Open Access

ARTICLE

A Metamodel-Based Global Algorithm for Mixed-Integer Nonlinear Optimization and the Application in Fuel Cell Vehicle Design

Haoxiang Jie^1,2, Huihong Shi³, Jianwan Ding^2,4, Yizhong Wu², Qian Yin²

1 No.711 Institute, China Shipbuilding Industry Corporation, Shanghai, China
2 National CAD supported Software Engineering Centre, Huazhong University of Science and Technology, Wuhan, PR China
3 Financial school, Capital University of Economics and business, Beijing, PR China
4 corresponding author, Email: dingjw@mail.hust.edu.cn

Computer Modeling in Engineering & Sciences 2015, 108(3), 193-214. https://doi.org/10.3970/cmes.2015.108.193

Abstract

This paper improves the adaptive metamodel-based global algorithm (AMGO), which is presented for unconstrained continuous problems, to solve mixed-integer nonlinear optimization involving black-box and expensive functions. The new proposed method is called as METADIR, which can be divided into two stages. In the first stage, the METADIR adopts extended DIRECT method to constantly subdivide the design space and identify the sub-region that may contain the optimal value. When iterative points gather into a sub-region to some extent, we terminate the search progress of DIRECT and turn to the next stage. In the second phase, a local metamodel is constructed in this potential optimal sub-region, and then an auxiliary optimization problem extended from AMGO is established based on the local metamodel to obtain the iterative points, which are then applied to update the metamodel adaptively. To show the performance of METADIR on both continuous and mixed-integer problems, numerical tests are presented on both kinds of problems. The METADIR method is compared with the original DIRECT on continuous problems, and compared with SO-MI and GA on mixed-integer problems. Test results show that the proposed method has better accuracy and needs less function evaluations. Finally, the new proposed method is applied into the component size optimization problem of fuel cell vehicle and achieves satisfied results.

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