EXPERIMENTS IN NONCONVEX OPTIMIZATION - STOCHASTIC-APPROXIMATION WITH FUNCTION SMOOTHING AND SIMULATED ANNEALING

The method of simulated annealing, to be referred to-after Szu (1986)-as classical simulated annealing (CSA), received much attention recently, especially for solving combinatorial problems (e.g., in the VLSI area), implementing the Boltzman machine for learning in neural networks, and recently for global function optimization. In Szu (1986a, 1987) the fast simulating annealing (FSA) algorithm was introduced-using the Cauchy rather than Gaussian sampling and fast cooling-and applied to finding the global minimum of a nonconvex multiextremal function. It has proved to be superior to the CSA technique. Recently, the method of stochastic approximation combined with convolution smoothing (to be referred to as SAS) was successfully used by Styblinski and Opalski (1984) for manufacturing yield optimization with deterministic parameters and non-differentiable p.d.f's (Tang & Styblinski, 1988). In this presentation, some analogies between the CSA/FSA and SAS algorithms are discussed in application to global function minimization. It is demonstrated that the SAS approach is much more accurate and efficient on the test examples tried than the FSA algorithm. Convenient statistical criteria are proposed and used for algorithm performance evaluation, together with test examples of controlled properties. © 1990.