GLOBAL OPTIMIZATION USING THE MULTISTART METHOD

Multistart is a stochastic global optimization method for finding the global optimum of highly nonlinear mechanical problems. In this paper we introduce and develop a variant of the multistart method in which a fraction of the sample points in the feasible region with smallest fu nction value are clustered using the Vector Quantization technique. Th e theories of lattices and sphere packing are used to define optimal l attices. These lattices are optimal with respect to quantization error and are used as code points for vector quantization. The implementati on of these ideas has resulted in the VQ-multistart algorithm for find ing the global optimum with substantial reductions in both the incore memory requirements and the computation time. We solve several mathema tical test problems and a mechanical optimal design problem using the VQ-multistart algorithm.