Global optimization method using SLE and adaptive RBF based on fuzzy clustering

High fidelity analysis models, which are beneficial to improving the design quality, have been more and more widely utilized in the modern engineering design optimization problems. However, the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable. In order to improve the efficiency of optimization involving high fidelity analysis models, the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models, which can greately reduce the computation time. An efficient heuristic global optimization method using adaptive radial basis function (RBF) based on fuzzy clustering (ARFC) is proposed. In this method, a novel algorithm of maximin Latin hypercube design using successive local enumeration (SLE) is employed to obtain sample points with good performance in both space-filling and projective uniformity properties, which does a great deal of good to metamodels accuracy. RBF method is adopted for constructing the metamodels, and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced. The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space. The numerical benchmark examples are used for validating the performance of ARFC. The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method (ARSM) proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum. This method improves the efficiency and global convergence of the optimization problems, and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.