Introducing a robust and efficient stopping criterion for MOEAs

Abstract

IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Abstract-Soft computing methods, and Multi-Objective Evolutionary Algorithms (MOEAs) in particular, lack a general convergence criterion which prevents these algorithms from detecting the generation where further evolution will provide little improvements (or none at all) over the current solution, making them waste computational resources. This paper presents the Least Squares Stopping Criterion (LSSC), an easily configurable and implementable, robust and efficient stopping criterion, based on simple statistical parameters and residue analysis, which tries to introduce as few setup parameters as possible, being them always related to the MOEAs research field rather than the techniques applied by the criterion.

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

“…• paradoxical requirement of a priori knowledge of the POF: for instance, the termination algorithm in [19] utilizes an indicator like generational distance, which can not be computed unless the POF is known a priori. • poor scalability with the number of objectives: the termination algorithms based on generational distance [19] and hypervolume [19], [24] may not be usable for MaOPs, since the computational cost of computing these indicators grows exponentially with the number of objectives. Hence, it is fair to infer that the impelling need for a robust termination criterion largely remains unfulfilled, implying a critical research gap which this paper aims to bridge.…”

“…The above offline and online implementations have also been compared in [23]. 4) The criterion in [24] detects convergence and calls for an MOEA's termination based on the adjustment of the indicator values (like hypervolume, ϵ-indicator, and mutual-dominance-rate (ratio of dominated solutions)) to a uniform model, computed through the least squares approximation and slope of the model. Its utility has been demonstrated on NSGA-II, SPEA2 and PESA.…”

Adaptive Multiobjective Memetic Optimization

“…The idea of using a dominance quality as an online criterion to evaluate the performance of a multiobjective evolutionary algorithm has been recently studied in (Guerrero, 2010;Trautmann et al, 2009;Bui et al, 2009). The motivation is that if a solution x is an optimal solution in the Pareto optimal set, there are no neighborhood individuals dominating x .…”