The Multi-AMR Buffer Storage, Retrieval, and Reshuffling Problem: Exact and Heuristic Approaches

Automated warehouses face a fundamental trade-off between maximizing storage density and achieving high retrieval throughput. While puzzle-based storage (PBS) architectures increase capacity by eliminating aisles, coordinating multiple robots in these high-density spaces is computationally challenging due to the potential for deadlocks. This paper introduces a novel multi-robot formulation for the ``ordered storage and retrieval problem at maximum capacity''. The focus is on rectangular grids accessible from a single boundary, where loads need to be first stored up to full capacity and then efficiently retrieved, given a planned departure sequence. This work bridges the gap between geometric feasibility and execution efficiency by leveraging the properties of relocation-free arrangements. These properties guide an online, prioritized multi-agent path-finding algorithm, which is the main contribution of this work. Unlike general centralized planners, the approach exploits the specific invariants of the storage arrangement to guarantee completeness and prevent deadlocks, enabling scalability. Experiments demonstrate that the method achieves near-linear improvement in makespan with respect to the number of robots, up to $m = C$, where $C$ is the grid width. Crucially, the algorithmic overhead of supporting robustness is negligible; the system handles uncertainty in departure sequences using robust storage arrangements with no significant penalty in execution speed compared to the non-robust baseline.

Double-Deck Multi-Agent Pickup and Delivery (DD-MAPD) models the multi-robot shelf rearrangement problem in automated warehouses. MAPF-DECOMP is a recent framework that first computes collision-free shelf trajectories with a MAPF solver and then assigns agents to execute them. While efficient, it enforces strict trajectory dependencies, often leading to poor execution quality due to idle agents and unnecessary shelf switching. We introduce CREST, a new execution framework that achieves more continuous shelf carrying by proactively releasing trajectory constraints during execution. Experiments on diverse warehouse layouts show that CREST consistently outperforms MAPF-DECOMP, reducing metrics related to agent travel, makespan, and shelf switching by up to 40.5%, 33.3%, and 44.4%, respectively, with even greater benefits under lift/place overhead. These results underscore the importance of execution-aware constraint release for scalable warehouse rearrangement. Code and data are available at https://github.com/ChristinaTan0704/CREST.

Coordinating multi-agent systems over spatially distributed areas requires solving a complex hierarchical problem: first distributing areas among agents (allocation) and subsequently determining the optimal visitation order (routing). Existing methods typically decouple these stages ignoring inter-stage dependencies or rely on decentralized heuristics that lack global context. In this work, we propose a centralized, fully end-to-end auto-regressive framework that jointly generates allocation decisions and routing sequences. The core contribution of our approach is a multi-stage decoding mechanism that unifies high-level allocation and low-level routing in a single autoregressive pass while maintaining a centralized global state. This enables the model to implicitly balance workload distribution with routing efficiency, avoiding local optima common in decentralized methods. Extensive experiments demonstrate that our method significantly outperforms diverse baselines, achieving up to a 20% improvement in solution quality over industrial solvers such as Google OR-Tools, IBM CPLEX, and LKH-3, while reducing computation time from hours to seconds.