Deterministic global optimization using interval constraint propagation techniques

Frederic Messine

RAIRO - Operations Research - Recherche Opérationnelle (2004)

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

Abstract

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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

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Messine, Frederic. "Deterministic global optimization using interval constraint propagation techniques." RAIRO - Operations Research - Recherche Opérationnelle 38.4 (2004): 277-293. <http://eudml.org/doc/245268>.

@article{Messine2004,
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 - Recherche Opérationnelle},
keywords = {interval analysis; branch-and-bound; global optimization; pruning/propagation techniques; Interval analysis; pruning},
language = {eng},
number = {4},
pages = {277-293},
publisher = {EDP-Sciences},
title = {Deterministic global optimization using interval constraint propagation techniques},
url = {http://eudml.org/doc/245268},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Messine, Frederic
TI - Deterministic global optimization using interval constraint propagation techniques
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2004
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; Interval analysis; pruning
UR - http://eudml.org/doc/245268
ER -

References

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  2. [2] E. Hansen, Global Optimization Using Interval Analysis. Marcel Dekker, Inc. 270 Madison Avenue, New York 10016 (1992). Zbl0762.90069MR1197883
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  14. [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. [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. [16] B. Nogarede, A.D. Kone and M. Lajoie-Mazenc, Optimal Design of Permanent-Magnet Machines Using an Analytical Field Modeling. Electromotion 2 (1995) 25–34. 
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  19. [19] P. Van Henterbryck, L. Michel and Y. Deville, Numerica: a Modelling Language for Global Optimization. MIT Press, Cambridge Mass (1997). 

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