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In this paper, we propose a method for efficiently solving the mixed-integer black-box optimization problem by utilizing the probability distribution models of integer variables in the CMA-ES algorithm. Firstly, some elite points among the generated ones during the evolution process of the CMA-ES algorithm are collected after some consecutive iterations to successively build the probability distribution model of integer variables. Then, the model is partially used to generate the values for the integer variables of candidate solutions in some next iterations. The numerical experiments on the MI-BBO benchmark problems will show that the probability distribution models of integer variables can guide the CMA-ES better to the optimal solution of the problem, as well as demonstrate the efficiency of the proposed method.
D. Nguyen (Sun,) studied this question.