In this work a heuristic to speed up the convergence of a feedback-based optimization scheme, when experiments can be run in batches, is discussed. The proposed approach allows to select the most promising experiment in the batch, as the one maximising the decrease of an associated Lyapunov function, and to define the inputs for the next batch, based on this. We suggest the application of the scheme to a biological setting, with the goal of maximizing the concentration of a product of interest in a bioreactor under a continuous perfusion framework, while at the same time minimizing the yield of a toxic byproduct. The potential of the approach is exposed by means of a simple synthetic example.