We introduce a new problem formulation, Double-Deck Multi-Agent Pickup and Delivery (DD-MAPD), which models the multi-robot shelf rearrangement problem in automated warehouses. DD-MAPD extends both Multi-Agent Pickup and Delivery (MAPD) and Multi-Agent Path Finding (MAPF) by allowing agents to move beneath shelves or lift and deliver a shelf to an arbitrary location, thereby changing the warehouse layout. We show that solving DD-MAPD is NP-hard. To tackle DD-MAPD, we propose MAPF-DECOMP, an algorithmic framework that decomposes a DD-MAPD instance into a MAPF instance for coordinating shelf trajectories and a subsequent MAPD instance with task dependencies for computing paths for agents. We also present an optimization technique to improve the performance of MAPF-DECOMP and demonstrate how to make MAPF-DECOMP complete for well-formed DD-MAPD instances, a realistic subclass of DD-MAPD instances. Our experimental results demonstrate the efficiency and effectiveness of MAPF-DECOMP, with the ability to compute high-quality solutions for large-scale instances with over one thousand shelves and hundreds of agents in just minutes of runtime.

翻译：我们提出了一种新的问题模型——双层多智能体取货与配送（DD-MAPD），用于建模自动化仓库中的多机器人货架重新布局问题。DD-MAPD扩展了多智能体取货与配送（MAPD）和多智能体路径规划（MAPF），允许智能体在货架下方移动，或举升并运送货架至任意位置，从而改变仓库布局。我们证明了解DD-MAPD问题具有NP难度。为求解DD-MAPD，我们提出了MAPF-DECOMP算法框架，该框架将DD-MAPD实例分解为一个协调货架轨迹的MAPF实例，以及一个后续的、带有任务依赖关系的MAPD实例用于计算智能体路径。我们还提出了一种优化技术以提高MAPF-DECOMP的性能，并展示了如何使MAPF-DECOMP对良构的DD-MAPD实例（即DD-MAPD的一个实际子类）具有完备性。实验结果表明，MAPF-DECOMP能高效地计算出高质量解，可在数分钟内解决包含超过一千个货架和数百个智能体的大规模实例。