Relative Frequencies of Generalized Simulated Annealing

Authors:
Jan Hannig;Edwin K. P. Chong;Sanjeev R. Kulkarni
Affiliations:
Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877;Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado 80523-1373;Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544
Venue:
Mathematics of Operations Research
Year:
2006

Citing 7
Cited 3

Cooling schedules for optimal annealing

Mathematics of Operations Research
Markov chains with rare transitions and simulated annealing

Mathematics of Operations Research
Simulated annealing type markov chains and their order balance equations

SIAM Journal on Control and Optimization
Stochastic discrete optimization

SIAM Journal on Control and Optimization
On the Convergence and Applications of Generalized Simulated Annealing

SIAM Journal on Control and Optimization
Stochastic Comparison Algorithm for Discrete Optimization with Estimation

SIAM Journal on Optimization
Noise conditions for prespecified convergence rates of stochastic approximation algorithms

IEEE Transactions on Information Theory

Computational applications of nonextensive statistical mechanics

Journal of Computational and Applied Mathematics
Adaptive parameterized improving hit-and-run for global optimization

Optimization Methods & Software - GLOBAL OPTIMIZATION
Adaptive search with stochastic acceptance probabilities for global optimization

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a class of nonhomogeneous Markov chains arising in simulated annealing and related stochastic search algorithms. Using only elementary first principles, we analyze the convergence and rate of convergence of the relative frequencies of visits to states in the Markov chain. We describe in detail three examples, including the standard simulated annealing algorithm, to show how our framework applies to specific stochastic search algorithmsthese examples have not previously been recognized to be sufficiently similar to share common analytical grounds. Our analysis, though elementary, provides the strongest sample path convergence results to date for simulated annealing-type Markov chains. Our results serve to illustrate that by taking a purely sample path view, surprisingly strong statements can be made using only relatively elementary tools.