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

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\!\!60 resolution and two 3-D problems (cantilever, MBB beam) at 40\!\!20\!\!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.

Reproductions