Exploring optimization landscapes: the role of chromatographic response functions in automated method development for liquid chromatography.

In this work, we developed a framework for the systematic comparison of chromatographic response functions (CRFs) in automated method development, focusing on both their scoring behavior and the response surfaces they induce. The results show that CRF choice strongly determines response surface structure and, consequently, the suitability of the resulting optimization problem. Different CRFs were found to produce substantially different landscape characteristics, ranging from smooth surfaces with extended regions of near-optimal solutions to irregular and highly multimodal landscapes. These differences were quantified using metrics such as ruggedness, derivatives, local extrema, and cumulative distribution functions. In particular, CRFs based on multiplicative criteria were observed to produce less suitable landscapes in untargeted optimization scenarios, whereas separation-based CRFs generally yielded more structured surfaces. The structure of the response surfaces was found to depend primarily on the CRF rather than on the specific sample, indicating that CRF selection is a dominant factor in determining optimization complexity. These effects become more pronounced with increasing dimensionality, with time-based criteria introducing additional complexity. Overall, the results indicate that CRFs should be evaluated not only in terms of chromatographic relevance but also in terms of the response surfaces they generate. The developed framework provides a basis for comparing CRFs through the response landscapes they induce and for formulating hypotheses regarding the resulting optimization difficulty, thereby enabling systematic evaluation in automated method development workflows.