Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-17T14:18:52.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Deterministic global optimization using interval constraint propagation techniques

Published online by Cambridge University Press:  15 December 2004

Frederic Messine
Frederic Messine*
Affiliation:
Laboratoire de Mathématiques Appliquées, FRE 2570, Université de Pau et des Pays de l'Adour, UFR Sciences et Techniques, Département d'Informatique, BP 1155, 64013 Pau Cedex, France; [email protected]; [email protected].
Get access

Abstract

The purpose of this article is to show the great interest of theuse of propagation (or pruning) techniques, inside classicalinterval Branch-and-Bound algorithms. Therefore, a propagationtechnique based on the construction of the calculus tree isentirely explained and some properties are presented without theneed of any formalism (excepted interval analysis). This approachis then validated on a real example: the optimal design of anelectrical rotating machine.

Keywords

Interval analysisBranch-and-Boundglobaloptimizationpruning/propagation techniques.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 4 , October 2004 , pp. 277 - 293
Copyright
© EDP Sciences, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

E. Fitan, F. Messine and B. Nogarede, The Electromagnetical Acuator Design Problem: A General and Rational Approach. IEEE T. Magn. 40 (2004).
E. Hansen, Global Optimization Using Interval Analysis. Marcel Dekker, Inc. 270 Madison Avenue, New York 10016 (1992).
J.-C. Gilbert, G. Le Vey and J. Masse, La différentiation automatique de fonctions représentées par des programmes. Rapports de Recherche de l'INRIA- Rocquencourt, 1557, Programme 5, Traitement du Signal, Automatique et Productique (1991).
Granvilliers, L., On the Combination of Interval Computating Solvers. Reliab. Comput. 7 (2001) 467–483. CrossRef
Granvilliers, L. and Benhamou, F., Progress in the Solving of a Circuit Design Problem. J. Global Optim. 20 (2001) 155–168. CrossRef
Jaulin, L., Interval Constraint Propagation with Application to Bounded-Error Estimation. Automatica 36 (2000) 1547–1562. CrossRef
R.B. Kearfott, Rigorous Global Search: Continuous Problems. Kluwer Academic Publishers, Dordrecht, Boston, London (1996).
O. Lhomme, A. Gotlieb and M. Ruher, Dynamic Optimization of Interval Narrowing Algorithms. J. Logic Program. 37 (1998).
F. Messine, Méthodes d'optimisation globale basées sur l'analyse d'intervalle pour la résolution de problèmes avec contraintes. Ph.D. Thesis, Institut National Polytechnique de Toulouse (1997).
Messine, F., Extension of Affine Arithmetic: Application to Global Optimization. J. Universal Comput. Sci. 8 (2002) 992–1015.
Messine, F. and Lagouanelle, J.L., Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization. J. Univ. Comput. Sci. 4 (1998) 589–603.
F. Messine, Méthodes de propagation de contraintes basées sur l'analyse d'intervalles pour l'optimisation globale déterministe. Rapport interne de recherche du Département Informatique de l'UPPA, R2I01-02, 18 pages (2002). Available on www.univ-pau.fr/~messine
F. Messine, V. Monturet and B. Nogarede, An Interval Branch and Bound Method Dedicated to the Optimal Design of Piezoelectric Actuators. Mathematics and Computers in Science and Engineering, ISBN 960-8052-36-X, WSES Press (2001) 174–180.
F. Messine, E. Fitan and B. Nogarede, The Inverse Problem Associated to the Optimal Design of Electromagnetic Actuators: Application to Rotating Machines with Magnetic Effects, in European Symposium on Numerical Methods in Electromagnetics, Proceedings JEE'02 (2002) 318–323.
Messine, F., Nogarede, B. and Lagouanelle, J.L., Optimal Design of Electromechanical Actuators: A New Method Based on Global Optimization. IEEE T. Magn. 34 (1998) 299–307. CrossRef
Nogarede, B., Kone, A.D. and Lajoie-Mazenc, M., Optimal Design of Permanent-Magnet Machines Using an Analytical Field Modeling. Electromotion 2 (1995) 25–34.
R.E. Moore, Interval Analysis. Prentice Hall, Inc. Englewood Cliffs, N.J. (1966).
H. Ratschek and J. Rokne, New computer methods for global optimization. ELLIS HORWOOD LIMITED Market Cross House, Cooper Street, Chichester, West Sussex, PO19 1EB, England (1988).
P. Van Henterbryck, L. Michel and Y. Deville, Numerica: a Modelling Language for Global Optimization. MIT Press, Cambridge Mass (1997).