A Simple Multi-Objective Optimization Based on the Cross-Entropy Method

A simple multi-objective cross-entropy method is presented in this paper, with only four parameters that facilitate the initial setting and tuning of the proposed strategy. The effects of these parameters on improved performance are analyzed on the basis of well-known test suites. The histogram interval number and the elite fraction had no significant influence on the execution time, so their respective values could be selected to maximize the quality of the Pareto front. On the contrary, the epoch number and the working population size had an impact on both the execution time and the quality of the Pareto front. Studying the rationale behind this behavior, we obtained clear guidelines for setting the most appropriate values, according to the characteristics of the problem under consideration. Moreover, the suitability of this method is analyzed based on a comparative study with other multi-objective optimization strategies. While the behavior of simple test suites was similar to all methods under consideration, the proposed algorithm outperformed the other methods considered in this paper in complex problems, with many decision variables. Finally, the efficiency of the proposed method is corroborated in a real case study represented by a two-objective optimization of the microdrilling process. The proposed strategy performed better than the other methods with a higher hyperarea and a shorter execution time.