A Hollow-Core Anti-Resonant Fiber Multi-Objective Multi-Modal Optimization Assisted by a Proxy Model Combined With Clustering Algorithm

To address the optimization problem of expensive multi-modal multi-objective black-box functions, this paper proposes a systematic optimization method based on a back propagation neural network as a proxy model, combined with clustering algorithm to cluster and differentiate multiple modes within the model. The method utilizes normalization and weighted summation of numerical experimental data to optimize the hyperparameters of the optimization algorithm's decision-making process. This approach resolves the multiple constraints of traditional optimization methods. Finally, applied to the hollow-core anti-resonant fiber with gap angle constraints to ensure its topological properties remain unchanged, the model optimizes three categories totaling six modes, optimizing the objectives of birefringence and loss. The top five optimal models achieve a minimum loss of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text {3.54} \times \text {10}^\text{-3}$</tex-math></inline-formula> dB/m, maximum birefringence of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text {1.25} \times \text {10}^\text{-4}$</tex-math></inline-formula>, higher order modulation enhanced receiver of 50, and bandwidth of 1.425 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m.