Serving large language models (LLMs) under tight memory and latency service-level objectives (SLOs), including on edge devices, requires jointly selecting the model size, batch size, quantization algorithm, and mixed-precision quantization recipes. Exhaustive search over this combinatorially large space is infeasible. Unlike data-center serving, which often prioritizes throughput or generation speed, resource-constrained deployments typically set memory and latency budgets as constraints and then seek the configuration with the highest generation quality among feasible ones. To this end, we propose ACSeL, a framework that identifies configurations predicted to satisfy deployment constraints while achieving high predicted generation quality. To enable efficient quality estimation, we use Relative Model Quality Degradation (RMQD), a proxy based on the divergence between the candidate and reference models' next-token distributions over a small calibration corpus. Across the evaluated model sizes and precisions, RMQD is inexpensive to evaluate and strongly correlated with downstream benchmark performance. ACSeL combines (i) a lightweight quality surrogate that predicts RMQD directly from a configuration; (ii) Few-shot Median Calibration (FMC), which calibrates operator-profile-based latency estimates using a small number of end-to-end profiles; and (iii) a structured search algorithm BandPareto for exploring layerwise mixed-precision configurations. Experiments on an NVIDIA RTX A6000 workstation and an NVIDIA Jetson Thor edge platform show that FMC substantially improves deployment feasibility, while BandPareto + FMC achieves the highest feasibility and the lowest RMQD gaps to the best measured configurations in the evaluation set.

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