International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 4, Pages 791-798
doi:10.1155/S0161171294001109
Simulated annealing on uncorrelated energy landscapes
Department of Mathematical Sciences, University of Nevada, Las Vegas 89154, NV, USA
Received 18 December 1992; Revised 6 November 1993
Copyright © 1994 Ben Goertzel and Malwane Ananda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.