For SOO, we explored several batch strategies: the straightforward top-k batch strategy, along with the Kriging Believer (KB) and Constant Liar (CL) batch strategies . The top-k batch strategy selects the k highest-ranked peptide sequences as per the acquisition function. While this method is computationally efficient, one would like to maximize sequence diversity within the next batch. The KB and CL batch strategies use an iterative greedy approach that: i) selects the highest-ranked peptide sequence according to the acquisition function, ii) add this observation with a certain value v, and update the surrogate model posterior, and iii) continues this process until a complete batch of k peptides is generated. For KB, v is the predicted posterior mean by the surrogate model, which represents an optimistic view, based on the assumption that the surrogate model accurately predicts without becoming trapped in sub-optimal regions. Conversely, the CL batch strategy uses an arbitrary fixed value v, here the worst pIC50 observed so far, mitigating this risk and thereby forcing the model to explore more dissimilar peptide sequences and promote diversity.