Solving bi-level optimization problems in engineering design using kriging models. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Xia, Yi; Liu, Xiaojie; Du, Gang
• Is Part Of: Engineering optimization. Volume 50:Issue 5(2018)
• Page Start: 856
• Page End: 876
• Publication Date: 2018-05-04
• Subjects: Engineering design -- Stackelberg game -- bi-level programming -- metamodelling -- kriging model; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2017.1358711
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: Stackelberg game-theoretic approaches are applied extensively in engineering design to handle distributed collaboration decisions. Bi-level genetic algorithms (BLGAs) and response surfaces have been used to solve the corresponding bi-level programming models. However, the computational costs for BLGAs often increase rapidly with the complexity of lower-level programs, and optimal solution functions sometimes cannot be approximated by response surfaces. This article proposes a new method, namely the optimal solution function approximation by kriging model (OSFAKM), in which kriging models are used to approximate the optimal solution functions. A detailed example demonstrates that OSFAKM can obtain better solutions than BLGAs and response surface-based methods, and at the same time reduce the workload of computation remarkably. Five benchmark problems and a case study of the optimal design of a thin-walled pressure vessel are also presented to illustrate the feasibility and potential of the proposed method for bi-level optimization in engineering design.