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.

翻译：高性能光学透镜的设计需要在表面曲率、玻璃选择、元件厚度与间距构成的高维强约束空间中进行探索。实践中，标准优化器（如基于梯度的局部搜索和进化策略）常收敛至单一局部最优解，忽略了众多对后续工程决策具有重要价值的、性能相当的替代方案。本文提出透镜描述符引导进化算法（LDG-EA），一种用于多模态透镜优化的两阶段框架。LDG-EA首先将设计空间划分为由曲率符号模式与材料折射率定义的行为描述符，随后学习描述符上的概率模型以将评估资源分配至有前景的区域。在每个描述符内，LDG-EA采用协方差矩阵自适应调整的山谷进化算法来获取多个不同的局部极小值，并可选择性地进行基于梯度的精细化优化。在一个包含24个变量（18个连续变量和6个整数变量）的六片式双高斯结构上，LDG-EA平均生成约14500个候选极小值，覆盖636个独立描述符，较CMA-ES基准方法提升一个数量级，同时将实际计算时间控制在一小时量级。尽管LDG-EA的最佳设计略逊于精细调校的参考透镜，但其性能仍处于同一量级。总体而言，所提出的LDG-EA能够在实际计算资源与时间预算内，生成具有多样性且保持竞争力的解决方案集合。