This, however, depends on the unknown <math>\ell</math>. The CE method aims to approximate the optimal PDF by adaptively selecting members of the parametric family that are closest (in the [[Kullback–Leibler divergence|Kullback–Leibler]] sense) to the optimal PDF <math>g^*</math>. Some modifications for improving the setting of parameters, convergence, and overall the computational efficiency of the cross-entropy method when dealing with multi-objective optimization problems have been introduced and reported<ref>{{cite journal |last1=Bekker |first1=J. |last2=Aldrich |first2=C. |title=The cross-entropy method in multi-objective optimisation: An assessment |journal=European Journal of Operational Research |date=2011 |volume=211 |issue=1 |pages=112-121 |doi=10.1016/j.ejor.2010.10.028}}</ref>, <ref>{{cite journal |last1=Giagkiozis |first1=I. |last2=Purshouse |first2=R.C. |last3=Fleming |first3=P.J. |title=Generalized decomposition and cross entropy methods for many-objective optimization |journal=Information Sciences |date=2014 |volume=282 |pages=363-387 |doi=10.1016/j.ins.2014.05.045}}</ref>,<ref>{{cite journal |last1=Haber |first1=R.E. |last2=Beruvides |first2=G. |last3=Quiza |first3=R. |last4=Hernandez |first4=A. |title=A simple multi-objective optimization based on the cross-entropy method |journal=IEEE Access |date=2017 |volume=5 |pages=22272-22281 |doi=10.1109/access.2017.2764047}}</ref>.
==Generic CE algorithm==
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parametric family are the sample mean and sample variance corresponding to the ''elite samples'', which are those samples that have objective function value <math>\geq\gamma</math>.
The worst of the elite samples is then used as the level parameter for the next iteration.
This yields the following randomized algorithm that happens to coincide with the so-called Estimation of Multivariate Normal Algorithm (EMNA), an [[estimation of distribution algorithm]].
This yields the following randomized algorithm that happens to coincide with the so-called Estimation of Multivariate Normal Algorithm (EMNA), an [[estimation of distribution algorithm]]. Some recent applications of the cross-entropy optimization method have been reported to solve the dynamic economic dispatch problem with a unit start-stop plan<ref>{{cite journal |last1=Xie |first1=M. |last2=Du |first2=Y. |last3=Wei |first3=W. |last4=Liu |first4=M. |title=A cross-entropy-based hybrid membrane computing method for power system unit commitment problems |journal=Energies |date=2019 |volume=12 |issue=3 |doi=10.3390/en12030486}}</ref>, parametrization of micromilling processes<ref>{{cite journal |last1=La Fe |first1=I. |last2=Beruvides |first2=G. |last3=Quiza |first3=R. |last4=Haber |first4=R.E. |last5=Rivas |first5=M. |title=Automatic Selection of Optimal Parameters Based on Simple Soft-Computing Methods: A Case Study of Micromilling Processes |journal=IEEE Transactions on Industrial Informatics |date=2019 |volume=15 |issue=2 |pages=800-811 |doi=10.1109/tii.2018.2816971}}</ref>, energy scheduling problems<ref>{{cite journal |last1=Wang |first1=L. |last2=Li |first2=Q. |last3=Zhang |first3=B. |last4=DIng |first4=R. |last5=Sun |first5=M. |title=Robust multi-objective optimization for energy production scheduling in microgrids |journal=Engineering Optimization |date=2019 |volume=51 |issue=2 |pages=332-351 |doi=10.1080/0305215x.2018.1457655}}</ref> and robotic automated storage and retrieval system<ref>{{cite journal |last1=Foumani |first1=M. |last2=Moeini |first2=A. |last3=Haythorpe |first3=M. |last4=Smith-Miles |first4=K. |title=A cross-entropy method for optimising robotic automated storage and retrieval systems |journal=International Journal of Production Research |date=2019 |volume=56 |issue=19 |pages=6450-6472 |doi=10.1080/00207543.2018.1456692}}</ref>.
