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We present a non-parametric compact genetic algorithm (cGA) employing a new update strategy of the probability vector (PV) based on Bayesian networks. Since the cGAs use the PV of the current population to reproduce offsprings of the next generation instead of the genetic operators such as crossover and mutation, the cGA needs no parameter tuning. Besides, the cGA has some advantages that the cGA can be easily implemented with reducing memory requirements. However, although the update of the PV is a core in the cGA, the PV is heuristically updated by a static population size in the most previous works. In this paper, we try to improve the updating scheme not using the population size, but using the Bayesian information given by the previous generations. For this purpose, we utilize the parameter learning scheme of an ABN. Moreover, the usefulness of the proposed probabilistic approach is empirically investigated by comparing with the original cGA and other cGAs.