Simulated annealing on uncorrelated energy landscapes. (1994)

• Record Type: Journal Article
• Authors: Goertzel, Ben; Ananda, Malwane
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 17:Number 4(1994)
• Page Start: 791
• Page End: 798
• Publication Date: 1994
• Subjects: simulated annealing -- evolutionary mutation -- uncorrelated functions; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171294001109
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A functionf : { 0, 1, 2, L, a } n → R is said to be uncorrelated ifProb [ 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 functionG is derived. Surprising numerical results are obtained, to the effect that for certain parametrized families of functions{ G c, c ∈ R }, wherec represents the “steepness” of the curveG ′ ( u ), the effectiveness of simulated annealing increases steadily withc 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.