In this study, using the MHC class I system as a test case, we demonstrate that it is possible to initiate a closed-loop DMT process starting with a single lead peptide exhibiting an IC50 towards our target of interest in the µM range and efficiently optimize its sequence to reach the optimal IC50 in less than 5 DMT cycles using batches of 96 peptides. Simultaneously, we evaluated multiple strategies for generating the initial batch of peptides, starting from the lead peptide, based either solely from its sequence (e.g., multi-alanine scanning) or using structure-based methods. This aspect of the work is crucial, as data is typically sparse when initiating new projects, and the initial design strategy employed significantly influences subsequent optimization rounds. We also explored different methods to encode peptide sequence information, such as amino acid descriptors, molecular fingerprints and pretrained protein Language Models (pLMs). The out-of-box performance of these pretrained pLMs, as well as their performance after fine-tuning on peptide sequences, was studied. In addition to different batch strategies, acquisition functions and the effect of the noise and batch size on BO performance, we also expanded beyond Single-Objective Optimization (SOO) and again benchmarked BO in the context of Multi-Objective Optimization (MOO) using dissimilar MHC class I alleles.