A RBF-based constrained global optimization algorithm for problems with computationally expensive objective and constraints

作者：Wu, Yizhong; Yin, Qian; Jie, Haoxiang^*; Wang, Boxing; Zhao, Jianjun

来源：Structural and Multidisciplinary Optimization, 2018, 58(4): 1633-1655.

DOI：10.1007/s00158-018-1987-2

• Metamodel
• Radial basis function
• Constrained optimization
• Computationally expensive function
• Global optimization

This paper presents a metamodel-based constrained optimization method, called Radial basis function-based Constrained Global Optimization (RCGO), to solve optimization problems involving computationally expensive objective function and inequality constraints. RCGO is an extension of the adaptive metamodel-based global optimization (AMGO) algorithm which can handle unconstrained black-box optimization problems. Firstly, a sequential sampling method is implemented to obtain the initial points for building the radial basis RBF) approximations to all computational expensive functions while enforcing a feasible solution. Then, an auxiliary objective function subject to the approximate constraints is constructed to determine the next iterative point and further improve the solution. During the process, a distance function with a group of exponents is introduced in the auxiliary function to balance the local exploitation and the global exploration. The RCGO method is tested on a series of benchmark problems, and the results demonstrate that RCGO needs fewer costly evaluations and can be applied for costly constrained problems with all infeasible start points. And the test results on the 30D problems demonstrate that RCGO has advantages in solving the problems. The proposed method is then applied to the design of a cycloid gear pump and desirable results are obtained.

• 出版日期2018-10
• 单位华中科技大学