Multi-stage design space reduction and metamodeling optimization method based on self-organizing maps and fuzzy clustering

• A multi-stage design space reduction methodology is proposed.
• Metamodel optimization is more cost effective to find the optimum design.
• Efficient metamodel can be built in the preliminary reduction space.
• The proper number of clusters is determined by utilizing cluster validity indices.
• Obtaining the accurate results of high nonlinear problems within a small region.

Design space exploration and metamodeling techniques have gained rapid dominance in complex engineering design problems. It is observed that the modeling efficiency and accuracy are directly associated with the design space. In order to reduce the complexity of the design space and improve modeling accuracy, a multi-stage design space reduction and metamodeling optimization methodology based on self-organizing maps and fuzzy clustering is proposed in this paper. By using the proposed three-stage optimization approach, the design space is systematically reduced to a relatively small promising region. Self-organizing maps are introduced to act as the preliminary reduction approach through analyzing the underlying mapping relations between design variables and system responses within the original samples. GK (Gustafson & Kessel) clustering algorithm is employed to determine the proper number of clusters by utilizing clustering validity indices, and sample points are clustered using fuzzy c-means (FCM) clustering method with the known number of clusters, so that the search can focus on the most promising area and be better supported by the constructed kriging metamodel. Empirical studies on benchmark problems with multi-humps and two practical nonlinear engineering design problems show the accurate results can be obtained within the reduced design space, which improve the overall efficiency significantly.