This paper presents a comparison of the criteria for updating the Kriging surrogate models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those in combination (EHVI + EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has recently been proposed as the criterion considering the stochastic improvement of the front of nondominated solutions in multi-objective optimization. EST is the value of each objective function estimated nonstochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in an unconstrained case, EHVI maintains a balance between accuracy, spread, and uniformity in nondominated solutions for Kriging-model-based multiobjective optimization. In addition, the present experiments suggested future investigation into techniques for handling constraints with uncertainties to enhance the capability of EHVI in constrained cases.
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September 2013
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Updating Kriging Surrogate Models Based on the Hypervolume Indicator in Multi-Objective Optimization
Koji Shimoyama,
Koji Shimoyama
1
Assistant Professor
Tohoku University,
e-mail: shimoyama@edge.ifs.tohoku.ac.jp
Institute of Fluid Science
,Tohoku University,
Sendai 980-8577
, Japan
e-mail: shimoyama@edge.ifs.tohoku.ac.jp
1Corresponding author.
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Koma Sato,
Koma Sato
Researcher
Hitachi, Ltd.,
e-mail: koma.sato.ky@hitachi.com
Hitachi Research Laboratory
,Hitachi, Ltd.,
Hitachinaka, Ibaraki 312-0034
, Japan
e-mail: koma.sato.ky@hitachi.com
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Shinkyu Jeong,
Shinkyu Jeong
Associate Professor
Kyunghee University,
e-mail: icarus@khu.ac.kr
Department of Mechanical Engineering
,Kyunghee University,
Yongin 446-701
, Korea
e-mail: icarus@khu.ac.kr
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Shigeru Obayashi
Shigeru Obayashi
Professor
Tohoku University,
e-mail: obayashi@ifs.tohoku.ac.jp
Institute of Fluid Science
,Tohoku University,
Sendai 980-8577
, Japan
e-mail: obayashi@ifs.tohoku.ac.jp
Search for other works by this author on:
Koji Shimoyama
Assistant Professor
Tohoku University,
e-mail: shimoyama@edge.ifs.tohoku.ac.jp
Institute of Fluid Science
,Tohoku University,
Sendai 980-8577
, Japan
e-mail: shimoyama@edge.ifs.tohoku.ac.jp
Koma Sato
Researcher
Hitachi, Ltd.,
e-mail: koma.sato.ky@hitachi.com
Hitachi Research Laboratory
,Hitachi, Ltd.,
Hitachinaka, Ibaraki 312-0034
, Japan
e-mail: koma.sato.ky@hitachi.com
Shinkyu Jeong
Associate Professor
Kyunghee University,
e-mail: icarus@khu.ac.kr
Department of Mechanical Engineering
,Kyunghee University,
Yongin 446-701
, Korea
e-mail: icarus@khu.ac.kr
Shigeru Obayashi
Professor
Tohoku University,
e-mail: obayashi@ifs.tohoku.ac.jp
Institute of Fluid Science
,Tohoku University,
Sendai 980-8577
, Japan
e-mail: obayashi@ifs.tohoku.ac.jp
1Corresponding author.
Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received September 24, 2012; final manuscript received May 15, 2013; published online July 2, 2013. Assoc. Editor: Bernard Yannou.
J. Mech. Des. Sep 2013, 135(9): 094503 (7 pages)
Published Online: July 2, 2013
Article history
Received:
September 24, 2012
Revision Received:
May 15, 2013
Accepted:
June 4, 2013
Citation
Shimoyama, K., Sato, K., Jeong, S., and Obayashi, S. (July 2, 2013). "Updating Kriging Surrogate Models Based on the Hypervolume Indicator in Multi-Objective Optimization." ASME. J. Mech. Des. September 2013; 135(9): 094503. https://doi.org/10.1115/1.4024849
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