# Cross Entropy Multi-objective Optimization Algorithm

• Gerardo Beruvides
Chapter
Part of the Springer Theses book series (Springer Theses)

## Abstract

This chapter presents two set of modifications respect to the cross entropy multi-objective optimization algorithm (MOCE) introduced by Bekker and Aldrich (Eur J Oper Res 211(1):112–121 [1]). First, a group of modifications are introduced in the cross entropy multi-objective optimization algorithm, also called (MOCE+), based on a new procedure for addressing constraints: (i) the use of variable cutoff values for selecting the elitist population; and, (ii) filtering of the elitist population after each epoch. The second and final modifications packages are introduced in the Simple Multi-Objective Cross Entropy method (SMOCE), based on only four parameters (epoch number, working population size, histogram interval number, and elite fraction) stored in the algorithm, in order to facilitate the tuning process. The final proposed method (SMOCE) is evaluated using different test suites. Furthermore, a comparison with some other well-known optimization methods is carried out. The comparative study demonstrates the good figures of merit of the SMOCE method in complex test suites. Finally, the proposed method is validated in the multi-objective optimization of a micro-drilling process. Two conflicting targets are considered: total drilling time and vibrations on the plane that is perpendicular to the drilling axis. The Pareto front, obtained through the optimization process, is analyzed through quality metrics and the available options in the decision-making process.

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