In this paper, we propose some improvements to the CMA-ES-PDM algorithm for solving mixed-integer black-box optimization problems. First, the discrete distribution model for the integer variables is fitted to a normal distribution. This fitted distribution is then further smoothed using an initial normal distribution that is quite similar to the uniform distribution over the search domain of integer variables. Second, when the upper bound of the probability within the model is reached for certain integer variables, the model is used exclusively for sampling the integer components of the candidate solutions. Additionally, the marginal probability of the model is selected randomly from a predefined set. The numerical experiments on the MI-BBO benchmark problems demonstrate that the proposed improvements enable CMA-ES-PDM to achieve better performance on some benchmark functions.
D. Nguyen (Mon,) studied this question.