Metamodel-based Global Optimization Using Fuzzy Clustering for Design Space Reduction

High fidelity analysis are utilized in modern engineering design optimization problems which involve expensive black-box models. For computation-intensive engineering design problems, efficient global optimization methods must be developed to relieve the computational burden. A new metamodel-based global optimization method using fuzzy clustering for design space reduction (MGO-FCR) is presented. The uniformly distributed initial sample points are generated by Latin hypercube design to construct the radial basis function metamodel, whose accuracy is improved with increasing number of sample points gradually. Fuzzy c-mean method and Gath-Geva clustering method are applied to divide the design space into several small interesting cluster spaces for low and high dimensional problems respectively. Modeling efficiency and accuracy are directly related to the design space, so unconcerned spaces are eliminated by the proposed reduction principle and two pseudo reduction algorithms. The reduction principle is developed to determine whether the current design space should be reduced and which space is eliminated. The first pseudo reduction algorithm improves the speed of clustering, while the second pseudo reduction algorithm ensures the design space to be reduced. Through several numerical benchmark functions, comparative studies with adaptive response surface method, approximated unimodal region elimination method and mode-pursuing sampling are carried out. The optimization results reveal that this method captures the real global optimum for all the numerical benchmark functions. And the number of function evaluations show that the efficiency of this method is favorable especially for high dimensional problems. Based on this global design optimization method, a design optimization of a lifting surface in high speed flow is carried out and this method saves about 10 h compared with genetic algorithms. This method possesses favorable performance on efficiency, robustness and capability of global convergence and gives a new optimization strategy for engineering design optimization problems involving expensive black box models.