A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the...

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Main Authors: Yaohui Li, Jingfang Shen, Ziliang Cai, Yizhong Wu, Shuting Wang
Format: Article
Language:English
Published: MDPI AG 2021-01-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/9/2/149
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spelling doaj-9c78a5a3e59d4ac8bf26c90c6cb0d6f22021-01-12T00:03:28ZengMDPI AGMathematics2227-73902021-01-01914914910.3390/math9020149A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box FunctionsYaohui Li0Jingfang Shen1Ziliang Cai2Yizhong Wu3Shuting Wang4School of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, ChinaCollege of Science, Huazhong Agricultural University, Wuhan 430070, ChinaSchool of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, ChinaNational CAD Centre, Huazhong University of Science and Technology, Wuhan 430070, ChinaNational CAD Centre, Huazhong University of Science and Technology, Wuhan 430070, ChinaThe kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.https://www.mdpi.com/2227-7390/9/2/149multi-objective constrained optimizationsurrogate modelkrigingblack-box function
collection DOAJ
language English
format Article
sources DOAJ
author Yaohui Li
Jingfang Shen
Ziliang Cai
Yizhong Wu
Shuting Wang
spellingShingle Yaohui Li
Jingfang Shen
Ziliang Cai
Yizhong Wu
Shuting Wang
A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions
Mathematics
multi-objective constrained optimization
surrogate model
kriging
black-box function
author_facet Yaohui Li
Jingfang Shen
Ziliang Cai
Yizhong Wu
Shuting Wang
author_sort Yaohui Li
title A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions
title_short A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions
title_full A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions
title_fullStr A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions
title_full_unstemmed A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions
title_sort kriging-assisted multi-objective constrained global optimization method for expensive black-box functions
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-01-01
description The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.
topic multi-objective constrained optimization
surrogate model
kriging
black-box function
url https://www.mdpi.com/2227-7390/9/2/149
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