Multi-Objective Layout Optimization for Multi-Robot Coordination in Automated Warehouse

We study the problem of multi-objective layout optimization for automated warehouses, where hundreds to thousands of robots are coordinated to transport packages from one location to another. Previous works have attempted to optimize the system throughput of warehouses by optimizing their layout (e.g., the physical locations of the storage shelves) while assuming a fixed storage capacity (i.e., the number of storage shelves). However, in practice, storage capacity also significantly affects the operating cost of the warehouse, because a smaller storage capacity requires the warehouse to occupy more land. Importantly, there are trade-offs between the storage capacity and throughput, because a larger storage capacity creates more obstacles for robots, complicating the multi-robot coordination and potentially reducing throughput. In this paper, we generalize the state-of-the-art single-objective layout optimization methods based on Quality Diversity (QD) algorithms to multiple objectives, where we optimize for a Pareto front (PF) of throughput and storage capacity. We show that our optimized PF significantly outperforms vanilla multi-objective optimization algorithms across various robot task distributions, robot coordination algorithms, and layout sizes. We additionally present a Mixed Integer Linear Programming Solver (MILP) that enforces the optimized layout to be biconnected, which helps the downstream coordination algorithm move the robots more effectively. Our code will be publicly available upon acceptance.