Abstract
The TRUST methodology addresses the unconstrained global optimization problem in terms of the evolution of a novel deterministic nonlinear dynamical system, which combines the concepts of subenergy tunneling and non-Lipschitzian “terminal” repellers. In this paper, the TRUST algorithms are generalized by extending the formalism to lower semicontinuous objective functions, and by allowing gradient-directed tunneling with componentwise flow direction reversal at the boundaries of the parameter domain. Known limitations of the methodology are summarized, and the reduction of a multi-dimensional problem to a one-dimensional case (e.g., via hyperspiral embedding) is discussed with regards to a formal convergence proof. Benchmark results are presented, which demonstrate that TRUST is substantially faster than previously published global optimization techniques.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aluffi-Pentini, F, Parisi, V., and Zirilli, F., “Global Optimization and Stochastic Differential Equations,”Journal of Optimization Theory and Applications,47, 1–15 (1985).
Ammar, H. and Cherruault Y., “Approximation of a Several Variables Function by a Single Variable Function and Application to Global Optimization,”Math. Comp, and Modeling,18, 17–21 (1993).
Aubin, J. P. and Najman, L., “L’Algorithme des Montagnes Russes pour 1’Optimization Globale,”C. R. Acad. Sei. Paris,319 (Serie I), 631–636 (1994).
Barhen, J., Zak, M., and Toomarian, N., “Non-Lipschitzian Neural Dynamics,” pp. 102–112 inAdvanced Neural Computers, ed. R. Eckmiller, North-Holland, Amsterdam, Holland, 1990.
Bilbro, G. L ., “Fast Stochastic Global Optimization,”IEEE Trans. Syst. Man. Cyber.,SMC-24(4), 684–689 (1994).
Bremermann, H. A., “A Method of Unconstrained Global Optimization,”Mathematical Bio-sciences,9, 1–15 (1970).
Cetin, B., Barhen, J., and Burdick, J., “Terminal Repeller Unconstrained Subenergy Tunneling (TRUST) for Fast Global Optimization,”J. Opt. Theory and Appl.,77, 97–126 (1993).
Chin, D. C., “A More Efficient Global Optimization Algorithm Based on Styblinski and Tang,”Neural Networks,7 (3), 573–574 (1994).
Dixon, L. C. W. and Jha, M., “Parallel Algorithms for Global Optimization,”J. Opt. Theory and Appl.,79, 385–395 (1993).
Floudas, C. A. and Pardalos, P. M.,State of the Art in Global Optimization: Computational Methods and Applications, Kluwer Academic Publishers (in preparation, 1995 );ibid, Procs., Second International Conference, Princeton, New Jersey (April 1995 ).
Ge, R., “A Filled Function Method for Finding a Global Minimizer of a Function of Several Variables,”Mathematical Programming,46, 191–204 (1990).
Horst, R. and Tuy, H.Global Optimization, 2d ed., Springer-Verlag, Berlin (1993).
Jones, D. R., Perttunen, C. D., and Stuckman, B. E., “Lipschitzian Optimization without the Lipschitz Constant,”J. Opt. Theory and Appl.,79, 157–181 (1993).
Kan, A. H. G. R. and Timmer, G. T., “A Stochastic Approach to Global Optimization,” pp. 245–262 inNumerical Optimization, eds. P. T. Boggs, R. H. Byrd, and R. B. Schnabel, SIAM, Philadelphia, Pennsylvania, 1985.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P., “Optimization by Simulated Annealing,”Science,220, 671–680 (1983).
Levy, A. V. and Montalvo, A., “The Tunneling Algorithm for the Global Minimization of Functions,”SIAM Journal on Scientific and Statistical Computing,6, 15–29 (1985).
Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, 1969.
Price, W. L., “A Controlled Random Search Procedure for Global Optimization,” in TowardGlobal Optimization 2, eds. L. C. W. Dixon and G.-P. Szegö, North-Holland, Amsterdam, Holland, 1978.
Ratschek, H. and Rokne, J.,New Computer Methods for Global Optimization, Ellis Horwood Limited, Chichester, United Kingdom, 1988.
Sergeyev, Y. D. and Grishagin, V. A., “A Parallel Method for Finding the Global Minimum of Univariate Functions,”J. Opt. Theory and Appl.,80, 513–536 (1994).
Styblinski, M. A. and Tang, T. S., “Experiments in Nonconvex Optimization: Stochastic Approximation with Function Smoothing and Simulated Annealing,”Neural Networks,3, 467–483 (1990).
Szu, H. and Hartley, R., “Fast Simulated Annealing,”Physics Letters,A 122, 157–162 (1987).
Tang, Z. and Koehler, G. J., “Deterministic Global Optimal FNN Training Algorithms,”Neural Networks,7, 301–311 (1994).
Törn, A. A., “A Search Clustering Approach to Global Optimization,”Toward Global Optimization 2, eds. L. C. W. Dixon and G.-P. Szegö, North-Holland, Amsterdam, Holland, 1978.
Törn, A. and Zilinskas, A.,Global Optimization, Springer-Verlag, Berlin, Germany, 1989.
Yao, Y., “Dynamic Tunneling Algorithm for Global Optimization,”IEEE Transactions on Systems, Man, and Cybernetics,19, 1222–1230 (1989).
Zak, M., “Terminal Attractors in Neural Networks,”Neural Networks,2, 259–274 (1989).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Barhen, J., Protopopescu, V. (1996). Generalized TRUST Algorithms for Global Optimization. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_11
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3437-8_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3439-2
Online ISBN: 978-1-4613-3437-8
eBook Packages: Springer Book Archive