Novel PCA-Based Lower-Dimensional Remapping of the Solution Space for a Genetic Algorithm Optimization: Estimating the Director Distribution in LC-Based SLM Devices

Abstract

This work introduces a novel computational approach based on Principal Component Analysis (PCA) for dimensionality reduction of the solution space in optimisation problems with known linear interdependencies among solution variables. By creating synthetic datasets with deliberately engineered properties and applying PCA, the solution space’s remapping significantly reduces its dimensionality, leading to faster computation and more robust convergence in optimisation processes. We demonstrate this method by integrating it with a Genetic Algorithm (GA) for solving the optimal director distribution in liquid crystal (LC) devices, specifically addressing 2D and complex 3D spatial light modulator (SLM) structures such as twisted nematic liquid crystals (TN-LC) and parallel-aligned liquid crystal on silicon (PA-LCoS), respectively. The phase profiles obtained from the director vector distributions for horizontal and vertical high-frequency binary phase gratings closely match the theoretical values derived from minimising the traditional elastic Frank–Oseen functional via Euler–Lagrange equations. Beyond this specific application, our method offers a general framework for reducing computational complexity in optimisation problems by directly reducing the dimensionality of the solution space. This approach is applicable across various optimisation scenarios with well-known linear interdependencies among solution variables, enabling significant reductions in computational costs and improvements in robustness and convergence.

Keywords

• principal component analysis (PCA)
• genetic algorithm (GA)
• solution space remapping
• liquid crystal (LC)
• spatial light modulators (SLM)
• dimensionality reduction