• Hyperopt 58 : Hyperopt, utilizing the TPE algorithm, offers a framework specifically designed to facilitate the application of Bayesian optimization for hyperparameter selection . TPE inherently handles categorical variables, eliminating the need for explicit encoding. The solving process comprises two phases: initial sampling and active learning. During the initial sampling phase, samples are randomly drawn from the design space. In the active-learning phase, TPE operates by optimizing a loss function over a tree-structured configuration space. In handling categorical (discrete) variables, it employs the Estimation of Distribution (EDA) approach, where candidate points are sampled according to binomial distributions . As for the continuous variables, the Covariance Matrix Adaptation -Evolution Strategy (CMA-ES, gradient-free) is utilized. TPE is computationally cheap and simple compared to many other algorithms within the BO framework . However, incorporating a relatively large number of constraints is challenging, and is not currently implemented . Watanabe and Hutter attempted to address this challenge by integrating the acquisition function of constrained BO by Gardner et al. . However, the proposed approach considers the probability of constraint improvement and still allows infeasible samples , which may be selected and tested in simulations but can not be queried for real experiments. It is also worth mentioning that this approach is proposed to address problems with unknown constraints. ment). We also note that, for mixed-integer cases, BoTorch finds the next point to test by iterating through all possible integer values in an outer loop and optimizing the remaining continuous variables while keeping the integer value fixed. Subsequently, it selects the integer value that returns the best evaluation on the acquisition function. This step can cause the computational time to increase significantly, especially when the number of integer (discrete) variables increases and/or the number of possible options for these variables increases. Alternative approach that utilize PR was proposed and implemented in to address this issue, but