Simulated annealing on uncorrelated energy landscapes. (1994) - Goertzel, Ben; Ananda, Malwane
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.