Optimizing Photonic Structures with Large Language Model Driven Algorithm Discovery

TL;DR

The paper tackles automated optimization algorithm design for photonic-structure design by extending the Large Language Model Evolutionary Algorithm (LLaMEA) with domain-specific prompts and diverse evolutionary strategies. It evaluates generated metaheuristics on real-world multilayer photonics problems (Bragg mirrors, ellipsometry, and photovoltaic anti-reflection coatings) using PyMoosh-based simulations and IOHexperimenter benchmarking, with AOCC as the primary feedback metric. Key contributions include structured problem descriptions and algorithmic insights in prompts, exploration of multiple ES configurations, and empirical evidence that LLM-generated algorithms can match or surpass traditional baselines like DE and CMA-ES on several instances, with robust convergence in many cases. The results demonstrate the practical feasibility of domain-focused LLM prompts coupled with evolutionary search to enable rapid, automated photonic inverse design, reducing the need for expert intervention and enabling scalable optimization across problem scales.

Abstract

We study how large language models can be used in combination with evolutionary computation techniques to automatically discover optimization algorithms for the design of photonic structures. Building on the Large Language Model Evolutionary Algorithm (LLaMEA) framework, we introduce structured prompt engineering tailored to multilayer photonic problems such as Bragg mirror, ellipsometry inverse analysis, and solar cell antireflection coatings. We systematically explore multiple evolutionary strategies, including (1+1), (1+5), (2+10), and others, to balance exploration and exploitation. Our experiments show that LLM-generated algorithms, generated using small-scale problem instances, can match or surpass established methods like quasi-oppositional differential evolution on large-scale realistic real-world problem instances. Notably, LLaMEA's self-debugging mutation loop, augmented by automatically extracted problem-specific insights, achieves strong anytime performance and reliable convergence across diverse problem scales. This work demonstrates the feasibility of domain-focused LLM prompts and evolutionary approaches in solving optical design tasks, paving the way for rapid, automated photonic inverse design.

Figures (6)

• Figure 1: Landscape of photonic structure optimizing problems in 2D. The darker the color, the more fit the structure.
• Figure 2: Examples of task prompts that add problem descriptions and algorithm insights that improve the performance of LLaMEA. The higher the AOCC, the better. Prompts with descriptions and insights both outperform other prompt settings for mini-Bragg and ellipsometry instances.
• Figure 3: Example of a task prompt that adds a problem description and algorithm insight that does not improve the effectiveness of LLaMEA. The higher the AOCC, the better. For photovoltaic instance, task prompts without description and insight works best. Considering that the initial AOCC is high for all task prompt settings, Fig. \ref{['fig:auc_description_insight_photovoltaic_start_with_same_solution']} shows the results for each LLaMEA run starting from the same solution to avoid the impact of initial gaps.
• Figure 4: Impact of different ES strategy choices. The preference for ES strategies is different for each problem and most of the time the difference is not significant.
• Figure 5: Convergency curves of best algorithms found by LLaMEA and baselines with different problem instances, averaged over 15 runs. $y$-axis represents fitness, the smaller, the better. $x$-axis represents evaluations of problem instances. Each subfigure represents a problem instance.