Fuzzy Clustering Based Hierarchical Metamodeling For Space Reduction and Design Optimization

For computation-intensive design problems, metamodeling techniques are commonly used to reduce the computational expense during optimization; however, they often have difficulty or even fail to model an unknown system in a large design space, especially when the number of available samples is limited. This paper proposes an intuitive method to systematically reduce the design space to a relatively small region. This method entails three main elements: 1) constructing surrogate approximations using either response surface or kriging models to capture unknown systems in the original large space; 2) calculating many inexpensive points from the obtained surrogate model, clustering these points using the Fuzzy c-means clustering method, and choosing an attractive cluster and its corresponding reduced design space; 3) progressively generating sample points to construct kriging models and identify the design optimum within the reduced design space. The proposed method is illustrated using the well-known six-hump camel back problem. The method is then applied to a constrained, highly nonlinear optimization problem and a real design problem. After comparing with other methods, it is found that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum with the presence of highly nonlinear constraints. The effect of using either response surface or kriging models in the original design space is also compared and discussed. Limitations of the proposed method are illustrated.