?. Output, M. M. Other, R. M. Alexandrov, and . Lewis, Comparative properties of collaborative optimization and other approaches to mdo, proceedings of the First ASMO UK/ISSMO Conference on Engineering Design Optimization, 1999.

J. T. Allison, Complex system optimization: A review of analytical target cascading , collaborative optimization, and other formulations, 2004.

J. T. Allison, D. Walsh, M. Kokkolaras, P. Y. Papalambros, and M. Cartmell, Analytical Target Cascading in Aircraft Design, 44th AIAA Aerospace Sciences Meeting and Exhibit, 2006.
DOI : 10.2514/6.2006-1325

N. E. Antoine, Aircraft optimization for minimal environment impact, 2004.

N. Bianchi, Radially-magnetised interior-permanent-magnet synchronous motor for high-speed drive: an analysis and finite-element combined design procedure, Electromotion, vol.6, pp.103-111, 1999.

A. Boglietti, A. Cavagnino, M. Lazzari, and A. Pastorelli, A simplified thermal model for variable-speed self-cooled industrial induction motor, IEEE Transactions on Industry Applications, vol.39, issue.4, pp.945-952, 2003.
DOI : 10.1109/TIA.2003.814555

. Bosch, Automotive handbook, 2004.

R. Bouchard and G. Olivier, Conception de moteurs asynchrones triphasés. Editions de l'´ ecole polytechnique de montréal, 1997.

G. E. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimeters : design, discovery, and innovation, 2005.

R. D. Braun and I. M. Kroo, Development and application of the collaborative optimization architecture in a multidisciplinary design environment, Multidisciplinary Design Optimization: State of the Art, pp.98-116, 1997.

S. Brisset, Démarches et outils pour la conception optimal des machines electriques. HabilitationáHabilitationá diriger des recherches, 2007.

S. Brisset and P. Brochet, Optimization of switched reluctance motors using deterministic methods with static and dynamic finite element simulations, IEEE Transactions on Magnetics, vol.34, issue.5, pp.2853-2856, 1998.
DOI : 10.1109/20.717664

J. Chiles and P. Delfiner, Geostatistics: Modeling Spatial Uncertainty, 1999.
DOI : 10.1002/9781118136188
URL : https://hal.archives-ouvertes.fr/hal-00795336

M. Cioffi, A. Formisano, and R. Martone, Statistical analysis in robust design of superconducting magnets, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.24, issue.2, pp.427-435, 2005.
DOI : 10.1108/03321640510586060

Y. Collette and P. Siarry, Optimisation multiobjectif, Edition Eyrolles, 2002.

R. D. Cook, Finite Element Modeling for Stress Analysis, 1994.

C. Coutel, F. Wurtz, J. Bigeon, and C. Chillet, Constrained optimisation of a linear actuator: comparison of two methods to deal with implicit parameters in the analytical model, IEEE International Electric Machines and Drives Conference. IEMDC'99. Proceedings (Cat. No.99EX272), pp.625-627, 1999.
DOI : 10.1109/IEMDC.1999.769195

E. Cramer, J. Dennis-jr, P. Frank, R. Lewis, and G. Shubin, Problem Formulation for Multidisciplinary Optimization, SIAM Journal on Optimization, vol.4, issue.4, pp.754-776, 1994.
DOI : 10.1137/0804044

F. De-toro, J. Ortega, J. Fernandez, and A. Diaz, PSFGA: a parallel genetic algorithm for multiobjective optimization, Proceedings 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing, pp.384-391, 2002.
DOI : 10.1109/EMPDP.2002.994315

K. Deb, A. Pratap, S. Agarwal, and T. 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

M. Debruyne, High power igbt traction drives. presented at the 5th, World Congress on Railway Research, 2001.

D. Derks, F. Gillon, and P. Brochet, Modelling of an axial synchronous 3 phase motor, Electromotion, vol.10, issue.4, pp.359-364, 2003.

J. Dréo, A. Pé, P. Siarry, and E. Taillard, Metaheuristics for Hard Optimization Methods and Case Studies, 2006.

P. Eustache, G. Meunier, and J. L. Coulomb, Finite element toolbox for generic coupling (magnetic, thermal, etc.), IEEE Transactions on Magnetics, vol.32, issue.3, pp.1461-1464, 1996.
DOI : 10.1109/20.497524

A. Fasquelle, D. Saury, S. Harmand, and A. Randria, Numerical study of fluid flow and heat transfer in an electrical motor, proceeding of ASME Joint U.S. ? European Fluids Engineering Summer Meeting, 2006.

J. Figueroa, L. Radaorozandry, J. Cros, and P. Viarouge, Comparative analysis of surface mount pm motor structures for a traction application, proceeding of International conference on Electrical Machine (ICEM), 2006.

F. Gillon, Modélisation et optimisation par plans d'expérience déun moteuràmoteur`moteurà commutationsélectroniquestationsélectroniques, 1997.

F. Gillon and P. Brochet, Shape optimization of a permanent magnet motor using the experimental design method, IEEE Transactions on Magnetics, vol.35, issue.3, pp.1278-1281, 1999.
DOI : 10.1109/20.767184

F. Gillon and P. Brochet, Screening and response surface method applied to the numerical optimization of electromagnetic devices, IEEE Transactions on Magnetics, vol.36, issue.4, pp.1163-1167, 2000.

A. Giunta, Aircraft multidisciplinary design optimization using design of experiments theory and response surface modeling methods, polytechnic institute and state university, 1997.

A. Giunta, S. Wojtkiewicz, and M. Eldred, Overview of Modern Design of Experiments Methods for Computational Simulations (Invited), 41st Aerospace Sciences Meeting and Exhibit, pp.2003-649, 2003.
DOI : 10.2514/6.2003-649

S. Giurgea, H. S. Zire, and A. Miraoui, Two-Stage Surrogate Model for Finite-Element-Based Optimization of Permanent-Magnet Synchronous Motor, IEEE Transactions on Magnetics, vol.43, issue.9, pp.3607-3613, 2007.
DOI : 10.1109/TMAG.2007.902348

H. Gutmann, A radial basis function method for global optimization, Journal of Global Optimization, vol.19, issue.3, pp.201-227, 2001.
DOI : 10.1023/A:1011255519438

J. R. Hendershot-jr and T. J. Miller, Design of brushless permanent-magnet motors. Magna physics publishing and Clarendon press, 1994.

J. W. Herrmann, Decomposition in product development, 2004.

S. Hiwa, T. Hiroyasu, and M. Miki, Hybrid optimization using direct, ga, and sqp for global exploration, IEEE Congress on Evolutionary Computation, pp.1709-1716, 2007.

J. H. Holland, Adaptation in natural and artificial systems, 1992.

J. Holtz, Pulsewidth modulation-a survey, IEEE Transactions on Industrial Electronics, vol.39, issue.5, pp.410-420, 1992.
DOI : 10.1109/41.161472

A. Hoppe, M. Kaufmann, and B. Lauber, Multidisciplinary optimization considering crash and nvh loadcases, proceeding of ATZ/MTZ Virtual Product Creation, 2005.

B. Husslage, G. Rennen, E. R. Dam, and D. D. Hertog, Space-filling latin hypercube designs for computer experiments. Discussion Paper 18, 2006.
DOI : 10.1007/s11081-010-9129-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.483.3850

C. H. Im, H. K. Kim, H. Jung, and K. Choi, A Novel Algorithm for Multimodal Function Optimization Based on Evolution Strategy, IEEE Transactions on Magnetics, vol.40, issue.2, pp.1224-1227, 2004.
DOI : 10.1109/TMAG.2004.824805

R. Jin, W. Chen, and T. W. Simpson, Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization, pp.1-13, 2001.

D. R. Jones, A taxonomy of global optimization methods based on response surfaces, Journal of Global Optimization, vol.21, issue.4, pp.345-383, 2001.
DOI : 10.1023/A:1012771025575

D. R. Jones, M. Schonlau, and W. J. Welch, Efficient global optimization of expensive black-box functions, Journal of Global Optimization, vol.13, issue.4, pp.455-492, 1998.
DOI : 10.1023/A:1008306431147

J. R. Kalagnanam and U. M. Diwekar, An Efficient Sampling Technique for Off-line Quality Control, Technometrics, vol.6, issue.3, pp.308-319, 1997.
DOI : 10.1080/00401706.1992.10484904

C. Kim and K. Nho, Heat sink design of high power converter, proceeding of 29th Annual IEEE Power Electronics Specialists Conference (PESC), pp.2122-2130, 1998.

H. M. Kim, N. F. Michelena, P. Y. Papalambros, and T. Jiang, Analytical Target Cascading in Automotive Vehicle Design, Journal of Mechanical Design, vol.125, issue.3, pp.481-489, 2003.
DOI : 10.1115/1.1586308

H. M. Kim, D. G. Rideout, P. Y. Papalambros, and J. L. Stein, Target Cascading in Optimal System Design, Journal of Mechanical Design, vol.125, issue.3, pp.474-480, 2003.
DOI : 10.1115/1.1582501

C. Kitts and S. Wood, Engineering: Our digital future, 2003.

J. P. Kleijnen, Sensitivity analysis of simulation experiments: regression analysis and statistical design, Mathematics and Computers in Simulation, vol.34, pp.3-4297, 1992.

J. P. Kleijnen, W. Van, and . Beers, Kriging for interpolation in random simulation, Journal of the Operational Research Society, 2002.

D. Knight, D. G. Elliott, Y. Jaluria, and N. Langrana, Automated optimal design using concurrent integrated experiment and simulation, AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 2002.
DOI : 10.2514/6.2002-5636

P. N. Koch, T. W. Simpson, J. K. Allen, and F. Mistree, Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size, Journal of Aircraft, vol.36, issue.1, pp.275-286, 1999.
DOI : 10.2514/2.2435

J. R. Koehler and A. B. Owen, 9 Computer experiments, Handbook of Statistics, pp.261-308, 1996.
DOI : 10.1016/S0169-7161(96)13011-X

S. Kreuawan, F. Gillon, P. Brochet, and D. Cypers, Optimal design of damping circuit on dc link railway traction system, International Journal of Electrical Engineering in Transportation (IJEET), vol.4, issue.1, pp.27-32, 2008.

S. Kreuawan, F. Gillon, and P. Brochet, Efficient global optimization, an efficient tool for optimal design, proceeding of 16th International Conference on the Computation of Electromagnetic Fields (Compumag), 2007.

S. Kreuawan, F. Gillon, and P. Brochet, Comparative study of design approach for electric machine in traction application, International Review of Electrical Engineering (IREE), vol.3, pp.455-465, 2008.

S. Kreuawan, F. Gillon, and P. Brochet, Multidisciplinary design optimization formulation in electromagnetic device optimal design, proceeding of 13th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC), 2008.

S. Kreuawan, F. Gillon, and P. Brochet, Surrogate-assisted multiobjective optimization for optimal design using finite element analysis, proceeding of 13th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC), 2008.

S. Kreuawan, F. Gillon, F. Moussouni, S. Brisset, and P. Brochet, Optimal design of traction motor in railway propulsion system, 2007 International Aegean Conference on Electrical Machines and Power Electronics, pp.343-348, 2007.
DOI : 10.1109/ACEMP.2007.4510527

S. Kreuawan, F. Moussouni, F. Gillon, S. Brisset, P. Brochet et al., Optimal design process applied to electric railway traction system, Transactions on Systems, Signals & Devices, 2008.

V. Lakshmanan, Using a Genetic Algorithm to Tune a Bounded Weak Echo Region Detection Algorithm, Journal of Applied Meteorology, vol.39, issue.2, pp.222-230, 2000.
DOI : 10.1175/1520-0450(2000)039<0222:UAGATT>2.0.CO;2

L. Lebensztajn, C. A. Marretto, M. C. Costa, and J. Coulomb, Kriging: A Useful Tool for Electromagnetic Device Optimization, IEEE Transactions on Magnetics, vol.40, issue.2, pp.1196-1199, 2004.
DOI : 10.1109/TMAG.2004.824542

M. Lebrun, Simulation et cao en automatique et mécatronique. Technique de l'ingénieur

S. Lok-santosh and . Naidu, Neural network surrogate model for multidisciplinary design optimization, Indian Instidute of Technology, 2004.

P. Luniewski and U. Jansen, Benefits of system-oriented IGBT module design for high power inverters, 2007 European Conference on Power Electronics and Applications, pp.1-10, 2007.
DOI : 10.1109/EPE.2007.4417527

C. N. Madu and C. Kuei, Regression metamodeling in computer simulation -the state of the art. Simulation Practice and Theory, pp.27-41, 1994.

F. Marignetti, Coupled electro magnetic thermal and fluid dynamical simulation of axial flux pm synchronous machines, proceeding of the COMSOL Users Conference, 2007.

T. Maruyama and H. Igarashi, A reliability analysis of electromagnetic devices using surrogate model, proceeding of 13th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC), 2008.

W. J. Marx, D. N. Mavris, and D. P. Schrage, Integrated product development for the wing structural design of the High Speed Civil Transport, 5th Symposium on Multidisciplinary Analysis and Optimization, 1994.
DOI : 10.2514/6.1994-4253

M. D. Mckay, R. J. Beckman, and W. J. Conover, A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code, Technometrics, vol.15, issue.1, pp.55-61, 2000.
DOI : 10.1214/aoms/1177703566

M. Meckesheimer, A. J. Booker, R. R. Barton, and T. W. Simpson, Computationally Inexpensive Metamodel Assessment Strategies, AIAA Journal, vol.40, issue.10, pp.2053-2060, 2002.
DOI : 10.2514/2.1538

V. Mester, Conception optimal systémique des composants des cha??nescha??nes de tractionélectrique tractionélectrique, p.22, 2007.

V. Mester, F. Gillon, S. Brisset, and P. Brochet, Global Optimal Design of a Wheel Traction Motor by a Systemic Approach of the Electric Drive Train, 2006 IEEE Vehicle Power and Propulsion Conference, 2006.
DOI : 10.1109/VPPC.2006.364341

V. Mester, F. Gillon, and P. Brochet, Optimal design of electric vehicles drive train, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.24, issue.3, pp.967-983, 2005.
DOI : 10.1108/03321640510598274

V. Mester, F. Gillon, M. Hecquet, and P. Brochet, Multidisciplinary Optimal Design of Electric Machines Using Multimodeling Approach, 2006 12th Biennial IEEE Conference on Electromagnetic Field Computation, 2006.
DOI : 10.1109/CEFC-06.2006.1633117

Z. Michalewicz, Genetic algorithms + data structures = evolution programs, 1996.
DOI : 10.1007/978-3-662-02830-8

K. Miettinen, Nonlinear multiobjective optimization, 1999.
DOI : 10.1007/978-1-4615-5563-6

P. H. Millor, D. Roberts, and D. R. Turner, Lumped parameter thermal model for electrical machine of tefc design Electric Power Application, IEE Proceedings B, vol.138, issue.5, pp.205-218, 1991.

P. Monté, Smoothing noisy data by kriging with nugget effects. Wavelet, Images and Surface Fitting, pp.371-378, 1994.

S. Morimoto, Y. Takeda, T. Hirasa, and K. Taniguchi, Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity, IEEE Transactions on Industry Applications, vol.26, issue.5, pp.866-871, 1990.
DOI : 10.1109/28.60058

F. Moussouni, Méthodologie et Outils adaptésadaptés`adaptésà l'optimisation globale et multicritère de systèmes complexes, 2008.

F. Moussouni, S. Brisset, and P. Brochet, Some results on the design of brushless dc wheel motor using sqp and ga, International Journal of Applied Electromagnetics and Mechanics (IJAEM), vol.26, pp.3-4233, 2007.

F. Moussouni, S. Brisset, and P. Brochet, Fast building of pareto optimal set: Application to a brushless dc wheel motor, proceeding of the 10th International Workshop on Optimization and Inverse Problems in Electromagnetism (OIPE), pp.48-49, 2008.

F. Moussouni, S. Kreuawan, S. Brisset, F. Gillon, P. Brochet et al., Multilevel design optimization using target cascading, proceeding of the 10th International Workshop on Optimization and Inverse Problems in Electromagnetism (OIPE), pp.10-11, 2008.

T. Ohnishi and N. Takahashi, Optimal design of efficient IPM motor using finite element method, IEEE Transactions on Magnetics, vol.36, issue.5, pp.3537-3539, 2000.
DOI : 10.1109/20.908891

P. Y. Papalambros, Extending the optimization paradigm in engineering design, proceeding of the 3rd International Symposium on Tools and Methods of Competitive Engineering, 2002.

D. Petrichenko, ContributionàContribution`Contributionà la modélisation etàet`età la conception optimal des turboalternateurs de faible puissance, 2007.

P. Rohl, D. N. Mavris, and D. P. Schrage, A multilevel decomposition procedure for the preliminary wing design of a high-speed civil transport aircraft, proceeding of 1st Industry/University Symposium on High Speed Civil Transport Vehicles, 1994.

L. Rondot, V. Mazauric, Y. Delannoy, and G. Meunier, Dedicating finite volume method (fvm) to electromagnetic plasma modeling: Circuit breaker application, proceeding of 13th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC), 2008.
URL : https://hal.archives-ouvertes.fr/hal-00365257

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. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol.4, issue.4, pp.409-435, 1989.
DOI : 10.1214/ss/1177012413

M. J. Sasena, Flexibility qnd Efficiency Enhancements for Constrained Global Design Optimization with Kriging Approximations, 2002.

M. J. Sasena, P. Y. Papalambros, and P. Goovaerts, Metamodeling sampling criteria in a global optimization framework, 8th Symposium on Multidisciplinary Analysis and Optimization, pp.2000-4921, 2000.
DOI : 10.2514/6.2000-4921

M. Schonlau, Computer experiments and global optimization, 1997.

M. Schonlau, W. Welch, and D. Jones, Global versus local search in constrained optimization of computer models. New Developments and Applications in Experimental Design, pp.11-25, 1998.

H. A. Simon, The sciences of the artificial, 1981.

T. W. Simpson, J. D. Peplinski, P. N. Koch, and J. K. 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

T. W. Simpson, J. Siddique, and . Jiao, Product platform and product family design -Methods and applications, 2005.

J. Sobieszczanski-sobieski, M. S. Emiley, J. S. Agte, and R. R. Sandusky, Advancement of bi-level integrated system synthesis (bliss) In proceeding of 38th AIAA Aerospace Sciences Meeting and Exhibit, pp.2000-0421, 2000.

J. Sobieszczanski-sobieski and R. T. Haftka, Multidisciplinary aerospace design optimization: survey of recent developments. Structural and Multidisciplinary Optimization, pp.1-23, 1997.

N. P. Tedford and J. Martins, On the common structure of mdo problems: a comparison of architectures. In proceedings of the 11th AIAA/ISSMO multidisciplinary analysis and optimization conference, 2006.

T. V. Tran, S. Brisset, D. Echeverria, D. Lahaye, and P. Brochet, Space-mapping techniques applied to the optimization of a safety isolating transformer, proceeding of the 13th International Symposium on the Electromagnetic Fields (ISEF), 2007.

T. V. Tran, F. Moussouni, S. Brisset, and P. Brochet, Combinatorial optimization of a safety isolating transformer using branch-and-bound method and genetic algorithm, proceeding of 16th International Conference on the Computation of Electromagnetic Fields (Compumag), 2007.

S. R. Trout, Material selection of permanent magnets, considering thermal properties correctly, Proceedings: Electrical Insulation Conference and Electrical Manufacturing and Coil Winding Conference (Cat. No.01CH37264), pp.365-370, 2001.
DOI : 10.1109/EEIC.2001.965683

A. M. Trzynadlowski, F. Blaabjerg, J. K. Pedersen, R. L. Kirlin, and S. Legowski, Random pulse width modulation techniques for converter-fed drive systems-a review, IEEE Transactions on Industry Applications, vol.30, issue.5, pp.1166-1175, 1994.
DOI : 10.1109/28.315226

D. A. Veldhuizen and G. B. Lamont, Multiobjective evolutionary algorithm test suites, Proceedings of the 1999 ACM symposium on Applied computing , SAC '99, pp.351-357, 1999.
DOI : 10.1145/298151.298382

P. Venkataraman, Applied Optimization with MATLAB Programming, 2002.

H. K. Versteeg and W. Malalasakera, An Introduction to Computational Fluid Dynamics ? The Finite Volume Method, 1999.

J. A. Visser, D. J. De-kock, and F. D. Conradie, Minimisation of heat sink mass using mathematical optimisation, Sixteenth Annual IEEE Semiconductor Thermal Measurement and Management Symposium (Cat. No.00CH37068), pp.252-259, 2000.
DOI : 10.1109/STHERM.2000.837091

S. Vivier, Stratégie d'optimisation par plans d'expériences et Application aux dispositifsélectrotechniques dispositifsélectrotechniques modélisés parélémentsparéléments finis, 2002.
DOI : 10.3166/rige.8.725-747

S. Wang and J. Kang, Shape optimization of bldc motor using 3-d finite element method, IEEE Transactions on Magnetics, vol.36, issue.4, pp.1119-1123, 2000.

J. Y. Wong, Theory of ground vehicles, 2001.

R. Wrobel and P. H. Mellor, Design Considerations of a Direct Drive Brushless Machine With Concentrated Windings, IEEE Transactions on Energy Conversion, vol.23, issue.1, pp.1-8, 2008.
DOI : 10.1109/TEC.2007.905073