The emergence and development of cancer is a consequence of the accumulation over time of genomic mutations involving a specific set of genes, which provides the cancer clones with a functional selective advantage. In this work, we model the order of accumulation of such mutations during the progression, which eventually leads to the disease, by means of probabilistic graphic models, i.e., Bayesian Networks (BNs). We investigate how to perform the task of learning the structure of such BNs, according to experimental evidence, adopting a global optimization meta-heuristics. In particular, in this work we rely on Genetic Algorithms, and to strongly reduce the execution time of the inference - which can also involve multiple repetitions to collect statistically significant assessments of the data - we distribute the calculations using both multi-threading and a multi-node architecture. The results show that our approach is characterized by good accuracy and specificity; we also demonstrate its feasibility, thanks to a 84× reduction of the overall execution time with respect to a traditional sequential implementation.