To handle noisy observations, we adopted a recent approach introduced by Semochkina et al. using the Multi-objective Euclidean Expected Quantile Improvement (MO-E-EQI) criterion to guide our optimization. As with many MOBO methods, this method includes: (i) establishing an initial belief (prior) about the system's behaviour, building a sampling plan, calculating the responses at those points and fitting a GP model to this data in line with those prior beliefs; (ii) strategically selecting new input points x for system's evaluation based on a criterion that maximizes acquisition function; (iii) incorporating the obtained results into the existing belief, leading to a more accurate understanding of the system's minimum and its corresponding input value. Figure illustrates an example of this process. Based on the eight noisy observations (circles) that have been already observed, a GP model was fitted with the noisy observations y(x). The next point for evaluation is then selected based on the distribution of an unobserved point Y (x) at a new location x, characterized by the GP's mean and variance. The algorithm can decide whether to go somewhere near the current best model mean (exploitation), or somewhere with large uncertainty (exploration), and gradually move towards the optimum. The initial belief about the function is represented by a Gaussian process .