The presence of discrete or mixed-variable constraints further complicates the optimization process. Constraints can be known or unknown a priori; in this paper, we limit the scope to problems with known constraints. Various BO methods have been developed for constrained problems in continuous spaces. For example, known constraints can be specified upfront to define the feasible region, which is then used to define an indicator function for feasibility. The indicator function can then be coupled with the acquisition strategies, such as expected improvement, to guide the search toward feasible samples . Also, polytope sampling strategies can be used to generate initial feasible samples. However, these methods were originally designed for continuous and smooth constraint landscapes, making them less effective and often inefficient when applied to discrete or mixed-variable constrained problems, particularly when dealing with a large number of constraints.