. Dans-ce-chapitre, Évolutif-MC sur des vrais problèmes d'optimisation en mise en forme Au début on a commencé par la résolution du problème 3D d'optimisation mono-objectif de remplissage d'une bielle (PB1 et PB2), proposé par notre partenaire industriel, Atelier des Janves. Ensuite, on a traité le problème 2D d'optimisation mono-objectif de remplissage d'une couronne (PCr1 et PCr2), proposé par Transvalor. Enfin, le reste de ce chapitre a été consacré à l'optimisation du tréfilage, qui est proposée par ArcelorMittal. Ce procédé de tréfilage est étudié sous forme de plusieurs problèmes d'optimisation mono-objectif, qui diffèrent par leur nombre de paramètres et par la fonction coût utilisée, tels que PT-2-D, PT-2-F, PT-2-SP, PT-3-D, PT-3- F, PT-3-SP, PT-4-D, PT-4-F et PT-4-SP et sous forme de deux problèmes d'optimisation multi-objectifs, PT-2 et PT-4

B. Abderrahmane and D. Regis, Review and Analysis of some Metamodeling Techniques used in Optimization, Institut National de Recherche en Informatique et en Automatique, 2009.

. Abedrabbo, Optimization of a Tube Hydroforming Process, AIP Conference Proceedings, pp.13-17, 2004.
DOI : 10.1063/1.1766687

M. Y. Ahmed and N. Qin, Comparison of Response Surface and Kriging Surrogates in Aerodynamic Design Optimization of Hypersonic Spiked Blunt Bodies, 13th International Conference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY, pp.13-26, 2009.

I. Batmaz and S. Tunali, Small response surface designs for metamodel estimation, European Journal of Operational Research, vol.145, issue.2, pp.455-470, 2003.
DOI : 10.1016/S0377-2217(02)00207-2

. Ayed, Contrôle de la striction et du plissement en emboutissage par optimisation des efforts serreflan, Septième Colloque National En Calcul Des Structures, 2005.

. Beume, SMS-EMOA: Multiobjective selection based on dominated hypervolume, European Journal of Operational Research, vol.181, issue.3, pp.1653-1669, 2007.
DOI : 10.1016/j.ejor.2006.08.008

H. G. Beyer and H. P. Schwefel, Evolution strategies, Scholarpedia, vol.2, issue.8, pp.3-52, 2002.
DOI : 10.4249/scholarpedia.1965

M. H. Bonte, Optimisation Strategies for Metal Forming Processes, 2007.

. Bonte, A metamodel based optimisation algorithm for metal forming processes Advanced methods in material forming, pp.55-72, 2007.

. Bonte, An optimisation strategy for industrial metal forming processes, Structural and Multidisciplinary Optimization, vol.147, issue.3???4, pp.571-586, 2008.
DOI : 10.1007/s00158-007-0206-3

. Huetink, Optimisation of metal forming processes using Finite Element simulations: A sequential approximate optimization algorithm and its comparision to other algorithms by application to forging, Structural and Multidisciplinary optimization 42, pp.797-810, 2010.

. Breitkopf, Moving least squares response surface approximation: Formulation and metal forming applications, Computers and structures 83, pp.1411-1428, 2005.
DOI : 10.1016/j.compstruc.2004.07.011

D. Büche, Multi-Objectives Evolutionary Optimization of Gas Turbine Components, 2003.

. Büche, Accelerating Evolutionary Algorithms With Gaussian Process Fitness Function Models, IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), vol.35, issue.2, pp.184-194, 2005.
DOI : 10.1109/TSMCC.2004.841917

. Cao, Analysis of an axisymmetric deep-drawn part forming using reduced forming steps, Journal of Materials Processing Technology, vol.117, issue.1-2, pp.193-200, 2001.
DOI : 10.1016/S0924-0136(01)01159-1

. Carr, Surface interpolation with radial basis functions for medical imaging, IEEE Transactions on Medical Imaging, vol.16, issue.1, pp.96-107, 1997.
DOI : 10.1109/42.552059

. Castro, Optimisation of shape and process parameters in metal forging using genetic algorithms, Journal of Materials Processing Technology, vol.146, issue.3, pp.356-364, 2004.
DOI : 10.1016/j.jmatprotec.2003.11.027

M. and C. A. Mount-campbell, Process optimization via neural network metamodeling, International Journal of Production Economics, vol.79, pp.93-100, 2002.

[. Jong and K. , The analysis of the behaviour of class of genetic adaptative systems, thèse de doctorat, 1975.

J. De, S. Jong, K. , and W. Spears, A formal analysis of the role of multi-point crossover in genetic algorithms, Annals of Mathematics and Artificial Intelligence, vol.5, pp.1-26, 1992.

K. Deb, Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems, Evolutionary Computation, vol.2, issue.3, pp.205-230, 1999.
DOI : 10.1162/evco.1995.3.1.1

K. Deb, Multi-objective Optimisation Using Evolutionary Algorithms: An Introduction, 2001.
DOI : 10.1007/978-0-85729-652-8_1

K. Deb, Single and Multi-Objective Optimization Using Evolutionary Algorithms, 2004.

D. Deb, K. , and S. Agrawal, Understanding Interactions among Genetic Algorithm Parameters, Indian Institute of Technology, Kanpur Genetic Algorithms Laboratory, 1999.

F. Ejday, M. Ejday, and L. Fourment, Metamodel Assisted Evolutionary Algorithm for Multi-objective Optimization of Non-steady Metal Forming Problems, International Journal of Material Forming, vol.3, issue.S1, pp.5-8, 2010.
DOI : 10.1007/s12289-010-0689-0
URL : https://hal.archives-ouvertes.fr/hal-00851431

F. Ejday, M. Ejday, and L. Fourment, Optimisation multi-objectifs ?? base de m??tamod??le pour des applications en mise en forme des m??taux, Mécanique & Industries, 2010.
DOI : 10.1051/meca/2010040

F. Ejday, M. Ejday, and L. Fourment, Meta-model assisted multi-objective optimization for non-steady 3D metal forming processes, International Journal of Material Forming, vol.11, issue.S1, pp.335-338, 2009.
DOI : 10.1007/s12289-009-0438-4
URL : https://hal.archives-ouvertes.fr/hal-00509299

F. Ejday, M. Ejday, and L. Fourment, Meta-model assisted Multi- Objective Optimization ? Application to nonsteady 3D metal forming processes, 8th World Congress on Structural and Multidisciplinary Optimization, 2009.

F. Ejday, M. Ejday, and L. Fourment, Meta-model assisted Multi- Objective Optimization for non-steady 3D metal forming applications, 7th EUROMECH Solid Mechanics Conference, 2009.

F. Ejday, M. Ejday, and L. Fourment, Optimisation multi-objectifs à base de métamodèle pour les problèmes de mise en forme, 2009.
DOI : 10.1051/meca/2010040

. Giannakoglou, Metamodel assisted evolution strategies, International Conference on parallel problem solving from nature, 2002.

. Emmerich, . Naujoks, M. Emmerich, and B. Naujoks, Metamodel Assisted Multiobjective Optimisation Strategies and their Application in Airfoil Design, Adaptive Computing in Design and Manufacture VI, pp.249-260, 2004.
DOI : 10.1007/978-0-85729-338-1_21

. Emmerich, Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels, IEEE Transactions on Evolutionary Computation, vol.10, issue.4, pp.421-439, 2006.
DOI : 10.1109/TEVC.2005.859463

. Emmerich, An EMO Algorithm Using the Hypervolume Measure as Selection Criterion, Third International Conference on Evolutionary Multi-Criterion Optimization, pp.62-76, 2005.
DOI : 10.1007/978-3-540-31880-4_5

. Fonseca, Simulation metamodeling through artificial neural networks, Engineering Applications of Artificial Intelligence, vol.16, issue.3, 2003.
DOI : 10.1016/S0952-1976(03)00043-5

. Fonseca, . Fleming, M. C. Fonseca, and P. J. Fleming, Multi-objective genetic algorithms made easy: Selection, sharing and mating restrictions, Proceedings of the 1st International Conference on Genetic Algorithms in Engineering Systems: Innovations and Application, pp.45-52, 1995.

F. Fourment, Gradient, Non-Gradient and Hybrid Algorithms for Optimizing 3D Forging Sequences with Uncertainties, AIP Conference Proceedings, pp.475-480, 2007.
DOI : 10.1063/1.2740856
URL : https://hal.archives-ouvertes.fr/hal-00510567

C. Fourment, L. Fourment, and J. L. Chenot, OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES???I. SHAPE OPTIMIZATION METHOD, International Journal for Numerical Methods in Engineering, vol.37, issue.1, pp.33-50, 1996.
DOI : 10.1002/(SICI)1097-0207(19960115)39:1<33::AID-NME844>3.0.CO;2-Z

. Fourment, OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES???II. APPLICATION OF SHAPE OPTIMIZATION IN FORGING, International Journal for Numerical Methods in Engineering, vol.21, issue.1, pp.51-65, 1996.
DOI : 10.1002/(SICI)1097-0207(19960115)39:1<51::AID-NME845>3.0.CO;2-#
URL : https://hal.archives-ouvertes.fr/hal-01462083

L. Fourment, T. Massé, S. Marie, R. Ducloux, M. Ejday et al., Optimization of a range of 2D and 3D bulk forming processes by a meta-model assisted evolution strategy, International Journal of Material Forming, vol.2, issue.S1, pp.343-346, 2009.
DOI : 10.1007/s12289-009-0476-y
URL : https://hal.archives-ouvertes.fr/hal-00509409

P. Massé and . Montmitonnet, Mono and multi-objective optimization techniques applied to a large range of industrial test cases using Metamodel assisted Evolutionary Algorithms, Proceedings of the 10th International Conference on Numerical Methods in Industrial Forming Processes, pp.833-840, 2010.

. Ghanmi, Optimisation multiobjectifs en mécanique des structures : Approche basée sur les surfaces de réponse adaptative, 2005.

E. Gildemyn, Caractérisation des procédés de fabrication de pieces de securité automobile. Optimisation multiobjectifs de la mise en forme, 2008.

. Tucker, Response surface approximation of Pareto optimal front in multi-objective optimization, Comput. Methods Appl. Mech. Engrg, vol.196, pp.879-893, 2007.

. Tucker, Response surface approximation of Pareto optimal front in multi-objective optimization, Proceedings of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1989.

H. Goldberg, D. E. Goldberg, and J. H. Holland, Genetic Algorithms and Machine Learning, Machine Learning, vol.3, issue.2/3, pp.95-99, 1988.
DOI : 10.1023/A:1022602019183

J. H. Holland, Outline for a Logical Theory of Adaptive Systems, Journal of the association of computing machinery 3, pp.297-314, 1962.
DOI : 10.1145/321127.321128

G. Ingarao, R. D. Lorenzo, and F. Micari, Internal pressure and counterpunch action design in Y-shaped tube hydroforming processes: A multi-objective optimisation approach, Computers & Structures, vol.87, issue.9-10, pp.591-602, 2009.
DOI : 10.1016/j.compstruc.2009.02.003

. Jensen, Optimization of the draw-die design in conventional deep-drawing in order to minimise tool wear, Journal of Materials Processing Technology, vol.83, issue.1-3, pp.106-114, 1998.
DOI : 10.1016/S0924-0136(98)00048-X

Y. Jin, A comprehensive survey of fitness approximation in evolutionary computation, Soft Computing, vol.9, issue.1, pp.3-12, 2005.
DOI : 10.1007/s00500-003-0328-5

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

. Jones, 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

A. Jourdan, How to repair a second-order surface for computer experiments by Kriging, Chemometrics and Intelligent Laboratory Systems 96, pp.108-116, 2009.
DOI : 10.1016/j.chemolab.2009.02.007
URL : https://hal.archives-ouvertes.fr/hal-00175059

Z. Jurkovic, M. Jurkovic, and S. Buljan, Optimization of extrusion force prediction model using different techniques, Journal of Achievements in Materials and Manufacturing Engineering, vol.17, pp.353-356, 2006.

P. D. Justesen, M. Kadkhodaei, M. Salimi, and M. Poursina, Multi-objective Optimization using Evolutionary AlgorithmsAnalysis of asymmetrical sheet rolling by a genetic algorithm, International Journal of Mechanical Sciences, vol.49, pp.622-634, 2007.

. Kim, Die shape design optimization of sheet metal stamping process using meshfree method, International Journal for Numerical Methods in Engineering, vol.181, issue.12, pp.1385-1405, 2001.
DOI : 10.1002/nme.181

J. P. Kleinermann and J. P. Ponthot, Parameter identification and shape/process optimization in metal forming simulation, Journal of Materials Processing Technology, vol.139, issue.1-3, pp.521-526, 2003.
DOI : 10.1016/S0924-0136(03)00530-2

H. Knowles, J. Knowles, and E. J. Hughes, Multiobjective Optimization on a Budget of 250 Evaluations, Third International Conference on Evolutionary Multi- Criterion Optimization (EMO 2005), pp.176-190, 2005.
DOI : 10.1007/978-3-540-31880-4_13

D. G. Krige, A statistical approach to some basic mine valuation problems on the Witwatersrand, Journal of the Chemical, Metallurgical and Mining Society of the South Africa, vol.52, pp.119-139, 1951.

J. Krok, An Extended Approach to Error Control in Experimental and Numerical Data Smoothing and Evaluation Using the Meshless FDM, Meshfree Computational Mechanics 11, pp.913-945, 2002.
DOI : 10.1002/nme.307

F. Kursawe, A variant of evolution strategies for vector optimization, Proceedings of the Parallel Problem Solving from Nature I (PPSN-I), pp.193-197, 1990.
DOI : 10.1007/BFb0029752

. Ledoux, Optimization method for stamping tools under reliability constraints using genetic algorithms and finite element simulations, Journal of Materials Processing Technology, vol.210, issue.3, pp.474-486, 2006.
DOI : 10.1016/j.jmatprotec.2009.10.010
URL : https://hal.archives-ouvertes.fr/hal-00451940

. Le-riche, Un état des lieux de l'optimisation évolutionnaire et de ses implications en sciences pour l'ingénieur", chapter in Modélisation Numérique: défis et perspectives, 2nd volume, pp.187-259, 2007.

. Riche, Gears Design with Shape Uncertainties Using Controlled Monte Carlo Simulations and Kriging, 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2009.
DOI : 10.2514/6.2009-2257
URL : https://hal.archives-ouvertes.fr/hal-00409760

J. H. Dijkstra and . Reiber, Metamodel-Assisted Mixed Integer Evolution Strategies and Their Application to Intravascular Ultrasound Image Analysis, IEEE Congress on Evolutionary Computation, pp.2764-2771, 2008.

Z. Lin, X. Juchen, W. Xinyun, and H. Guoan, Optimization of die profile for improving die life in the hot extrusion process, Journal of Materials Processing Technology, vol.142, issue.3, pp.659-664, 2003.
DOI : 10.1016/S0924-0136(03)00686-1

O. Liszka, T. Liszka, and J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics, Computers and Structures 11, pp.83-95, 1980.
DOI : 10.1016/0045-7949(80)90149-2

T. Massé, Study and Optimization of High Carbon Steel Flat Wires, thèse de doctorat, Mines ParisTech, 2010.

G. Matheron, Traité de géostatistique appliquée, 1962.

R. H. Myers, D. C. Montgomery, C. M. Anderson, and C. M. Anderson-cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2009.

. Naceur, Response surface methodology for the rapid design of aluminum sheet metal forming parameters, Materials & Design, vol.29, issue.4, pp.781-790, 2008.
DOI : 10.1016/j.matdes.2007.01.018

. Naceur, Response surface methodology for design of sheet forming parameters to control springback effects, Computers & Structures, vol.84, issue.26-27, pp.1651-1663, 2006.
DOI : 10.1016/j.compstruc.2006.04.005

. Naceur, Optimization of drawbead restraining forces and drawbead design in sheet metal forming process, International Journal of Mechanical Sciences, vol.43, issue.10, pp.2407-2434, 2001.
DOI : 10.1016/S0020-7403(01)00014-5

H. Naceur, Y. Q. Guob, and J. L. Batoz, Blank optimization in sheet metal forming using an evolutionary algorithm, Journal of Materials Processing Technology, vol.151, issue.1-3, pp.183-191, 2004.
DOI : 10.1016/j.jmatprotec.2004.04.036

. Naujoks, Multi-objective Optimization using S-metric Selection: Application to three-dimensional Solution Spaces, CEC'2005) (IEEE Service Center) 2, pp.1282-1289, 2005.

M. Oudjene, L. Ben-ayed, A. Delamézière, and J. L. Batoz, Shape optimization of clinching tools using the response surface methodology with Moving Least-Square approximation, Journal of Materials Processing Technology, vol.209, issue.1, pp.289-296, 2009.
DOI : 10.1016/j.jmatprotec.2008.02.030

D. Pawan, K. Pawan, S. Nain, and K. Deb, A Multi-Objective Optimization Procedure with Successive Approximate Models, 2005.

D. Pawan, K. Pawan, S. Nain, and K. Deb, A Multi-Objective Search and Optimization Procedure with Successive Approximate Models, 2004.

. Poloni, Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics, Computer Methods in Applied Mechanics and Engineering, vol.186, issue.2-4, pp.403-420, 2000.
DOI : 10.1016/S0045-7825(99)00394-1

K. Ponthot, J. P. Ponthot, and J. P. Kleinermann, A cascade optimization methodology for automatic parameter identification and shape/process optimization in metal forming simulation, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.41-43, pp.5472-5508, 2006.
DOI : 10.1016/j.cma.2005.11.012

. Poursina, Optimum pre-form dies in two-stage forging, Journal of Materials Processing Technology, vol.174, issue.1-3, pp.325-333, 2006.
DOI : 10.1016/j.jmatprotec.2006.01.015

K. Tucker, Surrogate-based analysis and optimization, Progress in Aerospace Sciences 41, pp.1-28, 2005.

K. Raza, W. Raza, and K. Y. Kim, Shape optimization of wire-wrapped fuel assembly using Kriging metamodeling technique, Nuclear Engineering and Design, vol.238, issue.6, pp.1332-1341, 2008.
DOI : 10.1016/j.nucengdes.2007.10.018

I. Rechenberg, Cybernetic solution path of an experimental problem, Royal Aircraft Establishment, UK, 1965.

S. Rippa, An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Advances in Computational Mathematics, vol.11, issue.2/3, pp.193-210, 1999.
DOI : 10.1023/A:1018975909870

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

O. Schenk and M. Hillmann, Optimal design of metal forming die surfaces with evolution strategies, Computers and structures 82, pp.1695-1705, 2004.

. Sobester, On the Design of Optimization Strategies Based on Global Response Surface Approximation Models, Journal of Global Optimization, vol.27, issue.5, pp.31-59, 2005.
DOI : 10.1007/s10898-004-6733-1

D. Spears, . Jong, W. Spears, and K. Jong, On the virtues of parameterised uniform crossover, Proceedings of the 4th International Conference on Genetic Algorithms, pp.230-236, 1991.

G. Syswerda, Uniform crossover in genetic algorithms, Proceedings of the Third International Conference on Genetic Algorithms, pp.2-8, 1989.

. Tanaka, GA-based decision support system for multi-criteria optimization, Proceedings of the International Conference on Systems, Man and Cybernetics, pp.1556-1561, 1995.

. Tunali, . Batmaz, S. Tunali, and I. Batmaz, Dealing with the least squares regression assumptions in simulation metamodeling, Computers & Industrial Engineering, vol.38, issue.2, pp.307-320, 2000.
DOI : 10.1016/S0360-8352(00)00046-2

R. Viennet, Multicriteria optimization using a genetic algorithm for determining a Pareto set, International Journal of Systems Science, vol.1, issue.2, pp.255-260, 1996.
DOI : 10.1109/21.293497

Y. Wei, L. Wei, and Y. Yuying, Multi-objective optimization of sheet metal forming process using Pareto-based genetic algorithm, Journal of Materials Processing Technology, vol.208, issue.1-3, pp.499-506, 2008.
DOI : 10.1016/j.jmatprotec.2008.01.014

H. Wu, C. Y. Wu, and Y. C. Hsu, Optimal Shape Design of an Extrusion Die Using Polynomial Networks and Genetic Algorithms, The International Journal of Advanced Manufacturing Technology, vol.19, issue.2, pp.79-87, 2002.
DOI : 10.1007/s001700200000

E. Zitzler, K. Deb, and L. Thiele, Comparison of Multiobjective Evolutionary Algorithms: Empirical Results, Evolutionary Computation, vol.8, issue.2, pp.173-195, 2000.
DOI : 10.1109/4235.797969

E. Zitzler, M. Laumanns, and S. Bleuler, A Tutorial on Evolutionary Multiobjective Optimization Metaheuristics for Multiobjective Optimisation, Workshop on Multiple Objective Metaheuristics, pp.3-38, 2002.