The cross-entropy method in multi-objective optimisation: An assessment

Abstract

Solving multi-objective problems requires the evaluation of two or more conflicting objective functions, which often demands a high amount of computational power. This demand increases rapidly when estimating values for objective functions of dynamic, stochastic problems, since a number of observations are needed for each evaluation set, of which there could be many. Computer simulation applications of real-world optimisations often suffer due to this phenomenon. Evolutionary algorithms are often applied to multi-objective problems. In this article, the cross-entropy method is proposed as an alternative, since it has been proven to converge quickly in the case of single-objective optimisation problems. We adapted the basic cross-entropy method for multi-objective optimisation and applied the proposed algorithm to known test problems. This was followed by an application to a dynamic, stochastic problem where a computer simulation model provides the objective function set. The results show that acceptable results can be obtained while doing relatively few evaluations.