The rapid scaling of large language models (LLMs) has significantly increased GPU memory pressure, which is further aggravated by training optimization techniques such as virtual pipeline and recomputation that disrupt tensor lifespans and introduce considerable memory fragmentation. Such fragmentation stems from the use of online GPU memory allocators in popular deep learning frameworks like PyTorch, which disregard tensor lifespans. As a result, this inefficiency can waste as much as 43% of memory and trigger out-of-memory errors, undermining the effectiveness of optimization methods. To address this, we introduce STAlloc, a GPU memory allocator for deep learning frameworks that reduces fragmentation by exploiting the spatial and temporal regularity in memory allocation behaviors of training workloads. STAlloc introduces a novel paradigm that combines offline planning with online allocation. The offline planning leverages spatio-temporal regularities to generate a near-optimal allocation plan, while the online allocation handles complex and dynamic models such as Mixture-of-Experts (MoE). Built as a pluggable PyTorch memory allocator, STAlloc reduces fragmentation ratio on average by 85.1% (up to 100%) across both dense and MoE models, with negligible overhead. This enables more efficient, high-throughput training configurations and improves throughput performance by up to 32.5%.

This paper investigates the optimization problem of scheduling autonomous mobile robots (AMRs) in hospital settings, considering dynamic requests with different priorities. The primary objective is to minimize the daily service cost by dynamically planning routes for the limited number of available AMRs. The total cost consists of AMR's purchase cost, transportation cost, delay penalty cost, and loss of denial of service. To address this problem, we have established a two-stage mathematical programming model. In the first stage, a tabu search algorithm is employed to plan prior routes for all known medical requests. The second stage involves planning for real-time received dynamic requests using the efficient insertion algorithm with decision rules, which enables quick response based on the time window and demand constraints of the dynamic requests. One of the main contributions of this study is to make resource allocation decisions based on the present number of service AMRs for dynamic requests with different priorities. Computational experiments using Lackner instances demonstrate the efficient insertion algorithm with decision rules is very fast and robust in solving the dynamic AMR routing problem with time windows and request priority. Additionally, we provide managerial insights concerning the AMR's safety stock settings, which can aid in decision-making processes.