Lens Optimisation Achieves Multimodal Designs, Bypassing Local Optima with Ldg-Ea

Optimising complex optical systems presents a significant challenge, demanding exploration of vast and constrained design spaces to identify truly high-performing lenses. Researchers Kirill Antonov, Teus Tukker, and Tiago Botari, alongside colleagues from Leiden University and ASML, address this problem with a novel approach detailed in their new work. Their Lens Descriptor-Guided Evolutionary Algorithm (LDG-EA) moves beyond traditional optimisation methods by first partitioning the design space and then strategically allocating evaluations towards promising regions, ultimately generating a far more diverse set of candidate solutions. This is particularly significant as it allows engineers to consider multiple viable options, rather than being limited to a single local optimum, and the team demonstrate LDG-EA’s ability to produce around 14,500 candidate minima within a practical one-hour timeframe, exceeding the performance of existing methods like CMA-ES.

This is particularly significant as it allows engineers to consider multiple viable options, rather than being limited to a single local optimum, and the team demonstrate LDG-EA’s ability to produce around 14,500 candidate minima within a practical one-hour timeframe, exceeding the performance of existing methods like CMA-ES.

Lens design via behaviour descriptor partitioning offers significant

This breakthrough addresses a critical challenge in lens design: the tendency of standard Optimisation techniques to become trapped in local optima, overlooking potentially superior alternative designs crucial for engineering decisions. This is optionally followed by gradient-based refinement to further enhance performance. The study reveals that while the best design produced by LDG-EA is marginally inferior to a meticulously fine-tuned reference lens, it remains within the same performance range.

Crucially, the research establishes a method for systematically covering diverse high-quality designs, supporting downstream engineering choices such as validation of structural constraints, consideration of glass availability, and selection of designs optimised for cost, manufacturability, and tolerance characteristics. This work opens up possibilities for a more robust and efficient lens design process, moving beyond the limitations of traditional designer-in-the-loop workflows and commercial software that often focus on refining existing layouts. By explicitly exploiting the structure of lens-design landscapes through interpretable behaviour descriptors, LDG-EA balances solution quality with diversity, enabling a tailored multimodal search. The team’s approach contrasts with existing multimodal optimisers by defining lens-specific niches a priori, enforcing diversity across design patterns and paving the way for more innovative and adaptable optical systems.

Lens optimisation via descriptor guided evolution offers improved

LDG-EA then learned a probabilistic model over these descriptors to allocate evaluations efficiently, prioritising areas likely to yield high-quality lens designs. Optionally, the team incorporated gradient-based refinement to further enhance the performance of identified designs. Experiments employed a 24-variable system, comprising 18 continuous and 6 integer parameters, within a six-element Double-Gauss topology. Researchers visualised the optimisation landscape using a method selecting points between three local minima, revealing multiple optima indicative of distinct families of high-quality designs.

LDG-EA balances solution quality and diversity by defining lens-specific niches a priori through behaviour descriptors that capture curvature and glass patterns. This descriptor-driven partition explicitly enforces diversity across design patterns, enabling robust multimodal search tailored to lens design. The best LDG-EA design achieved performance comparable to a fine-tuned reference lens, demonstrating competitive quality within practical computational budgets.

LDG-EA diversifies lens designs via ray tracing simulations

The research team implemented an automatic differentiable optical simulator to compute the value of the objective function, utilising a standard ray-tracing algorithm coupled with automatic differentiation for efficient gradient calculations. Experiments were conducted on a Rocky Linux 9 cluster node equipped with 512 GB RAM and two AMD EPYC 7702 CPUs, each with 64 cores, for a total of 128 cores and 256 hardware threads. Local optimisation within a single behaviour descriptor required approximately 4.5 minutes of wall-clock time, allowing a full 15-generation LDG-EA run to complete within approximately one hour. Results demonstrate that LDG-EA generated an average of 14741 local-minimum candidates, with a standard deviation of approximately 2049, across the full evaluation budget.

These candidates were distributed over an average of 636 distinct behaviour descriptors, a figure below the theoretical maximum of 750, indicating stabilisation of the descriptor distribution during the search process. In contrast, a CMA-ES baseline algorithm located only around 400 solutions overall, with just 181 achieving objective values at least as good as the worst LDG-EA solution. Measurements confirm that LDG-EA produced solutions with objective values ranging from 7 × 10−4 to 2.0. The unrefined Double-Gauss template initially had a value of 5 × 10−4, which improved to 7 × 10−5 after gradient-based optimisation.

The best candidate generated by the full LDG-EA pipeline, including gradient-based optimisation, achieved a value of 3 × 10−4. The CMA-ES baseline’s best solution reached only 1 × 10−3, and its second-best was already worse than 36 distinct LDG-EA solutions. Further refinement of the top five LDG-EA solutions using the BFGS quasi-Newton method yielded an additional improvement in the objective function ranging from ×1.0 to ×3.6. Tests prove that LDG-EA learns a non-uniform distribution over the descriptor space, favouring descriptors where the subsequent optimisation stage discovers higher-quality solutions. Ablation studies, replacing the descriptor sampling with uniform random sampling, revealed a significant improvement in solution quality with LDG-EA compared to the ablated variant, as demonstrated by the downward shift of violin plots and the increasing mean solution quality over generations.

LDG-EA unlocks diverse multimodal lens optimisation for improved

Traditional optimisation methods often become trapped in local optima, limiting the exploration of potentially superior lens designs. The research demonstrates that LDG-EA significantly expands the diversity of generated lens designs compared to conventional methods like CMA-ES. While the best lens design produced by LDG-EA was marginally inferior to a highly refined reference lens, its performance remained comparable. The authors acknowledge a limitation in their current implementation, which assumes positive first curvature and disregards descriptors with negative values, an aspect they intend to address in future work.

Further research will also explore expanding the framework to accommodate more complex lens topologies and optimisation objectives. The ability to identify numerous viable designs is particularly significant for engineering applications where trade-offs between performance characteristics are crucial. Although the current implementation has constraints regarding curvature assumptions, the demonstrated improvements in diversity and computational efficiency represent a substantial step towards more robust and versatile lens optimisation techniques.