C. , R. Du, and C. De, 79 3. 1 INTRODUCTION, p.80

]. A. Bibliographieabde81, J. Abdel-razek, M. Coulomb, J. Feliachi, and . Sabonnadiere, The calculation of electromagnetic torque in saturated electric machines within combined numerical and analytical solutions of the field equations, IEEE Transactions on Magnetics, vol.17, issue.6, pp.3250-3252, 1981.

]. Y. Amae01 and . Amara, Contribution à la conception et à la commande des machines synchrones à double excitation, Thèse de Doctorat, 2001.

Y. Amara and G. Barakat, Analytical Modeling of Magnetic Field in Surface Mounted Permanent-Magnet Tubular Linear Machines, IEEE Transactions on Magnetics, vol.46, issue.11, pp.3870-3884, 2010.
DOI : 10.1109/TMAG.2010.2053850

C. Audet, J. Denni, D. Moore, A. Booker, and P. Frank, A surrogate-model-based method for constrained optimization, 8th Symposium on Multidisciplinary Analysis and Optimization, 2000.
DOI : 10.2514/6.2000-4891

]. M. Ayd01, S. Aydin, T. A. Huang, and . Lipo, Design and 3D electromagnetic field analysis of non-slotted and slotted TORUS type axial flux surface mounted permanent magnet disc machines, IEEE International on Electric Machines and Drives Conference IEMDC, pp.645-651, 2001.

M. Aydin, J. Yao, E. Kayikci, S. Huang, and T. A. Lipo, Design Considerations and Experimental Results of an Axial Flux PM Motor With Field Control, Research Report, vol.23, 2004.

J. Azzouzi, Contribution à la modélisation et à l'optimisation des machines synchrones à aimants permanents à flux axial. Application au cas de l'aérogénérateur, Thèse de Doctorat, 2007.

]. M. Bakr00, J. W. Bakr, M. A. Bandler, J. E. Ismail, Q. Rayas-sanchez et al., Neural space-mapping optimization for EM-based design, IEEE Transactions on Microwave Theory and Techniques, vol.48, issue.12, pp.2307-2315, 2000.
DOI : 10.1109/22.898979

J. W. Bandler, Q. Cheng, D. H. Gebre-mariam, K. Madsen, F. Pedersen et al., EM-based surrogate modeling and design exploiting implicit, frequency and output space mappings, IEEE MTT-S International Microwave Symposium Digest, 2003, pp.1003-1006, 2003.
DOI : 10.1109/MWSYM.2003.1212538

. Sondergaard, Space mapping: the state of the art, IEEE Transactions on Microwave Theory and Techniques, vol.52, issue.1, pp.337-361, 2004.

J. W. Bandler, R. Biernacki, P. A. Shao-hua-chen, R. H. Grobelny, and . Hemmers, Space mapping technique for electromagnetic optimization, IEEE Transactions on Microwave Theory and Techniques, vol.42, issue.12, pp.2536-2544, 1994.
DOI : 10.1109/22.339794

]. O. Barr03 and . Barre, Contribution à l'étude des formulations de calcul de la force magnétique en magnétostatique, approche numérique et validation expérimentale, Thèse de Doctorat, 2003.

A. Basudhar, C. Dribusch, S. Lacaze, and S. Missoum, Constrained efficient global optimization with support vector machines, Structural and Multidisciplinary Optimization, vol.129, issue.4, pp.201-221, 2012.
DOI : 10.1007/s00158-011-0745-5

]. B. Baxt93 and . Baxter, The Interpolation Theory of Radial Basis Functions, Thèse de Doctorat, Trinity College, 1993.

]. B. Belh00 and . Habib, Méthodologie pour le Développement de Plates Formes Intégrées dédiées à la Conception en Génie Electrique, Thèse de Doctorat, 2000.

]. A. Bell10, Y. Bellara, G. Amara, P. Barakat, and . Reghem, Analytical modelling of the magnetic field in axial flux permanent magnet machines with semi-closed slots at no load, XIX Electrical Machines International Conference (ICEM), pp.1-6, 2010.

]. A. Bena08, S. Benabou, S. Georges, and . Clénet, Permanent magnet modelling for dynamic applications, Journal of Magnetism and Magnetic Materials, vol.320, issue.6, pp.830-835, 2008.

]. R. Bena12 and . Ayed, Eco-conception d'une chaine de traction ferroviaire, Thèse de Doctorat, 2012.

]. A. Berb12, R. Berbecea, F. Ben-ayed, S. Gillon, P. Brisset et al., Comparison of Efficient Global Optimization and Output Space Mapping on the Biobjective Optimization of a Safety Isolating Transformer, IEEE Transactions on Magnetics, vol.48, issue.2, pp.791-794, 2012.

]. J. Bere10 and . Beretta, Motorisation hybride thermique-électrique Techniques de l'ingénieur Groupes motopropulseurs (GMP) automobiles : contrôles et hybridation, base documentaire : TIB169DUO, no. ref. article : bm2760, 2010.

]. A. Bett10 and . Bettayeb, Pertes à haute fréquence dans les rotors des machines synchrones à aimants alimentées par onduleur de tension, Thèse de Doctorat, Ecole Supérieure d'Electricité (SUPELEC), 2010.

]. F. Bloc99 and . Bloch, Source de Champ Intense 4 Tesla à Aimants Permanents, 1999.

E. Bommé, Modélisation et Optimisation des Machines Electriques Discoïdes à Double Entrefer

]. M. Bouk07 and . Boukadoum, Réseaux de neurones à base radiale Boulter and I. McCrae, ARTEMIS: Assessment and reliability of transport emission models and inventory systems ? Final Report, 2007.

]. N. Boul84 and . Boules, Two-Dimensional Field Analysis of Cylindrical Machines with Permanent Magnet Excitation, IEEE Transactions on Industry Applications, vol.20, issue.5, pp.1267-1277, 1984.

]. N. Boul85 and . Boules, Prediction of No-Load Flux Density Distribution in Permanent Magnet Machines, IEEE Transactions on Industry Applications, issue.3, pp.633-643, 1985.

]. N. Boul90 and . Boules, Design optimization of permanent magnet DC motors, IEEE Transactions on Industry Applications, vol.26, issue.4, pp.786-792, 1990.

]. T. Busc96, J. D. Busch, T. A. Law, and . Lipo, Magnetic circuit modeling of the field regulated reluctance machine. Part II: saturation modeling and results, IEEE Transactions on Energy Conversion, vol.11, issue.1, pp.56-61, 1996.

]. M. Cald01 and . Costa, Optimisation de Dispositifs Electromagnétiques dans un contexe d'Analyse par la méthode des Eléments Finis, Thèse de Doctorat, 2001.

C. J. Carpenter, Magnetic equivalent circuits, Proceedings of the Institution of, pp.1503-1511, 1968.
DOI : 10.1049/piee.1968.0265

]. F. Casa94 and . Casanellas, Losses in PWM inverters using IGBTs Electric Power Applications, IEE Proceedings, vol.141, issue.5, pp.235-239, 1994.

]. C. Chan02 and . Chan, The state of the art of electric and hybrid vehicles, Proceedings of the IEEE, pp.247-275, 2002.
DOI : 10.1109/5.989873

]. B. Chao94, S. X. Chao, Z. J. Chen, T. Liu, and . Low, Electromagnetic field analysis in rotational electric machines using finite element-analytical hybrid method, IEEE Transactions on Magnetics, vol.30, issue.6, pp.4314-4316, 1994.
DOI : 10.1109/20.334072

]. E. Cher49 and . Cherry, The Duality between Interlinked Electric and Magnetic Circuits and the Formation of Transformer Equivalent Circuits, Proceedings of the Physical Society, 1949.
DOI : 10.1088/0370-1301/62/2/303

]. Choi01, D. Choi, I. Kim, S. Park, and . Hahn, A new design technique of magnetic systems using space mapping algorithm, IEEE Transactions on Magnetics, vol.37, issue.5, pp.3627-3630, 2001.

J. Clément, Optimisation multidisciplinaire : étude théorique et application à la conception des avions en phase d'avant-projet, Thèse de Doctorat, 2009.

]. Y. Coll02, P. Collette, and . Siarry, Optimisation multiobjectif, 2002.

M. A. Copeland and G. R. Slemon, An Analysis of the Hysteresis Motor I - Analysis of the Idealized Machine, IEEE Transactions on Power Apparatus and Systems, vol.82, issue.65, pp.34-42, 1963.
DOI : 10.1109/TPAS.1963.291395

]. Coul03, A. Coulomb, M. C. Kobetski, Y. Costa, U. Maréchal et al., Comparison of radial basis function approximation techniques, COMPEL:The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol.22, issue.3, pp.616-629, 2003.

]. A. Daan06 and . Daanoune, Contribution à l'Etude et à l'Optimisation d'une Machine Synchrone à Double Excitation pour Véhicules Hybrides, Thèse de Doctorat, 2006.

]. B. Dagu12 and . Dagusé, Optimisation de systèmes d'entraînement, Thèse de Doctorat, 2012.

]. K. Deb02, A. Deb, S. Pratap, T. Agarwal, and . Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, vol.6, issue.2, pp.182-197, 2002.
DOI : 10.1109/4235.996017

E. De-cecco, Contribution au développement d'un outil logiciel d'aide à la conception de systèmes électromagnétiques. Application aux machines synchrones à aimants permanents, Thèse de Doctorat, 2005.

A. Delale, L. Albert, L. Gerbaud, and F. Wurtz, Automatic Generation of Sizing Models for the Optimization of Electromagnetic Devices Using Reluctance Networks, IEEE Transactions on Magnetics, vol.40, issue.2, pp.830-833, 2004.
DOI : 10.1109/TMAG.2004.824908

]. C. Delf95, B. Delforge, and . Lemaire, Induction machine modeling using finite element and permeance network methods, IEEE Transactions on Magnetics, vol.31, issue.3, pp.2092-2095, 1995.

]. R. Deod97, S. Deodhar, I. Andersson, T. J. Boldea, and . Miller, The flux-reversal machine: a new brushless doubly-salient permanent-magnet machine, IEEE Transactions on Industry Applications, vol.33, issue.4, pp.925-934, 1997.

H. W. Derbas, J. M. Williams, A. C. Koenig, and S. D. Pekarek, A Comparison of Nodal- and Mesh-Based Magnetic Equivalent Circuit Models, IEEE Transactions on Energy Conversion, vol.24, issue.2, pp.388-396, 2009.
DOI : 10.1109/TEC.2008.2002037

]. A. Diger05, G. M. Di-gerlando, R. Foglia, M. Perini, and . Ubaldini, Design and operation aspects of field regulated PM synchronous machines with concentrated armature windings, IEEE International Conference on Electric Machines and Drives, pp.1165-1172, 2005.

]. T. Do10 and . Do, Simulation dynamique des actionneurs et capteurs électromagnétiques par réseaux de réluctances : modèles, méthodes et outils, Thèse de Doctorat, 2010.

D. Echeverría and P. Hemker, Space Mapping and Defect Correction, Computational Methods in Applied Mathematics, vol.5, issue.2, pp.107-136, 2005.
DOI : 10.2478/cmam-2005-0006

D. Echeverría, D. Lahaye, and P. Hemker, Space Mapping and Defect Correction, Model Order Reduction: Theory, Research Aspects and Applications Schilders, H. Vorst, and J
DOI : 10.2478/cmam-2005-0006

]. L. Enci05, D. Encica, E. A. Echeverría, A. Lomonova, P. Vandenput et al., Efficient optimal design of electromagnetic actuators using space-mapping, 6th World Congress on Structural and Multidisciplinary Optimization, 2005.

]. L. Enci08, J. J. Encica, E. A. Paulides, A. J. Lomonova, and . Vandenput, Electromagnetic and Thermal Design of a Linear Actuator Using Output Polynomial Space Mapping, IEEE Transactions on Industry Applications, vol.44, issue.2, pp.534-542, 2008.

]. A. Fann03, A. Fannie, and . Montisci, A neural inverse problem approach for optimal design, IEEE Transactions on Magnetics, vol.39, issue.3, pp.1305-1308, 2003.
DOI : 10.1109/TMAG.2003.810541

]. A. Fasq07 and . Fasquelle, Contribution à la modélisation multi-physique : électro-vibro-acoustique et aérothermique de machines de traction, Thèse de Doctorat, 2007.

]. D. Fink03, DIRECT Optimization Algorithm User Guide, 2003.

]. E. Fita04, F. Fitan, B. Messine, and . Nogarede, The electromagnetic actuator design problem: a general and rational approach, IEEE Transactions on Magnetics, vol.40, issue.3, pp.1579-1590, 2004.

]. A. Fons00 and . Fonseca, Comparaison de machines à aimants permanents pour la traction de véhicules électriques et hybrides, Thèse de Doctorat, 2000.

]. J. Font07 and . Fontchastagner, Résolution du problème inverse de conception d'actionneurs électromagnétiques par association de méthodes déterministes d'optimisation globale avec des modèles analytiques et numériques, Thèse de Doctorat, 2007.

]. E. Furl97, M. A. Furlani, and . Knewtson, A three-dimensional field solution for permanent-magnet axialfield motors, IEEE Transactions on Magnetics, vol.33, issue.3, pp.2322-2325, 1997.

]. L. Gasc04 and . Gasc, Conception d'un actionneur à aimants permanents à faibles ondulations de couple pour assistance de direction automobile Approches par la structure et par la commande, Thèse de Doctorat, 2004.

H. Gholizad, M. Mirsalim, and M. Mirzayee, Dynamic Analysis of Highly Saturated Switched Reluctance Motors Using Coupled Magnetic Equivalent Circuit and the Analytical Solution, 6th International Conference on Computational Electromagnetics (CEM), pp.1-2, 2006.

]. J. Gier08, R. Gieras, M. Wang, and . Kamper, Axial Flux Permanent Magnet Brushless Machines, 2008.

]. F. Gill09 and . Gillon, Méthodologies de Conception Optimale des Composants Electromagnétiques, Habilitation à Diriger des Recherches, 2009.

]. F. Gill97 and . Gillon, Modélisation et Optimisation par Plans d'Expériences d'un moteur à commutations électriques, Thèse de Doctorat, 1997.

J. Gong, Modélisation et Conception Optimale d'un Moteur Linéaire à Induction pour Système de Traction Ferroviaire, Thèse de Doctorat, 2011.

J. Goupy, Les plans d'Expériences Revue Modulad, pp.74-116, 2006.

D. Grenier and B. Dehez, Circuit magnétique-électroaimant, 2003.

]. Q. Gu05, Q. Gu, and . Hao, Three-dimensional analytic model for permanent magnet electric machines with finite core length, Electr Eng, vol.87, issue.6, pp.305-314, 2005.

M. Hecquet, Contribution à l'Instrumentation de la Démarche de Conception des Machines Electriques, Habilitation à Diriger des Recherches, 2006.

M. Hecquet and P. Brochet, Mod??lisation d'un alternateur automobile par un r??seau de perm??ances coupl?? ?? des circuits ??lectriques, Journal de Physique III, vol.6, issue.8, pp.1099-1116, 1996.
DOI : 10.1051/jp3:1996171

]. E. Hoan95 and . Hoang, Etude, Modélisation et Mesure des Pertes Magnétiques dans les moteurs à Réluctance Variable à Double Saillance, Thèse de Doctorat, 1995.

]. S. Holm07, H. Holm, J. A. Polinder, and . Ferreira, Analytical Modeling of a Permanent-Magnet Synchronous Machine in a Flywheel, IEEE Transactions on Magnetics, vol.43, issue.5, pp.1955-1967, 2007.
DOI : 10.1109/TMAG.2007.892791

]. V. Hons87 and . Honsinger, Sizing Equations for Electrical Machinery, IEEE Transactions on Energy Conversion, issue.2 1, pp.116-121, 1987.

]. W. Hua05, Z. Q. Hua, M. Zhu, Y. Cheng, D. Pang et al., Comparison of flux-switching and doublysalient permanent magnet brushless machines, Proceedings of the Eighth International Conference on Electrical Machines and Systems, ICEMS, pp.165-170, 2005.

]. S. Huan96, J. Huang, F. Luo, T. A. Leonardi, and . Lipo, A general approach to sizing and power density equations for comparison of electrical machines, Conference Record of the 1996 IEEE the Industry Applications Conference. Thirty-First IAS Annual Meeting, IAS '96, pp.836-842, 1996.

]. S. Huan99, J. Huang, F. Luo, T. A. Leonardi, and . Lipo, A comparison of power density for axial flux machines based on general purpose sizing equations, IEEE Transactions on Energy Conversion, vol.14, issue.2, pp.185-192, 1999.

]. G. Jeha10 and . Jehan, Problématique de la recharge des véhicules rechargeables (VE-VHR), 2010.

]. D. Jone98, M. Jones, W. I. Schonlau, and . Welch, Efficient Global Optimization of Expensive Black-Box Functions, Journal of Global Optimization, pp.455-492, 1998.

]. H. Juss08, P. Jussila, A. Salminen, J. Parviainen, J. Nerg et al., Concentrated winding axial flux permanent magnet motor with plastic bonded magnets and sintered segmented magnets, 18th International Conference on Electrical Machines, ICEM, pp.1-5, 2008.

]. H. Juss09 and . Jussila, Concentrated Winding Multiphase Permanent Magnet Machine Design and Electromagnetic Properties-Case Axial Flux Machine, Thèse de Doctorat, 2009.

Y. Kano, T. Kosaka, and N. Matsui, Simple Nonlinear Magnetic Analysis for Permanent-Magnet Motors, IEEE Transactions on Industry Applications, vol.41, issue.5, pp.1205-1214, 2005.
DOI : 10.1109/TIA.2005.853376

]. B. Kou05, L. Kou, S. Li, F. Cheng, and . Meng, Operating control of efficiently generating induction motor for driving hybrid electric vehicle, IEEE Transactions on Magnetics, vol.41, issue.1, pp.488-491, 2005.

]. S. Kozi07, J. W. Koziel, and . Bandler, Microwave Device Modeling Using Space-Mapping and Radial Basis Functions, S International Microwave Symposium, pp.799-802, 2007.

]. S. Kozi08, J. W. Koziel, and . Bandler, Support-vector-regression-based output space-mapping for microwave device modeling, IEEE MTT-S International Microwave Symposium Digest, pp.615-618, 2008.

]. S. Kozi09, J. W. Koziel, K. Bandler, and . Madsen, Space Mapping With Adaptive Response Correction for Microwave Design Optimization, IEEE Transactions on Microwave Theory and Techniques, vol.57, issue.2, pp.478-486, 2009.

]. S. Kozi11, L. Koziel, and . Leifsson, Low-cost parameter extraction and surrogate optimization for space mapping design using EM-based coarse models, Progress In Electromagnetics Research B, vol.31, pp.117-137, 2011.

]. S. Kozie10, S. Koziel, M. H. Ogurtov, and . Bakr, Variable-fidelity design optimization of microwave devices using multi-dimensional cauchy approximation and coarsely discretized electromagnetic models, Progress In Electromagnetics Research B, vol.21, pp.1-26, 2010.

G. Krebs, E. De-cecco, and C. Marchand, Design approach of an axial flux motor for electrical powertrain vehicle, 2012 XXth International Conference on Electrical Machines, pp.2812-2817, 2012.
DOI : 10.1109/ICElMach.2012.6350285
URL : https://hal.archives-ouvertes.fr/hal-00779585

]. S. Kreua08 and . Kreuawan, Modelling and optimal design in railway applications, Thèse de Doctorat, 2008.

]. A. Krin12, S. Krings, A. Nategh, H. Stening, O. Grop et al., Measurement and modeling of iron losses in electrical machines, 5th International Conference Magnetism and Metallurgy WMM'12, pp.2012-101

]. I. Kroo04 and . Kroo, Distributed Multidisciplinary Design and Collaborative Optimization VKI lecture series on Optimization Methods & Tools for Multicriteria/Multidisciplinary Design, 2004.

]. E. Lait65 and . Laithwaite, Electromagnetic levitation, Proceedings of the Institution of Electrical Engineers, vol.112, issue.12, pp.2361-2375, 1965.

]. J. Law96, T. J. Law, T. A. Busch, and . Lipo, Magnetic circuit modelling of the field regulated reluctance machine. Part I: model development, IEEE Transactions on Energy Conversion, vol.11, issue.1, pp.49-55, 1996.
DOI : 10.1109/60.486575

J. , L. Besnerais, V. Lanfranchi, M. Hecquet, and P. Brochet, Multiobjective Optimization of Induction Machines Including Mixed Variables and Noise Minimization, IEEE Transactions on Magnetics, vol.44, issue.6, pp.1102-1105, 2008.

]. V. Leco00 and . Leconte, Simulation des convertisseurs électromécaniques, Thèse de Doctorat, 2000.

]. L. Li11 and . Li, Etude et Mise au Point d'une Nouvelle Famille d'Alterno-Démarreurs pour Véhicules Hybrides et Electriques, Thèse de Doctorat, 2011.

]. F. Lian94, Y. Liang, T. A. Liao, and . Lipo, Shunteur pour moteur a pole doublement saillant avec aimants permanents de stator, p.54554731995

]. C. Liu09, S. C. Liu, and . Lee, Magnetic field modeling and optimal operational control of a single-side axial-flux permanent magnet motor with center poles, Journal of Magnetism and Magnetic Materials, vol.304, issue.1, pp.454-456, 2009.

H. C. Lovatt and P. A. Watterson, Energy stored in permanent magnets, IEEE Transactions on Magnetics, vol.35, issue.1, pp.505-507, 1999.
DOI : 10.1109/20.737473

]. J. Luo98, D. Luo, T. A. Qin, S. Lipo, S. Li et al., Axial flux circumferential current permanent magnet (AFCC) machine, IAS Annual Meeting Industry Applications Conference, pp.144-151, 1998.

]. A. Mahm12, N. A. Mahmoudi, H. W. Rahim, and . Ping, Axial-flux permanent-magnet motor design for electric vehicle direct drive using sizing equation and finite element analysis, Progress In Electromagnetics Research, vol.122, pp.467-496, 2012.

D. Maquin, Eléments de Théorie des Graphes, Institut Polytechnique de Lorraine, 2003.

F. Messine, B. Nogarede, and J. Lagouanelle, Optimal design of electromechanical actuators: a new method based on global optimization, IEEE Transactions on Magnetics, vol.34, issue.1, pp.299-308, 1998.
DOI : 10.1109/20.650361

V. Mester, Conception Optimale Systémique des Composants des Chaînes de traction Electrique
DOI : 10.3166/rige.11.695-715

]. D. Mili86, M. Milimonfared, J. F. Parchemin, R. Rialland, and . Bennefille, Echauffements et pertes rotoriques d'un moteur synchrone autopiloté, pp.585-593, 1986.

T. Miura, S. Chino, M. Takemoto, S. Ogasawara, A. Chiba et al., A ferrite permanent magnet axial gap motor with segmented rotor structure for the next generation hybrid vehicle, The XIX International Conference on Electrical Machines, ICEM 2010, pp.1-6, 2010.
DOI : 10.1109/ICELMACH.2010.5607864

M. Molga and C. Smutnicki, Test functions for optimization needs, 2005.

]. O. Moue10 and . Mouelhi, Contribution à l'optimisation multiobjectif en conception multidisciplinaire, Thèse de Doctorat, Institut National des Sciences Appliquées de Lyon, 2010.

]. B. Mult01 and . Multon, Motorisation des véhicules électriques, 2001.

]. B. Nedj12 and . Nedjar, Modélisation basée sur la méthode des réseaux de perméances en vue de l'optimisation de machines synchrones à simple et à double excitation, Thèse de Doctorat, 2012.

P. H. Nguyen, Impacts des modèles de pertes sur l'optimisation sur cycle d'un ensemble convertisseur ? machine synchrone, Thèse de Doctorat, 2011.

]. J. Noce06, S. J. Nocedal, M. J. Wright, and . Orr, Numerical Optimization Introduction to Radial Basis Function Networks, 1996.

]. V. Osto89 and . Ostovic, A novel method for evaluation of transient states in saturated electric machines, IEEE Transactions on Industry Applications, vol.25, issue.1, pp.96-100, 1989.

]. J. Peir05, S. Peiro, and . Sherwin, Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations, Materials Modeling, pp.1-32, 2005.
DOI : 10.1007/978-1-4020-3286-8_127

]. D. Petr07 and . Petrichenko, Contribution à la modélisation et à la conception optimale des turbo-alternateurs de faible puissance, Thèse de Doctorat, 2007.

]. H. Poli99, M. J. Polinder, and . Hoeijmakers, Eddy-current losses in the segmented surface-mounted magnets of a PM machine, IEE Proceedings Electric Power Applications, pp.261-266, 1999.

J. Pouget, Conception Robuste des Machines Asynchrones pour la Traction Ferroviaire, Thèse de Doctorat, 2009.

]. F. Prof97, Z. Profumo, A. Zhang, and . Tenconi, Axial flux machines drives: a new viable solution for electric cars, IEEE Transactions on Industrial Electronics, vol.44, issue.1, pp.39-45, 1997.

T. Raminosoa, Optimisation des performances des machines synchro-réluctantes par réseaux de pérmeances, Thèse de Doctorat, Institut National Polytechnique de Lorraine, 2006.

]. Z. Ran12, O. Ran, Q. Drouichie, and . Fu, Modélisation et simulation d'un moteur roue et d'une génératrice éolienne, 2012.

J. Regnier, Conception de systèmes hétérogènes en Génie Électrique par optimisation évolutionnaire multicritère, Thèse de Doctorat, 2003.

T. Ruimin and W. Erzhi, A new boundary element method for calculating the magnetic field of permanent magnetic machine, ICEMS'2001. Proceedings of the Fifth International Conference on Electrical Machines and Systems (IEEE Cat. No.01EX501), pp.1181-1183, 2001.
DOI : 10.1109/ICEMS.2001.971891

]. J. Sack89, W. J. Sacks, T. J. Welch, H. P. Mitchell, and . Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-423, 1989.

]. B. Sare00, L. Sareni, A. Krahenbuhl, and . Nicolas, Efficient genetic algorithms for solving hard constrained optimization problems, IEEE Transactions on Magnetics, vol.36, issue.4, pp.1027-1030, 2000.

]. M. Sase02, P. Sasena, P. Papalambros, and . Goovaerts, Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization, pp.263-278, 2002.

M. Schonlau, Computer Experiments and Global Optimization, Thèse de Doctorat, 1997.

]. S. Shan04, G. G. Shan, and . Wang, An Efficient Pareto Set Identification Approach for Multiobjective Optimization on Black-Box Functions, Journal of Mechanical Design, vol.127, issue.5, pp.866-874, 2004.
DOI : 10.1115/1.1904639

H. Shaogang, X. Yonghong, and Q. Shancai, Calculation of the third harmonic excitation of synchronous generator using tooth flux method, International Conference on Electrical Machines and Systems, ICEMS, pp.1206-1209, 2007.

]. K. Shim03, K. Shima, M. Ide, K. Takahashi, and . Oka, Steady-state magnetic circuit analysis of salient-pole synchronous machines considering cross-magnetization, IEMDC 2001. IEEE International Electric Machines and Drives Conference (Cat. No.01EX485), pp.213-218, 2003.
DOI : 10.1109/IEMDC.2001.939419

T. Simpson, J. Poplinski, P. N. Koch, and J. Allen, Metamodels for Computer-based Engineering Design: Survey and recommendations, Engineering with Computers, vol.17, issue.2, pp.129-150, 2001.
DOI : 10.1007/PL00007198

]. N. Srin94, K. Srinivas, and . Deb, Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms, Evolutionary Computation, vol.2, issue.3, 1994.

]. A. Tako08 and . Takorabet, Dimensionnement d'une machine à double excitation de structure innovante pour une application alternateur automobile. Comparaison à des structures classiques, Thèse de Doctorat, 2008.

M. Tanaka, H. Watanabe, Y. Furukawa, and T. Tanino, GA-based decision support system for multicriteria optimization, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, pp.1556-1561, 1995.
DOI : 10.1109/ICSMC.1995.537993

]. J. Tapi03, M. Tapia, S. Aydin, T. A. Huang, and . Lipo, Sizing equation analysis for field controlled PM machines: a unified approach, IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03., 2003.
DOI : 10.1109/IEMDC.2003.1210374

]. H. Tieg13, Y. Tiegna, G. Amara, and . Barakat, Overview of analytical models of permanent magnet electrical machines for analysis and design purposes, Mathematics and Computers in Simulation, vol.90, issue.0, pp.162-177, 2013.

]. T. Tran07, S. Tran, P. Brisset, and . Brochet, Combinatorial and multi-level optimizations of a safety isolating transformer, International Journal of Applied Electromagnetics and Mechanics, vol.26, pp.3-4, 2007.

]. T. Tran09 and . Tran, Problèmes Combinatoires et Modèles Multi-Niveaux pour la Conception Optimale des Machines Électriques, Thèse de Doctorat, 2009.

D. Van-veldhuizen, Multiobjective Evolutionary Algorithms: Classifications, Analyses and New Innovations, Thèse de Doctorat, Faculty of the Graduate School of Engineering of Air Force Institute of Technology, 1999.

]. S. Vivi02 and . Vivier, Stratégies d'optimisation par la méthode des plans d'expériences et Application aux dispositifs électrotechniques modélisés par éléments finis, Thèse de Doctorat, 2002.

]. S. Vivi11, D. Vivier, G. Lemoine, and . Friedrich, Fast optimization of an IPMSM with Space Mapping technique, " presented at the Energy Conversion Congress and Exposition (ECCE), pp.3679-3686, 2011.

D. Whitley, A genetic algorithm tutorial, Statistics and Computing, vol.4, issue.2, pp.65-85, 1994.
DOI : 10.1007/BF00175354

]. S. Willi82, A. C. Williamson, and . Smith, Steady-state analysis of 3-phase cage motors with rotor-bar and end-ring faults Electric Power Applications, IEE Proceedings B, vol.129, issue.3, p.93, 1982.

]. L. Wu11, Z. Q. Wu, D. Zhu, M. Staton, D. Popescu et al., An Improved Subdomain Model for Predicting Magnetic Field of Surface-Mounted Permanent Magnet Machines Accounting for Tooth- Tips, IEEE Transactions on Magnetics, vol.47, issue.6, pp.1693-1704, 2011.

]. F. Wurt08 and . Wurtz, Conceptions de la conception pour le génie électrique, Habilitation à Diriger des Recherches, 2008.

F. Wurtz, Une nouvelle approche pour la conception sous contraintes de machines électriques

]. S. Xiao13, M. Xiao, J. K. Rotaru, and . Sykulski, Adaptive Weighted Expected Improvement With Rewards Approach in Kriging Assisted Electromagnetic Design, IEEE Transactions on Magnetics, vol.49, issue.5, pp.2057-2060, 2013.
DOI : 10.1109/TMAG.2013.2240662

]. Z. Yuej11, J. Yuejin, L. Libing, T. Chunjiang, J. Guanzhen et al., Semi-analytical method for airgap main magnetic field computation of direct drive permanent magnet torque motors, International Conference on Electrical Machines and Systems (ICEMS), pp.1-4, 2011.

]. M. Zera06, M. E. Zeraoulia, D. Benbouzid, and . Diallo, Electric Motor Drive Selection Issues for HEV Propulsion Systems: A Comparative Study, IEEE Transactions on Vehicular Technology, vol.55, issue.6, pp.1756-1764, 2006.

]. Y. Zhil98 and . Zhilichev, Three-dimensional analytic model of permanent magnet axial flux machine, IEEE Transactions on Magnetics, vol.34, issue.6, pp.3897-3901, 1998.

]. Z. Zhu96, D. Zhu, and . Howe, Electrical Machines and Drives for Electric, Hybrid, and Fuel Cell Vehicles, Proceedings of the IEEE, pp.746-765, 2007.
DOI : 10.1109/JPROC.2006.892482

M. Hage-hassan, G. Remy, G. Krebs, and C. Marchand, Radial output space mapping for electromechanical systems design, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.33, issue.3
DOI : 10.1108/COMPEL-05-2013-0192
URL : https://hal.archives-ouvertes.fr/hal-00779592

M. Hage-hassan, G. Remy, G. Krebs, and C. Marchand, Radial output space mapping for electromechanical systems design, 12th International Workshop on Optimization and Inverse Problems in Electromagnetism (OIPE), pp.22-23, 2012.
DOI : 10.1108/COMPEL-05-2013-0192
URL : https://hal.archives-ouvertes.fr/hal-00779592

M. Hage-hassan, G. Krebs, and C. Marchand, A simplified time stepping nonlinear mesh based reluctance network for machine design, 2013 International Electric Machines & Drives Conference, pp.12-15879, 2013.
DOI : 10.1109/IEMDC.2013.6556201
URL : https://hal.archives-ouvertes.fr/hal-00932659

M. Hage-hassan, G. Krebs, G. Remy, and C. Marchand, Embedded multilevel optimization for time-stepping mesh-based reluctance network, Conference on the Computation of Electromagnetic Fields (COPUMAG), pp.30-34

M. Hage-hassan, G. Krebs, G. Remy, and C. Marchand, Multi-objective optimization of an Axial-Flux PM Actuator with space mapping technique, 9th IET International Conference on Computation in Electromagnetics (CEM 2014)
DOI : 10.1049/cp.2014.0227
URL : https://hal.archives-ouvertes.fr/hal-01103669

M. Hage and H. , Modélisation et optimisation de machines à flux axial, Saint-Nazaire, FR, pp.5-6, 2013.