Lens-descriptor guided evolutionary algorithm for optimization of complex optical systems with glass choice

TL;DR

This work tackles the multimodal optimization challenge in complex optical-lens design, where traditional optimizers often converge to a single local optimum and fail to capture a diverse set of viable designs. It introduces the Lens Descriptor-Guided Evolutionary Algorithm (LDG-EA), a two-stage framework that partitions the design space into interpretable behavior descriptors, learns a descriptor distribution, and uses Hill-Valley Evolutionary Algorithm with CMSA-ES to locate multiple local minima within descriptor-defined subspaces, optionally refining with gradients. LDG-EA achieves a dramatic increase in discovered minima (around 14,741 across 636 descriptors) within hour-scale budgets on a six-element Double-Gauss topology, while delivering competitive RMS performance relative to a fine-tuned reference. The approach provides a practical, parallelizable pathway to generating diverse, high-quality lens designs, enabling downstream decisions related to manufacturability, cost, and tolerance, and offering a flexible starting point for subsequent optimization stages.

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.

Figures (6)

• 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 antonov2024quality. This method selects points between three local minima, identified through a local-search algorithm. The horizontal axes correspond to a plane in the high-dimensional design space, and the vertical axis shows the reversed merit function (the higher, the better). Multiple optima indicate distinct families of high-quality designs.
• 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 all behavior descriptors $\mathcal{X}.$ Two boxes on the right show examples of lenses with the same behavior descriptors $\bm{x}{^{\left(1\right)}}$ and $\bm{x}{^{\left(2\right)}}$ respectively. Note that singlet lenses in the same box have different thicknesses and different curvature values, but still have the same behavior descriptor due to the definition of our mapping $\mathcal{D}.$
• Figure 3: The Lens-Descriptor-Guided Evolutionary Algorithm (LDG-EA) applied to a two-dimensional test function. Panels (1.a), (1.b), etc. match the corresponding stages described in Sec. \ref{['sec:stages']}. In panel (1.a), the descriptors are indicated by black squares over the domain of the test function. Green ticks in Stage 1 denote sampled descriptors, while in Stage 2 green ticks denote descriptors selected after evaluation of the descriptor-level objectives $f^{(t,i)}$; a black cross marks a descriptor that is not selected. The two plots at the bottom visualize the update of the probabilistic distribution over descriptors, $p{^{\left(t\right)}}(\bm{x})$, according to the formula displayed in panel (2.b).
• Figure 4: Reference Double‐Gauss lens system. Element glasses are labeled by Schott catalog code and colored by their sorted refractive index at the d‐line (587.6 nm) over the catalog.
• Figure 5: Top five lens designs from one randomly selected LDG-EA run (first row) and their locally refined counterparts obtained with BFGS (second row). The third row reports the additional post-optimization gain in $F$, computed as $F(\bm{\theta}^{\text{(before)}})/F(\bm{\theta}^{\text{(after)}})$. Element glasses are labeled by Schott catalog code and colored by their sorted refractive index at the d‐line (587.6 nm) over the catalog.

Theorems & Definitions (1)

• Definition 1: Lens equivalence with respect to the descriptor and performance