While BO-based and other surrogate-based approaches have been successfully employed in many applications, including material discoveries , chemical synthesis 4, , and engineering design , their effectiveness is limited when addressing optimization problems with mixed-variable domains. These domains encompass data structures characterized by a combination of continuous, integer, and categorical variables, and are frequently encountered in real-world chemical problems. As implemented in the current BoTorch package (v-0.11.3), a common method employed by BO approaches to handle mixedinteger/mixed-variable cases involves iterating through all potential integer/categorical values in an outer loop while optimizing the continuous variables. This process becomes cumbersome and impractical with an increasing number of integer/categorical variables 4, .