retrieve SKUs efficiently. Traditional heuristics and optimization-based approaches struggle with scalability, while recent machine learning methods often rely on sequential decision-making, leading to high solution latency and suboptimal agent coordination. In this work, we propose a novel hierarchical and parallel decoding approach for solving the min-max variant of the MSPRP via multi-agent reinforcement learning. While our approach generates a joint distribution over agent actions, allowing for fast decoding and effective picker coordination, our method introduces a sequential action selection to avoid conflicts in the multi-dimensional action space. Experiments show state-of-the-art performance in both solution quality and inference speed, particularly for large-scale and out-of-distribution instances. Our code is publicly available at http://github.com/LTluttmann/marl4msprp.