Deterministic global optimization using interval constraint propagation techniques

Frederic Messine

RAIRO - Operations Research (2010)

  • Volume: 38, Issue: 4, page 277-293
  • ISSN: 0399-0559

Abstract

top
The purpose of this article is to show the great interest of the use of propagation (or pruning) techniques, inside classical interval Branch-and-Bound algorithms. Therefore, a propagation technique based on the construction of the calculus tree is entirely explained and some properties are presented without the need of any formalism (excepted interval analysis). This approach is then validated on a real example: the optimal design of an electrical rotating machine.

How to cite

top

Messine, Frederic. "Deterministic global optimization using interval constraint propagation techniques." RAIRO - Operations Research 38.4 (2010): 277-293. <http://eudml.org/doc/105315>.

@article{Messine2010,
abstract = { The purpose of this article is to show the great interest of the use of propagation (or pruning) techniques, inside classical interval Branch-and-Bound algorithms. Therefore, a propagation technique based on the construction of the calculus tree is entirely explained and some properties are presented without the need of any formalism (excepted interval analysis). This approach is then validated on a real example: the optimal design of an electrical rotating machine. },
author = {Messine, Frederic},
journal = {RAIRO - Operations Research},
keywords = {Interval analysis; Branch-and-Bound; global optimization; pruning/propagation techniques.; branch-and-bound; global optimization; pruning},
language = {eng},
month = {3},
number = {4},
pages = {277-293},
publisher = {EDP Sciences},
title = {Deterministic global optimization using interval constraint propagation techniques},
url = {http://eudml.org/doc/105315},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Messine, Frederic
TI - Deterministic global optimization using interval constraint propagation techniques
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 4
SP - 277
EP - 293
AB - The purpose of this article is to show the great interest of the use of propagation (or pruning) techniques, inside classical interval Branch-and-Bound algorithms. Therefore, a propagation technique based on the construction of the calculus tree is entirely explained and some properties are presented without the need of any formalism (excepted interval analysis). This approach is then validated on a real example: the optimal design of an electrical rotating machine.
LA - eng
KW - Interval analysis; Branch-and-Bound; global optimization; pruning/propagation techniques.; branch-and-bound; global optimization; pruning
UR - http://eudml.org/doc/105315
ER -

References

top
  1. E. Fitan, F. Messine and B. Nogarede, The Electromagnetical Acuator Design Problem: A General and Rational Approach. IEEE T. Magn.40 (2004).  
  2. E. Hansen, Global Optimization Using Interval Analysis. Marcel Dekker, Inc. 270 Madison Avenue, New York 10016 (1992).  
  3. 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).  
  4. L. Granvilliers, On the Combination of Interval Computating Solvers. Reliab. Comput.7 (2001) 467–483.  
  5. L. Granvilliers and F. Benhamou, Progress in the Solving of a Circuit Design Problem. J. Global Optim.20 (2001) 155–168.  
  6. L. Jaulin, Interval Constraint Propagation with Application to Bounded-Error Estimation. Automatica36 (2000) 1547–1562.  
  7. R.B. Kearfott, Rigorous Global Search: Continuous Problems. Kluwer Academic Publishers, Dordrecht, Boston, London (1996).  
  8. O. Lhomme, A. Gotlieb and M. Ruher, Dynamic Optimization of Interval Narrowing Algorithms. J. Logic Program.37 (1998).  
  9. 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).  
  10. F. Messine, Extension of Affine Arithmetic: Application to Global Optimization. J. Universal Comput. Sci.8 (2002) 992–1015.  
  11. F. Messine and J.L. Lagouanelle, Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization. J. Univ. Comput. Sci.4 (1998) 589–603.  
  12. 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  
  13. 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.  
  14. 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.  
  15. F. Messine, B. Nogarede and J.L. Lagouanelle, Optimal Design of Electromechanical Actuators: A New Method Based on Global Optimization. IEEE T. Magn.34 (1998) 299–307.  
  16. B. Nogarede, A.D. Kone and M. Lajoie-Mazenc, Optimal Design of Permanent-Magnet Machines Using an Analytical Field Modeling. Electromotion2 (1995) 25–34.  
  17. R.E. Moore, Interval Analysis. Prentice Hall, Inc. Englewood Cliffs, N.J. (1966).  
  18. 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).  
  19. P. Van Henterbryck, L. Michel and Y. Deville, Numerica: a Modelling Language for Global Optimization. MIT Press, Cambridge Mass (1997).  

NotesEmbed ?

top

You must be logged in to post comments.