International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 791-798
doi:10.1155/S0161171294001109
Abstract
A function f:{0,1,2,L,a}n→R is said to be uncorrelated if Prob[f(x)≤u]=G(u). This paper studies the effectiveness of simulated annealing as a strategy for optimizing uncorrelated functions. A recurrence relation expressing the effectiveness of the algorithm in terms of the function G is derived. Surprising numerical results are obtained, to the effect that for certain parametrized families of functions {Gc, c∈R}, where c represents the “steepness” of the curve G′(u), the effectiveness of simulated annealing increases steadily with c These results suggest that on the average annealing is effective whenever most points have very small objective function values, but a few points have very large objective function values.