d-MALIBOO: a Bayesian Optimization framework for dealing with Discrete Variables

Cloud computing has become essential for delivering flexible and scalable resources. In this environment, finding the optimal hardware-software configuration is crucial and often involves solving constrained black-box problems on discrete multidimensional domains. These optimizations must be performed within a limited number of evaluations to contain costs. Bayesian Optimization (BO) addresses this problem by providing near-optimal solutions with few iterations. However, the original BO algorithm was designed for continuous and unbounded domains. On the other hand, Machine Learning (ML) models are powerful tools for predicting the values of a black-box function. In this work, we present d-MALIBOO, a framework that integrates BO and ML techniques to improve the efficiency of finding optimal solutions in discrete and bounded domains. While BO suggests the next point to be evaluated by effectively balancing exploration and exploitation, ML models are valuable for determining feasibility regions and focusing the search for the optimum. Experimental results show that our algorithm outperforms alternative methods from the literature in all tested environments, especially in complex optimization scenarios, resulting in an improvement in regret by approximately 2–8 times.