We evaluated these approaches in extreme cases, limiting batches to one or two unique temperatures (see Methods). Despite highly restrictive batch constraints, both approaches were able to identify high-performing experiments, yielding above 90 hypervolume (%) across all benchmarks (Fig. ). We observed similar performances between the two approaches for batch constraints of 2 unique temperatures. However, when constrained to 1 unique temperature, the naive approach consistently underperformed compared to the nested approach (see Supplementary Information section 4 for statistical tests). Hence, for the experimental deployment of our workflow, we proceeded with the nested approach for handling batch constraints, combined with the q-NEHVI acquisition function. We note that while these two strategies were observed to perform the best overall across the benchmark datasets evaluated in this study, the optimal algorithm may depend on the specific dataset considered.