Stopping criteria for differential evolution in constrained single-objective optimization

Abstract

Because real-world problems generally include computationally expensive objective and constraint functions, an optimization run should be terminated as soon as convergence to the optimum has been obtained. However, detection of this condition is not a trivial task. Because the global optimum is usually unknown, distance measures cannot be applied for this purpose. Stopping after a predefined number of function evaluations has not only the disadvantage that trial-and-error methods have to be applied for determining a suitable number of function evaluations, but the number of function evaluations at which convergence occurs may also be subject to large fluctuations due to the randomness involved in evolutionary algorithms. Therefore, stopping criteria should be applied which react adaptively to the state of the optimization run. In this work several stopping criteria are introduced that consider the improvement, movement or distribution of population members to derive a suitable time for terminating the Differential Evolution algorithm. Their application for other evolutionary algorithms is also discussed. Based on an extensive test set the criteria are evaluated using Differential Evolution, and it is shown that a distribution-based criterion considering objective space yields the best results concerning the convergence rate as well as the additional computational effort. © 2008 Springer-Verlag Berlin Heidelberg.