Comparison of optimization algorithms for automated method development of gradient profiles

Optimization algorithms play an important role in method development workflows for gradient elution liquid chromatography. Their effectiveness has not been evaluated for chromatographic method development using standardized comparisons across factors such as sample complexity, chromatographic response functions (CRFs), gradient complexity, and application type. This study compares six optimization algorithms - Bayesian optimization (BO), differential evolution (DE), a genetic algorithm (GA), covariance-matrix adaptation evolution strategy (CMA-ES), random search, and grid search - for the development of gradient elution LC methods. Utilizing a multi-linear retention modeling framework, these algorithms were assessed across diverse samples, CRFs, and gradient segments, considering two observation modes: dry (in silico, deconvoluted), and wet (search-based, requiring peak detection). The optimization algorithms were evaluated based on their data (i.e. number of iterations) and time efficiency. Of the algorithms compared in this study, DE proved to be a highly competitive method for dry optimization purposes in terms of both data and time efficiency. BO outperformed all other algorithms in terms of data efficiency and was found to be most effective for search-based optimization, which requires a low number of iterations (<200). However, BO was found to be impractical for dry optimization requiring a large iteration budget due to its unfavorable computational scaling. It was observed that both the CRF and the sample have a strong influence on the efficiency of the algorithms, emphasizing the need for better benchmark samples and highlighting the importance of assessing CRF-induced complexity in the optimization landscape.