A cumulative evidential stopping criterion for multiobjective optimization evolutionary algorithms

Abstract

In this work we present a novel and efficient algorithm independent stopping criterion, called the MGBM criterion, suitable for Multiobjective Optimization Evolutionary Algorithms (MOEAs). The criterion, after each iteration of the optimization algorithm, gathers evidence of the improvement of the solutions obtained so far. A global (execution wise) evidence accumulation process inspired by recursive Bayesian estimation decides when the optimization should be stopped. Evidenceis collected using a novel relative improvement measure constructed on top of the Pareto dominance relations. The evidence gathered after each iteration is accumulated and updated following a rule based on a simplified version of a discrete Kalman filter. Our criterion is particularly useful in complex and/or high-dimensional problems where the traditional procedure of stopping after a predefined amount of iterations cannot be used and the waste of computational resources can induceto a detriment of the quality of the results. Although the criterion discussed here is meant for MOEAs,it can be easily adapted to other soft computing or numerical methods by substituting the local improvement metric with a suitable one.