Abstract
This paper summarizes large deviations results for Markov chains with exponential transitions, and discusses their applications in comparing stochastic optimization algorithms. In the second half, two specific algorithms will be focussed on: Mutation/Selection vs parallel simulated annealing. Conditions which tell when an algorithm should be preferred to the other will be given. These conditions combine the parameters of both algorithms and a number of relevant geometric quantities.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.H.L Aarts and J.H.M Korst. Simulated annealing and Boltzmann machines, Wiley, New York, 1988.
O. Catoni. Rough large deviation estimates for simulated annealing: Application to exponential schedules. Ann. Probab., 20 (1991), 3, 1109–1146.
R. Cerf. The dynamics of mutation-selection algorithms with large population sizes. Ann. Inst. H. Poincaré Probab. Statist., 32 (1996), 455–508.
T.E. Davis and J.C. Principe. A simulated annealing like convergence theory for the simple genetic algorithm. In R.K. Belew and L.B. Booker eds. Proceedings of the fourth Int. Conf. on Genetic Algorithms, San Mateo CA, Morgan Kauffman, 174–181, 1991.
O. François. An evolutionary strategy for global minimization and its Markov chain analysis, IEEE Transactions on Evolutionary Computation, 2, (1998), 77–90.
O. François. Global optimization with exploration/selection algorithms and simulated annealing, Preprint, (2000).
M.I. Freidlin and A.D. Wentzell. Random perturbations of dynamical systems, Springer Verlag, New York, 1984.
B. Hajek. Cooling schedules for optimal annealing, Math. Oper. Res, 13 (1988), 311–329.
S.W. Mahfoud and D.E. Golberg. Parallel recombinative simulated annealing: A genetic algorithm. Parallel Computing, 21 (1995), 1, 1995.
E. Van Nimwegen, J.P. Crutchfield and M. Mitchell. Statistical dynamics of the royal road genetic algorithm. Theor. Comput. Sci., 229 (1999), 41–102.
G. Rudolph. Massively parallel simulated annealing and its relation to evolutionary algorithms, Evolutionary Computation, 1,4, (1993), 361–383.
G. Rudolph. Finite Markov chain results in evolutionary computation: A tour d’horizon, Fundamenta Informaticae, (1998), 1–22.
J. Suzuki. A further result on the Markov chain model of genetic algorithm and its application to a simulated annealing-like theory, IEEE Trans. Systems, Man, and Cybernetics-B, 28,1 (1998), 95–102.
A. Trouvé. Asymptotical behaviour of several interacting annealing processes, Probab. Theory Related Fields, 102 (1995), 123–143.
A. Trouvé. Cycle decomposition and simulated annealing, SIAM J. Control Optim., 34,3 (1996), 966–986.
J.N. Tsitsiklis. Markov chains with rare transitions and simulated annealing, Math. Oper. Res., 14 (1989) 70–90.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
François, O. (2000). Large Deviations, Evolutionary Computation and Comparisons of Algorithms. In: Schoenauer, M., et al. Parallel Problem Solving from Nature PPSN VI. PPSN 2000. Lecture Notes in Computer Science, vol 1917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45356-3_8
Download citation
DOI: https://doi.org/10.1007/3-540-45356-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41056-0
Online ISBN: 978-3-540-45356-7
eBook Packages: Springer Book Archive