Abstract
Complete extensions of standard deterministic Branch-and-Bound algorithms based on interval analysis are presented hereafter in order to solve design problems which can be formulated as non-homogeneous mixed-constrained global optimization problems. This involves the consideration of variables of different kinds: real, integer, logical or categorical. In order to solve interesting design problems with an important number of variables, some accelerating procedures must be introduced in these extended algorithms. They are based on constraint propagation techniques and are explained in this chapter. In order to validate the designing methodology, rotating machines with permanent magnets are considered. The corresponding analytical model is recalled and some global optimal design solutions are presented and discussed.
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
Fitan, E., Messine, F., and Nogarede, B. (2003). A general analytical model of electrical permanent magnet machine dedicated to optimal design. COMPEL—International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 22(4):1037–1050.
Fitan, E., Messine, F., and Nogarede, B. (2004). The electromagnetical actuators design problem: A general and rational approach. IEEE Transaction on Magnetics, 40(3):1579–1590.
Hansen, E. (1992). Global Optimization using Interval Analysis. Marcel Dekker, Inc., 270 Madison Avenue, New York 100016, USA.
Kearfott, R.B. (1996). Rigorous Global Search: Continuous Problems. Kluwer Academic Publishers, Drodrecht, Boston, London.
Kone, A.D., Nogarede, B., and Lajoie-Mazenc, M. (1993). Le dimensionnement des actionneurs électriques: un problème de programmation non-linéaire. Journal de Physique, III:285–301.
Messine, F. (1997). Méthodes d'optimisation global basées sur l'analyse d'intervalles pour la résolution de problèmes avec contraintes. Ph.D. Thesis, Institut National de Polytechnique de Toulouse, France.
Messine, F. (2004). Deterministic global optimization using interval constraint propagation techniques. RAIRO Operations Research, 38(4):277–294.
Messine, F., Monturet, V., and Nogarede, B. (2001). An interval branch and bound method dedicated to the optimal design of piezoelectric actuators. In: N. Mastorakis, V. Mladenov, B. Suter, and L.J. Wang (eds.), Advances in Scientific Computing, Computational Intelligence, and Applications, pp. 174–180. Mathematics and Computers in Science and Engineering.
Messine, F., Nogarede, B., and Lagouanelle, J.L. (1998). Optimal design of electromechanical actuators: a new method based on global optimization. IEEE Transaction on Magnetics, 34(1):299–307.
Moore, R.E. (1966). Interval Analysis. Prentice Hall, Englewood Cliffs, NJ.
Neittaanmäki, P., Rudnicki, M., and Savini, A. (1996). Inverse Problems and Optimal Design in Electricity and Magnetism. Clarendon Press, Oxford.
Nogarede, B. (2001). Machines tournantes: principles et constitutions. Techniques de l'Ingénieur, D3410 and D3411, France.
Nogarede, B., Kone, A.D., and Lajoie-Mazenc, M. (1995). Optimal design of permanent-magnet machines using analytical field modeling. Electromotion, 2(1):25–34.
Ratschek, H. and Rokne, J. (1988). New Computer Methods for Global Optimization. Ellis Horwood Limited Market Cross House, England.
Van Henterbryck, P., Michel, L., and Deville, Y. (1997). Numerica: A Modelling Language for Global Optimization. MIT Press, Cambridge Mass.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Messine, F. (2005). A Deterministic Global Optimization Algorithm for Design Problems. In: Audet, C., Hansen, P., Savard, G. (eds) Essays and Surveys in Global Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-387-25570-2_10
Download citation
DOI: https://doi.org/10.1007/0-387-25570-2_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25569-9
Online ISBN: 978-0-387-25570-5
eBook Packages: Business and EconomicsBusiness and Management (R0)