# Optimizing 2D+1 Packing in Constrained Environments Using Deep Reinforcement Learning

arXiv: https://arxiv.org/abs/2503.17573 · HTML: https://mlsanity.com/paper/2503.17573/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot navigation and UAV control, one of 15 directions in Deep reinforcement learning methods.
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot navigation and UAV control](https://mlsanity.com/deeprl/rl-for-robot-navigation-and-uav-control/)

## Builds on (most cited first, 9 of 9)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Heuristic-Guided Reinforcement Learning](https://mlsanity.com/paper/2106.02757/) (2021)
- [Learning Practically Feasible Policies for Online 3D Bin Packing](https://mlsanity.com/paper/2108.13680/) (2021)
- [A2C is a special case of PPO](https://mlsanity.com/paper/2205.09123/) (2022)
- [Self-play Learning Strategies for Resource Assignment in Open-RAN Networks](https://mlsanity.com/paper/2103.02649/) (2021)
- [Online 3D Bin Packing Reinforcement Learning Solution with Buffer](https://mlsanity.com/paper/2208.07123/) (2022)
- [One model Packs Thousands of Items with Recurrent Conditional Query Learning](https://mlsanity.com/paper/2111.06726/) (2021)
- [Learning based 2D Irregular Shape Packing](https://mlsanity.com/paper/2309.10329/) (2023)

## Abstract (arXiv)

This paper proposes a novel approach based on deep reinforcement learning (DRL) for the 2D+1 packing problem with spatial constraints. This problem is an extension of the traditional 2D packing problem, incorporating an additional constraint on the height dimension. Therefore, a simulator using the OpenAI Gym framework has been developed to efficiently simulate the packing of rectangular pieces onto two boards with height constraints. Furthermore, the simulator supports multidiscrete actions, enabling the selection of a position on either board and the type of piece to place. Finally, two DRL-based methods (Proximal Policy Optimization -- PPO and the Advantage Actor-Critic -- A2C) have been employed to learn a packing strategy and demonstrate its performance compared to a well-known heuristic baseline (MaxRect-BL). In the experiments carried out, the PPO-based approach proved to be a good solution for solving complex packaging problems and highlighted its potential to optimize resource utilization in various industrial applications, such as the manufacturing of aerospace composites.