  The cross-entropy method (CE) developed by R. Rubinstein is an elegant
practical principle for simulating rare events. The method approximates the
probability of the rare event by means of a family of probabilistic models. The
method has been extended to optimization, by considering an optimal event as a
rare event. CE works rather good when dealing with deterministic function
optimization. Now, it appears that two conditions are needed for a good
convergence of the method. First, it is necessary to have a family of models
sufficiently flexible for discriminating the optimal events. Indirectly, it
appears also that the function to be optimized should be deterministic. The
purpose of this paper is to consider the case of partially discriminating model
family, and of stochastic functions. It will be shown on simple examples that
the CE could fail when relaxing these hypotheses. Alternative improvements of
the CE method are investigated and compared on random examples in order to
handle this issue.
