[论文解读] Lens-descriptor guided evolutionary algorithm for optimization of complex optical systems with glass choice

Kirill Antonov, Teus Tukker+4 more|arXiv (Cornell University)|Jan 29, 2026

Advanced optical system design被引用 0

一句话总结

LDG-EA 是一个两阶段的描述符引导的多模态优化框架，联合优化曲率、厚度、间距和玻璃选择，在可接受的计算时间内产生多样化的高质量设计。

ABSTRACT

Designing high-performance optical lenses entails exploring a high-dimensional, tightly constrained space of surface curvatures, glass choices, element thicknesses, and spacings. In practice, standard optimizers (e.g., gradient-based local search and evolutionary strategies) often converge to a single local optimum, overlooking many comparably good alternatives that matter for downstream engineering decisions. We propose the Lens Descriptor-Guided Evolutionary Algorithm (LDG-EA), a two-stage framework for multimodal lens optimization. LDG-EA first partitions the design space into behavior descriptors defined by curvature-sign patterns and material indices, then learns a probabilistic model over descriptors to allocate evaluations toward promising regions. Within each descriptor, LDG-EA applies the Hill-Valley Evolutionary Algorithm with covariance-matrix self-adaptation to recover multiple distinct local minima, optionally followed by gradient-based refinement. On a 24-variable (18 continuous and 6 integer), six-element Double-Gauss topology, LDG-EA generates on average around 14500 candidate minima spanning 636 unique descriptors, an order of magnitude more than a CMA-ES baseline, while keeping wall-clock time at one hour scale. Although the best LDG-EA design is slightly worse than a fine-tuned reference lens, it remains in the same performance range. Overall, the proposed LDG-EA produces a diverse set of solutions while maintaining competitive quality within practical computational budgets and wall-clock time.

研究动机与目标

• Formalize lens-design behavior descriptors that capture curvature signs and material indices.
• Develop LDG-EA to adaptively sample descriptors, using HV-EA to locate multiple local minima per descriptor.
• Enable learning of descriptor models to bias sampling toward promising design patterns.
• Achieve a diverse set of high-quality lens designs within practical computational budgets.

提出的方法

• Define a finite set of behavior descriptors X representing curvature signs and glass indices.
• Stage 1: sample λ descriptors from a distribution p(x) and run a descriptor-constrained search inside each descriptor with budget B.
• Stage 2: select the μ best descriptors by their descriptor-level objective f and update p(x) via UMDA-style update to emphasize top descriptors.
• Within each descriptor, apply Hill-Valley Evolutionary Algorithm (HV-EA) with CMSA-ES as the internal optimizer to locate multiple local minima.
• Optionally refine top solutions with gradient-based optimization (e.g., BFGS) after HV-EA.

Figure 1: Two views of the optimization landscape for a four‐element camera lens, where variables are curvatures, distances, and materials of glasses, visualized using the method from work [ 2 ] . This method selects points between three local minima, identified through a local-search algorithm. The

实验结果

研究问题

• RQ1 Can a descriptor-guided multimodal search yield a diverse portfolio of high-quality lens designs with glass choice included?
• RQ2 How many distinct local optima and behavior-descriptor regions can LDG-EA uncover for a practical six-element Double-Gauss lens?
• RQ3 Does learning a descriptor distribution improve exploration-exploitation balance compared to descriptor-agnostic baselines?

主要发现

• LDG-EA produced on average 14,741 local-minimum candidates across 636 distinct descriptors (five runs).
• The method yielded about 1 hour wall-clock time on the tested hardware with parallelizable HV-EA runs.
• LDG-EA's best post-processed design reached F = 3×10^-4, outperforming the CMA-ES baseline (best F = 1×10^-3) and approaching the tuned reference (F ≈ 7×10^-5 after refinement).
• Baseline CMA-ES located roughly 400 solutions, of which 181 matched or exceeded the worst LDG-EA performance under the same budget.
• LDG-EA demonstrated rapid improvement in mean/worst-case F within the first five generations and kept discovering outlier improvements in later iterations.

Figure 2: (a) Visualization of behavior descriptor mapping: singlet lens $\bm{\theta}$ shown in the figure is mapped to its behavior descriptor $\bm{x}=(1,0,3)$ by the defined mapping $\bm{x}=\mathcal{D}(\bm{\theta}).$ The glass material is represented by the color. (b) Visualization of the space of