Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization

• URL: http://arxiv.org/abs/2603.25099v1
• Date: Thu, 26 Mar 2026 07:14:31 GMT
• Title: Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization
• Abstract summary: We present a framework in which a large language model acts as an online controller for SIMP optimization.<n>A hard grayness gate prevents premature binarization, and a meta-optimization loop uses a second pass to tune the agent's call frequency.<n>The agent achieves the final compliance on every benchmark: $-5.7%$ to $-1% relative to the fixed baseline, with all solutions fully binary.
• Score: 4.365822392824561
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 $r_{\min}$, 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.

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