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Article

A Comparative Study of Infill Sampling Criteria for Computationally Expensive Constrained Optimization Problems

1
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
2
Centre of Excellence in Mathematics, CHE, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Received: 26 August 2020 / Revised: 23 September 2020 / Accepted: 25 September 2020 / Published: 3 October 2020
(This article belongs to the Special Issue Modelling and Simulation of Natural Phenomena of Current Interest)
Engineering optimization problems often involve computationally expensive black-box simulations of underlying physical phenomena. This paper compares the performance of four constrained optimization algorithms relying on a Gaussian process model and an infill sampling criterion under the framework of Bayesian optimization. The four infill sampling criteria include expected feasible improvement (EFI), constrained expected improvement (CEI), stepwise uncertainty reduction (SUR), and augmented Lagrangian (AL). Numerical tests were rigorously performed on a benchmark set consisting of nine constrained optimization problems with features commonly found in engineering, as well as a constrained structural engineering design optimization problem. Based upon several measures including statistical analysis, our results suggest that, overall, the EFI and CEI algorithms are significantly more efficient and robust than the other two methods, in the sense of providing the most improvement within a very limited number of objective and constraint function evaluations, and also in the number of trials for which a feasible solution could be located. View Full-Text
Keywords: expensive function; expected improvement; constrained Bayesian optimization; Gaussian process; infill sampling criterion expensive function; expected improvement; constrained Bayesian optimization; Gaussian process; infill sampling criterion
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MDPI and ACS Style

Chaiyotha, K.; Krityakierne, T. A Comparative Study of Infill Sampling Criteria for Computationally Expensive Constrained Optimization Problems. Symmetry 2020, 12, 1631. https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101631

AMA Style

Chaiyotha K, Krityakierne T. A Comparative Study of Infill Sampling Criteria for Computationally Expensive Constrained Optimization Problems. Symmetry. 2020; 12(10):1631. https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101631

Chicago/Turabian Style

Chaiyotha, Kittisak, and Tipaluck Krityakierne. 2020. "A Comparative Study of Infill Sampling Criteria for Computationally Expensive Constrained Optimization Problems" Symmetry 12, no. 10: 1631. https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101631

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