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The search for an optimal node elimination sequence for the triangulation of Bayesian networks is an NP-hard problem. In this paper, a new method, called the TAGA algorithm, is proposed to search for the optimal node elimination sequence. TAGA adjusts the probabilities of crossover and mutation operators by itself, and provides an adaptive ranking-based selection operator that adjusts the pressure of selection according to the evolution of the population. Therefore the algorithm not only maintains the diversity of the population and avoids premature convergence, but also improves on-line and off-line performances. Experimental results show that the TAGA algorithm outperforms a simple genetic algorithm, an existing adaptive genetic algorithm, and simulated annealing on three Bayesian networks. [ABSTRACT FROM AUTHOR]