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A stopping criterion based on Kalman estimation techniques with several progress indicators

The need for a stopping criterion in MOEA's is a repeatedly mentioned matter in the domain of MOOP's, even though it is usually left aside as secondary, while stopping criteria are still usually based on an a-priori chosen number of maximum iterations. In this paper we want to present a stopping criterion for MOEA's based on three different indicators already present in the community. These indicators, some of which were originally designed for solution quality measuring (as a function of the distance to the optimal Pareto front), will be processed so they can be applied as part of a global criterion, based on estimation theory to achieve a cumulative evidence measure to be used in the stopping decision (by means of a Kalman filter). The implications of this cumulative evidence are analyzed, to get a problem and algorithm independent stopping criterion (for each individual indicator). Finally, the stopping criterion is presented from a data fusion perspective, using the different individual indicators' stopping criteria together, in order to get a final global stopping criterion.