We study the problem of optimizing physical layouts for automated warehouses, where hundreds to thousands of robots are coordinated to transport packages. Previous works have shown that optimizing the warehouse layout (e.g., the physical location of the storage shelves) significantly improves throughput. However, state-of-the-art layout optimization approaches are based on evolutionary optimization methods, which treat the entire warehouse as a black box and rely on random mutation to search for high-quality layouts. While the optimization outcomes are promising, these methods require a massive number of simulations to evaluate candidate solutions, making them sample-inefficient. In this paper, we present Stress-Relief Annealing (SRA), a polynomial-time simulation-free layout optimization algorithm. SRA turns the task demand into a per-vertex \emph{stress field} that predicts where traffic will concentrate in the warehouse; the field's peak provably caps the throughput. Our experimental results show that (1) SRA improves both the throughput and the scalability of a human-designed warehouse, roughly doubling the number of robots it can sustain, (2) it matches or exceeds the throughput of the evolutionary baselines while taking only 19 minutes on one CPU core, against their 25,000 simulations and 25 hours on a 64-core machine, and (3) the gain generalizes across different Multi-Agent Path Finding algorithms, non-uniform task demands, and a warehouse with doubled dimensions.
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.
In warehouse logistics, parcels released from the outfeed of an automated storage system must be routed through conveyor networks to workstations. Beyond collision avoidance, practical operations impose an additional requirement of order-contiguous arrivals: at each delivery point, parcels belonging to the same order must arrive as a consecutive block in the arrival sequence to reduce downstream re-sorting effort. We formalize this problem as online multi-agent path finding with order-contiguity (online MAPF-OC), where agents (i.e., parcels) appear over time and exit upon delivery. To efficiently solve online MAPF-OC, we propose Dual-Ordering Prioritized Planning (DOPP), a complete polynomial-time algorithm with a three-level structure that (i) searches order-level arrival sequences, (ii) refines agent-level priorities, and (iii) synthesizes feasible solutions via prioritized planning. Experiments on various conveyor-network layouts, including those derived from actual warehouses, demonstrate DOPP's practical scalability and ability to generate high-quality plans within tight time budgets.
Automated fulfillment warehouses must continuously assign and execute pickup-and-delivery work while avoiding congestion. In many-to-many Multi-Agent Pickup and Delivery (MAPD), a request specifies a stock-keeping unit rather than fixed endpoints, requiring the controller to select an agent, source, and destination before path planning. Existing graph-guidance methods primarily influence routing after goals are fixed, leaving endpoint instantiation uninformed by recent traffic. We introduce Stigmergic Graph Memory (SGM), a bounded, decaying memory layer that records recent execution signals on warehouse nodes and directed edges to rank feasible endpoints and route preferences without altering collision constraints or planner validity. Across paired request streams on five layouts, three load levels, and 25 seeds per condition, SGM outperforms two reconstructed many-to-many allocation baselines in all 15 map-load conditions, with paired throughput gains of 20.5-36.7%. These results show that recent execution memory can improve warehouse throughput by shaping which feasible goals enter the planner, not only how agents travel to already fixed goals.