OCD: Online Convergence Detection for Evolutionary Multi-Objective Algorithms Based on Statistical Testing

Wagner, Tobias; Trautmann, Heike; Naujoks, Boris

doi:10.1007/978-3-642-01020-0_19

Cited by 30 publications

(26 citation statements)

References 22 publications

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“…Its online implementation in [22] replaces the Kolmogorov-Smirnov statistical test by the χ 2 -variance test and t-test [20]. The above offline and online implementations have also been compared in [23].…”

Section: Past Research On Termination Criterion Formentioning

confidence: 99%

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Saxena

Sinha

Duro

et al. 2016

IEEE Trans. Evol. Computat.

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Multi-objective Evolutionary Algorithms evolve a population of solutions through successive generations towards the Pareto-optimal Front. One of the most critical questions faced by the researchers and practitioners in this domain, relates to the number of generations that may be sufficient for an algorithm to offer a good approximation of the Pareto-optimal Front, for a given problem. Ironically, till date this question largely remains unanswered and the number of generations are arbitrarily fixed a priori, with potentially punitive implications. If the a priori fixed generations are insufficient, then the algorithm reports suboptimal solutions. In contrast, if the a priori fixed generations are far-too-many, it implies waste of computational resources. This paper proposes a novel entropy based dissimilarity measure that helps identify on-the-fly the number of generations beyond which an algorithm stabilizes, implying that either a good approximation has been obtained, or that it can not be obtained due to the stagnation of the algorithm in the search space. Given that, in either case no further improvement in the approximation can be obtained, despite additional computational expense, the proposed dissimilarity measure provides a termination criterion and facilitates a termination detection algorithm. The generality, on-the-fly implementation, low computational complexity, and the demonstrated efficacy of the proposed termination detection algorithm, on a wide range of multi-and many-objective test problems, define the novel contribution of this paper.

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Section: Past Research On Termination Criterion Formentioning

confidence: 99%

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Saxena

Sinha

Duro

et al. 2016

IEEE Trans. Evol. Computat.

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“…There is a recent concern about obtaining general stopping criteria which can be applied to a wide range of algorithms and problems [3], [12], [13], [14], [19], dealing especially with industrial applications [20]. There are, as well, different non-general approaches: design of special algorithms which can guarantee local optimality of solutions [21], using as well the gradient of the hypervolume to guarantee diversity and spread [22] (which may be considered a transformation of the hypervolume into a progress indicator), or the design of algorithm specific stopping criterion, based on values used by the selection criterion [23] (in this reference the authors use the crowding distance for an NSGA-II [24] based stopping criterion).…”

Section: Global Stopping Criteriamentioning

confidence: 99%

“…Focused on statistical testing, [3], [19], [20] determine the stopping criterion as a linear combination of the values of different indicators, using statistical tests for the analysis of the variance and the trend of their considered window over the different indicators' values.…”

Section: Global Stopping Criteriamentioning

confidence: 99%

“…There are a number of underlying factors regarding the applicability of such algorithms, where the lack of a convergence criterion was among the first ones which researchers had to deal with [3]. The traditional solution to this problem was the establishment of an a priori number of maximum generations for the algorithm [4], which, at least, managed to set a boundary for the algorithm's running time.…”

Section: Introductionmentioning

confidence: 99%

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Introducing a robust and efficient stopping criterion for MOEAs

Guerrero

Martí

Berlanga

et al. 2010

IEEE Congress on Evolutionary Computation

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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.

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“…In a follow-up paper, Wagner et al [34] advanced this idea to develop 663 an online convergence detection (OCD) criterion by carrying out 2 -variance test and t-test for linear behavior on different performance metrics. They stopped simulation when either of the tests indicated convergence.…”

Section: Introductionmentioning

confidence: 98%

A non‐dominance‐based online stopping criterion for multi‐objective evolutionary algorithms

Goel

Stander

2010

Numerical Meth Engineering

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SUMMARYA non-dominance criterion-based metric that tracks the growth of an archive of non-dominated solutions over a few generations is proposed to generate a convergence curve for multi-objective evolutionary algorithms (MOEAs). It was observed that, similar to single-objective optimization problems, there were significant advances toward the Pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured. This convergence curve was used to terminate the MOEA search to obtain a good trade-off between the computational cost and the quality of the solutions. Two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric.

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OCD: Online Convergence Detection for Evolutionary Multi-Objective Algorithms Based on Statistical Testing

Cited by 30 publications

References 22 publications

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Entropy-Based Termination Criterion for Multiobjective Evolutionary Algorithms

Introducing a robust and efficient stopping criterion for MOEAs

A non‐dominance‐based online stopping criterion for multi‐objective evolutionary algorithms

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