Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization
cs.CE, cs.AI
Submitted: 2026-03-26
Updated: 2026-05-15
Comments: 32 pages, 11 figures
Journal ref: Adv. Eng. Softw. 223 (2026) 104304
DOI: 10.1016/j.advengsoft.2026.104304
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time,
Terminology
Abstract
We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time, state-conditioned parameter decisions. At every k-th iteration, the LLM receives a structured observation - current compliance, grayness index, stagnation counter, checkerboard measure, volume fraction, and budget consumption - and outputs numerical values for the penalization exponent p, projection sharpness β, filter radius r, and move limit δ via a Direct Numeric Control interface. A hard grayness gate prevents premature binarization, and a meta-optimization loop uses a second LLM pass to tune the agent's call frequency and gate threshold across runs. We benchmark the agent against four baselines - fixed (no-continuation), standard three-field continuation, an expert heuristic, and a schedule-only ablation - on three 2-D problems (cantilever, MBB beam, L-bracket) at 120! times!60 resolution and two 3-D problems (cantilever, MBB beam) at 40! times!20! times!10 resolution, all run for 300 iterations. A standardized 40-iteration sharpening tail is applied from the best valid snapshot so that compliance differences reflect only the exploration phase. The LLM agent achieves the lowest final compliance on every benchmark: -5.7% to-18.1% relative to the fixed baseline, with all solutions fully binary. The schedule-only ablation underperforms the fixed baseline on two of three problems, confirming that the LLM's real-time intervention - not the schedule geometry - drives the gain. Code and reproduction scripts will be released upon publication.
Sources
- GPT-4 Technical Report
- Evaluating Large Language Models Trained on Code
- Neural reparameterization improves structural optimization
- Population Based Training of Neural Networks
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