A comparative study on surrogate models for SAEAs
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A comparative study on surrogate models for SAEAs Mônica A. C. Valadão1,3 · Lucas S. Batista2 Received: 31 May 2019 / Accepted: 22 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Surrogate model assisted evolutionary algorithms (SAEAs) are metamodel-based strategies usually employed on the optimization of problems that demand a high computational cost to be evaluated. SAEAs employ metamodels, like Kriging and radial basis function (RBF), to speed up convergence towards good quality solutions and to reduce the number of function evaluations. However, investigations concerning the influence of metamodels in SAEAs performance have not been developed yet. In this context, this paper performs an investigative study on commonly adopted metamodels to compare the ordinary Kriging (OK), first-order universal Kriging (UK1), second-order universal Kriging (UK2), blind Kriging (BK) and RBF metamodels performance when embedded into a single-objective SAEA Framework (SAEA/F). The results obtained suggest that the OK metamodel presents a slightly better improvement than the others, although it does not present statistically significant difference in relation to UK1, UK2, and BK. The RBF showed the lowest computational cost, but the worst performance. However, this worse performance is around 2% in relation to the other metamodels. Furthermore, the results show that BK presents the highest computational cost without any significant improvement in solution quality when compared to OK, UK1, and UK2. Keywords Kriging · RBF · Surrogate model assisted evolutionary algorithms
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11590020-01575-2) contains supplementary material, which is available to authorized users.
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Mônica A. C. Valadão [email protected] Lucas S. Batista [email protected]
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Graduate Program in Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-901, Brazil
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Department of Electrical Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-901, Brazil
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Science and Technology Institute, Universidade Federal dos Vales do Jequitinhonha e Mucuri, Diamantina, MG 39100-000, Brazil
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M. A. C. Valadão, L. S. Batista
1 Introduction Evolutionary algorithms (EA) represent an interesting option to deal with real-world optimization problems since they do not depend on problem features, such as continuity, differentiability, smoothness and convexity [1–3]. However, it might not be possible to apply these methods in problems with expensive evaluation functions [4– 6]. To address this issue, several approaches integrate metamodels and EAs to reduce the number of evaluation functions required. In such methods, the metamodel is used to give an estimate of the true fitness in specific stages of EAs, e.g., to evaluate all or a subset of candidate solutions on a metamodel (prediction function) in each iteration. These approaches are termed as surrogate model assisted evolutionary algo
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