Solving bi-level optimization problems in engineering design using kriging models |
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Authors: | Yi Xia Xiaojie Liu Gang Du |
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Affiliation: | College of Management and Economics, Tianjin University, Tianjin, PR China |
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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. |
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Keywords: | Engineering design Stackelberg game bi-level programming metamodelling kriging model |
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