Solving bi-level optimization problems in engineering design using kriging models

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.

KEYWORDS:

• Engineering design
• Stackelberg game
• bi-level programming
• metamodelling
• kriging model

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by National Natural Science Foundation of China [project numbers 71071104 and 71371132].