Benchmarking Improved Variants of CMA-ES-PDM on the bbob-mixint Testbed

The CMA-ES-PDM is a variant of the CMA-ES algorithm designed for solving mixed-integer black-box optimization (MI-BBO) problems. This algorithm uses probability distribution models, constructed during the search process, to generate the integer components of some candidate solutions. Recently, several novel techniques have been proposed for the CMA-ES-PDM algorithm to enhance its performance. 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 closely resembles a 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. In this work, we evaluate some improved variants of the CMA-ES-PDM on the bbob-mixint test suite, which includes problems with various properties for MI-BBO. The experimental results show that the variants of CMA-ES-PDM perform well on classes of separable functions, low or moderately conditioned functions, and highly conditioned unimodal functions. Notably, the proposed algorithms outperform other methods on some specific functions.