ENHANCED SIMULATED ANNEALING FOR GLOBALLY MINIMIZING FUNCTIONS OF MANY-CONTINUOUS VARIABLES

A new global optimization algorithm for functions of many continuous v ariables is presented, derived from the basic Simulated Annealing meth od. Our main contribution lies in dealing with high-dimensionality min imization problems, which are often difficult to solve by all known mi nimization methods with or without gradient. In this article we take a special interest in the variables discretization issue. We also devel op and implement several complementary stopping criteria. The original Metropolis iterative random search, which takes place in a Euclidean space R-n, is replaced by another similar exploration, performed withi n a succession of Euclidean spaces R-p, with p << n. This Enhanced Sim ulated Annealing (ESA) algorithm was validated first on classical high ly multimodal functions of 2 to 100 variables. We obtained significant reductions in the number of function evaluations compared to six othe r global optimization algorithms, selected according to previously pub lished computational results for the same set of test functions. In mo st cases, ESA was able to closely approximate known global optima. The reduced ESA computational cost helped us to refine further the obtain ed global results, through the use of some local search. We have used this new minimizing procedure to solve complex circuit design problems , for which the objective function evaluation can be exceedingly costl y.