Stress-Relief Annealing: Polynomial-Time Simulation-Free Layout Optimization for Automated Warehouses

2026-08-02

AI Summary

This work addresses the inefficiency of existing black-box evolutionary methods for automated warehouse layout optimization, which rely heavily on simulation and suffer from low sample efficiency and high computational cost. The paper proposes the first simulation-free, polynomial-time layout optimization algorithm that translates task demands into a vertex-level stress field to predict traffic hotspots and leverages a provable upper bound on this stress field to guide layout design. By integrating stress field modeling with multi-agent path planning, the method achieves throughput comparable to or exceeding that of evolutionary algorithms requiring 25,000 simulations over 25 hours, while completing optimization in just 19 minutes on a single-core CPU. It further demonstrates strong generalizability across diverse task distributions and warehouse scales, substantially enhancing computational efficiency and scalability.

Abstract

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.

Problem

• layout optimization
• automated warehouses
• throughput
• sample efficiency
• simulation-free

Innovation

• Stress-Relief Annealing
• simulation-free optimization
• warehouse layout optimization
• stress field
• polynomial-time algorithm