6. Case studies
7.2 Further research
Concerning the SFDP** approach for finding Maximin designs, it may be an interesting option to vary more than one design site at a time. This may lead to faster convergence of the algorithm, especially when combinations of design sites are chosen in a clever way. Further, due to the observation that noncollapsingness in one dimension corresponds to space-fillingness in that dimension, another possible extension is to use the SFDP** method to create a design that is noncollapsing in one or more user-defined dimensions. This becomes important when we are not certain whether these dimensions are important for all response parameters. Restricting the design space to Orthogonal Array based sub-spaces may be a good approach for this goal (see Chapter 1, Owen [1992] and Tang [1993]).
Concerning the Symbolic Regression approach described in Chapter 3, there are some open issues for further research. One significant improvement of the algorithm may be found by first applying a number of transformations to the response data. Then, the search procedure can check the meta- model on all transformations without much computational effort, and select not only the best transformation functions for the design parameters, but also the best transformation function for the response parameter. Another interesting extension to the algorithm would be the use of rational functions of transformation functions. This would increase the number of parameters in the meta- model that can efficiently be estimated, and therefore this extension would probably increase the quality of the resulting meta-model. Finally, it would be beneficial to be able to dynamically alter the number of terms and the depth of the trees during the search.
So far, we treated the three systematic error types that occur during simulation-based design optimization (simulation error, meta-model error, and implementation error) separately. An interesting subject for further research is to analyze how these errors can be modeled in one robust counterpart problem simultaneously.
The CMM approach is sensitive to meta-model errors due to error propagation. Future research should focus on finding optimal settings of design parameters that are relatively insensitive (i.e., robust) to these errors. Techniques from Chapter 4 may be used for this goal. Another interesting issue is the clustering of black boxes for the CMM approach. Future research should investigate the allocation of black boxes to clusters, such that, e.g., the total simulation throughput time is minimized for a certain coordination method.
REFERENCES
Aarts, E.H.L., Korst J.H.M. [1989], Simulated Annealing and Boltzmann Machines: a Stochastic Approach to Combinatorial Optimization and Neural Computing, Wiley, Chichester.
Alexandrov, N.M., Dennis, J.E., Lewis, R.M., Torczon, V. [1998], A trust region framework for managing use of approximation models in optimization, Journal on Structural Optimization, 15 (1), pp. 16-23.
Andres, T.H., Hajas, W.C. [1993], Using iterated fractional factorial design to screen parameters in sensitivity analysis of a probabilistic risk assessment model, In: Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing in Nuclear Applications, 2, pp. 328-337, Karlsruhe.
Arnold, S.F. [1981], The Theory of Linear Models and Multivariate Analysis, Wiley, New York.
Balling, R.J., Sobieszczanski-Sobieski, J. [1996], Optimization of coupled systems: a critical overview of approaches, AIAA Journal, 34, pp. 6-17.
Barthelemy, J.F.M., Haftka, R.T. [1993], Approximation concepts for optimum structural design - a review, Journal on Structural Optimization, 5, pp. 129-144.
Bates, R.A., Buck, R.J., Riccomagio, E., Wynn, H.P. [1996a], Experimental design and observation for large systems (with discussion), Journal of the Royal Statistical Society, Series B, 37, pp. 77-94. Bates, R.A., Gilliver, R., Hughes A., Shahin, T., Sivaloganathan, S., Wynn, H.P. [1999], Fast
optimization of mechanical designs using computer aided design computer aided engineering emulation: a case study, In: Proceedings of the Institution of Mechanical Engineers, Journal of Automobiel Engineering, 213 (D1), pp. 27-35.
Bates, R.A., Wynn H.P. [1996b], Tolerancing and optimization for model-based robust engineering design, Quality and Reliability Engineering International, 12 (2), pp. 119-127.
Bates, S.J., Sienz, J., Langley, D.S. [2003], Formulation of the Audze-Eglais uniform Latin hypercube design of experiments, Advances in Engineering Software, 34 (8), pp. 493-506.
Bellman, R. [1961], Adaptive Control Processes: A Guided Tour, Princeton University Press.
Ben-Tal, A., Nemirovski A. [2002], Robust optimization - methodology and applications, Mathematical Programming, 92 (3), pp. 453-480.
Bertram, V. [2003], Optimization in ship design, In: Optimistic Optimization in Marine Design, pp. 27- 52, Mensch & Buch Verlag, Berlin.
Box, G.E.P. Draper, N.R. [1959], A basis for the selection of a response surface design, Journal of the American Statistical Association, 54, pp. 622-654.
Braun, R. [1996], Collaborative Optimization: An Architecture for Large-scale Distributed Design, Doctoral dissertation, Stanford University, Stanford.
Breiman, L., Friedman, J.H. [1997], Predicting multivariate responses in multiple linear regression, Journal of the Royal Statistical Society, Series B, 59 (1), pp. 3-54.
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J. [1984], Classification and Regression Trees, Wadsworth International Group, Belmont.
Broyden, C.G. [1965], A Class of Methods for Solving Nonlinear Simultaneous Equations, Mathematics of Computation, 19 (92), pp. 577-593.
Campolongo, F., Kleijnen, J.P.C., Andres, T.H. [2000], Screening methods, In: Sensitivity Analysis, pp. 65–89, Wiley, Chichester.
Chen, S., Wang, L., Wu, X., Wang, X. [2003], Multi-objective genetic algorithms and their application to ship fleet optimization, In: Proceedings of the 8th Interanational Marine Design Conference,
2, pp. 319-327, Athens.
Clarke, S.M., Griebsch, J.H., Simpson, T.W. [2003], Analysis of support vector regression for approximation of complex engineering analyses, In: Proceedings of DETC ’ 03, ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago.
Conn, A., Toint, P. [1996], An algorithm using quadratic interpolation for unconstrained derivative free optimization. In: Nonlinear Optimization and Applications, pp. 27-47, Plenum, New York. Cressie, N.A.C. [1993], Statistics for Spatial Data, John Wiley & Sons, Inc., New York.
Cristianni, N., Shawe-Taylor, J., [2000], An Introduction to Support Vector Machines and other Kernel-based Learning Methods, Cambridge University Press, Cambridge.
Currin, C., Mitchell, T., Morris, M., Ylvisaker D., [1991], Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments, Journal of the American Statistical Association, 86 (416), pp. 953-963.
Cuyt, A., Verdonk, B. [1992], Multivariate rational data fitting: general data structure, maximal accuracy and object orientation, Numerical Algorithms, 3, pp. 159-172.
Czyzak, P., Jaszkiewicz, A. [1998], Pareto Simulated Annealing - a metaheuristic technique for multiple-objective combinatorial optimization, Journal of Multi-Criteria Decision Analysis, pp. 34- 47.
Dam, E.R. van [2005], Two-dimensional minimax Latin hypercube designs, CentER Discussion Paper 2005-105, Tilburg University, Tilburg.
Dam, E.R. van, Husslage, B.G.M., Hertog, D. den, Melissen, J.B.M. [2006], Maximin latin hypercube designs in two dimensions, Operations Research (to appear).
Dhaene, T., Geest, J. de [2005], Self-organizing multivariate constrained meta-modeling technique for passive microwave and RF components, Future Generation Computer Systems, 21, pp. 1040- 1046.
Dimnaku, A., Kincaid, R., Trosset, M.W. [2002], Approximate solutions of continuous dispersion problems, In: Proceedings of the 2002 ISOLDE conference.
Doltsinis, I., Kang, Z. [2004], Robust design of structures using optimization methods, Computer Methods in Applied Mechanics and Engineering, 193 (23-26), pp. 2221-2237.
Draper, N.R., Smith, H. [1985], Applied Regression Analysis, 2nd Edition, Wiley, Chichester.
Drezner, Z. [1995], Facility Location: A Survey of Applications and Methods, Springer-Verlag, New York. Drezner, Z., Erkut, E. [1995], Solving the p-dispersion problem using non-linear programming,
Journal of the Operational Research Society, 46, pp. 516-520.
Driessen, L.T. [2006], Simulation-Based Optimization for Product and Process Design, Doctoral dissertation, Tilburg University, Tilburg.
Drudd, A.S. [1994], CONOPT - A large scale GRG code, ORSA Journal on Computing, 6, pp. 207- 216.
Efron, B., Tibshirani, R.J. [1993], An Introduction to the Bootstrap, Chapman & Hall, New York. Etman, L.F.P. [1997], Optimization of Multibody Systems Using Approximation Concepts, Doctoral
dissertation, Technical University Eindhoven, Eindhoven.
Fang, K.T., Ma, C.X., Winker, P. [2002], Centered L2-discrepancy of random sampling and latin hypercube design, and construction of uniform designs, Mathematics of Computation, 71, pp. 275- 296.
Fang, K.T., Wang, Y. [1994], Number-theoretic Methods in Statistics, Chapman & Hall, New York. Fishman, G.S. [2001], Discrete-Event Simulation: Modeling, Programming, and Analysis, Springer-Verlag,
Berlin.
Friedman, J., [1991], Multivariate adaptive regression splines (with discussion), Annals of Statistics, 19 (1), pp. 1-141.
Gambling, M., Jones, R.D., Toropov, V.V., Alvarez, L.F. [2001], Application of optimization strategies to problems with highly non-linear response. In: Proceedings of the 3rd ASMO UK/ISSMO Conference on Engineering Design Optimization, pp. 249-256, Harrogate.
Gammon, M.A., Alkan, A. [2003], Initial vessel design by evolutionary optimization, In: Proceedings of the 8th International Marine Design Conference , 1, pp. 77-88.
Garishina, N.V., Vladislavleva, C.J. [2004], On development of a complexity measure for symbolic regression via genetic programming, Technical report 04.03, Mathmematics for industry program of the Stan Ackermans Institute, Eindhoven.
Gu, X., Renaud, J.E., Batill, S.M., Brach, R.M., Budhiraja, A.S. [2000], Worst case propagated uncertainty of multidisciplinary systems in robust design optimization, Structural and Multidisciplinary Optimization, 20 (3), pp. 190-213.
Guner, M., Gammon, M.A. [2003], Optimization of total propulsive efficiency in a propellerstator combination using an evolutionary algorithm, In: Proceedings of the 8th International Marine Design Conference, 2, pp. 55-66.
Gutmann, H. [2001], A radial basis function method for global optimization, Journal of Global Optimization, 19 (3), pp. 201-227.
Hammersley, J.M. [1960], Monte Carlo methods for solving multivariate problems, Annals of the New York Academy of Science, 86, pp. 844-874.
Hertog, D. den, Stehouwer, H.P. [2002], Optimizing color picture tubes by high-cost nonlinear programming, European Journal on Operations Research, 140 (2), pp. 197-211.
Hertog, D. den, Kleijnen, J.P.C., Siem, A.Y.D. [2006], The correct Kriging variance estimated by bootstrapping, Journal of the Operational Research Society, 57, pp. 400-409.
Hickernell, F.J. [1998], A generalized discrepancy and quadrature error bound, Mathematics of Computation, 67 (221), pp. 299-322.
Hooke, R., Jeeves, T.A. [1961], Direct search solution of numerical and statistical problems, Journal of the Association for Computing Machinery, 8, pp. 219-229.
Husslage, B.G,M, Dam, E.R. van, Hertog, D. den, Stehouwer, H.P., Stinstra, E.D. [2003], Collaborative metamodeling: coordinating simulation-based product design, Concurrent Engineering: Research and Applications, 11, pp. 267-277.
Husslage, B.G.M., Dam, E.R. van, Hertog, D. den [2005], Nested maximin Latin hypercube designs in two dimensions, CentER Discussion Paper 2005-79, Tilburg University, Tilburg.
IMO [1991], Resolution A684(17), Explanatory notes to the solas regulations on subdivision and damage stability of cargo ships of 100 metres in length and over, London.
IMO [1992], Subdivision and Damage Stability of Cargo Ships, In: Consolidated Text of the International Convention for the Safety of Life at Sea, 1974, and its Protocol of 1978: Articles, Annex and Certificates, pp. 89-100, London.
Jensen, J.J. [1995], Damage stability rules in relation to ship design, In: Proceedings of the West European Conference on Marine Technology: Ship Safety and Protection of the Environment from a Technical Point-of- view, Copenhagen, pp. 71-96.
Jin, R., Chen, W., Sudjianto, A. [2002], On sequential sampling for global metamodeling in engineering design, In: Proceedings of DETC02, ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2002/DAC-34092, Montreal.
Jin, R., Chen, W., Sudjianto, A. [2005], An efficient algorithm for constructing optimal design of computer experiments, Journal of Statistical Planning and Inference, 134 (1), pp. 268-287.
Johnson, M.E., Moore, L.M. , Ylvisaker, D. [1990], Minimax and maximin distance designs, Journal of Statistical Planning and Inference , 26, pp. 131-148.
Jones, D.R., Schonlau, M., Welch, W.J. [1998], Efficient global optimization of expensive black-box functions, Journal of Global Optimization, 13, pp. 455-492.
Jones, D.R. [2001], A taxonomy of global optimization methods based on response surfaces, Journal of Global Optimization, 21 (4), pp. 345-383.
Kalagnanam, J.R., Diwekar, U.M. [1997], An efficient sampling technique for off-line quality control, Technometrics, 39 (3), pp. 308-319.
Keijzer, M. [2003], Improving symbolic regression with interval arithmetic and linear scaling, In: Genetic Programming, Proceedings of EuroGP'2003, 2610, pp. 71-83, Essex.
Keulen, F. van, Vervenne, K. [2002], Gradient-enhanced response surface building, In: Proceedings of the Ninth AIAA/ISSMO Symposium and Exhibit on Multidisciplinary Analysis and Optimization, Atlanta.
Kim, H.M., Michelena, N.F., Papalambros, P.Y., Jiang, T. [2000], Target cascading in optimal system design, In: Proceedings of the 2000 ASME Design Automation Conference, Baltimore.
Kleijnen, J.P.C. [1987], Statistical Tools for Simulation Practitioners, Marcel Dekker, New York.
Kleijnen, J.P.C. [1995], Verification and validation of simulation models, European Journal on Operations Research, 82 (1), pp. 145-162.
Kleijnen, J.P.C., Beers, W.C.M. van [2004], Application-driven sequential designs for simulation experiments: Kriging metamodelling, Journal of the Operational Research Society, 55 (8), pp. 876-883. Kleijnen, J.P.C., Bettonvil, B., Persson, F. [2006], Screening for the important factors in large discrete-event simulation models: sequential bifurcation and its applications, In: Screening: Methods for experimentation in industry, drug discovery, and genetics , Springer-Verlag, New York, pp. 287-307.
Kleijnen, J.P.C., Sargent, R.G. [2000], A methodology for the fitting and validation of metamodels in simulation, European Journal of Operational Research, 120 (1), pp. 14-29.
Koch, P.N, Mavris, D., Allen, J.K., and Mistree, F. [1998], Modeling noise in approximation-based robust design: a comparison and critical discussion, In: Proceedings of DETC’98, 1998 ASME Design Engineering Technical Conferences, Atlanta.
Koch, P.N., Evans, J.P., Powell, D. [2002], Interdigitation for effective design space exploration using iSIGHT, Structural and Multidisciplinary Optimization, 23 (2), pp. 111-126.
Koch, P.N., Yang, R.J., Gu, L. [2004], Design for six sigma through robust optimization, Structural and Multidisciplinary Optimization, 26 (3-4), pp. 235-248.
Koehler, J.R., Owen, A.B. [1996], Computer Experiments, In: Handbook of Statistics, 13, pp. 261-308, Elsevier Science B.V., Boston.
Koza, J.R. [1992], Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge.
Krishman, V. [1996], Managing the simultaneous execution of coupled phases in concurrent product development, IEEE Transaction on Management, 43 (2), pp. 210-217.
Law, A.M., Kelton, W.D. [2000], Simulation Modelling and Analysis, McGraw-Hill Series in Industrial Egineering and Management Science, 3rd edition, McGraw-Hill, New York.
Lindley, D.V. [1956], On a measure of the information provided by an experiment, Annals of Mathematical Statistics, 27, pp. 986-1005.
Liu, L., Wakeland, W. [2005], Does more uniformly distributed sampling generally lead to more accurate prediction in computer experiments?, Proceedings from the 2005 Winter Simulation Conference, pp. 2561-2571.
Locatelli, M., Raber, U. [2002], Packing equal circles into a square: a deterministic global optimization approach, Discrete Applied Mathematics ,122, pp. 139-166.
Loh, H.T., Papalambros, P.Y. [1991], A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems, Journal of Mechanical Design, 113 (3), pp. 325-334. Lophaven, S.N., Nielsen, H.B., Sondergaard, J. [2002], DACE: A matlab kriging toolbox version 2.0,
Technical report IMM-TR-2002-12, Technical University of Denmark, Copenhagen.
Marazzi, M., Nocedal, J. [2002], Wedge trust region methods for derivative free optimization, Mathematical Programming, 91 (2), pp. 289-305.
Mathews, J.H., Fink, K.D. [2004], Numerical Methods Using Matlab, 4th edition, Prentice Hall Inc,
Upper Saddle River.
Mavris, D.N., Bandte, O., Schrage, D.P. [1996], Application of Probabilistic Methods for the Determination of an Economically Robust HSCT Configuration, AIAA-96-4090, pp. 968-987.
McKay, M.D., Beckman, R.J. , Conover, W.J. [1979], A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (2), pp. 239-45.
Meckesheimer, M., Barton, R.R., Simpson, T.W., Booker, A. [2001], Computationally inexpensive metamodel assessment strategies, In: Proceedings of the ASME Design Technical Conferences-Design Automation Conference, Pittsburgh.
Michelena, N., Papalambros, P. Y., [1997], A hypergraph framework for optimal model-based decomposition of design problems, Journal of Computational Optimization and Applications, 8, pp. 173-196.
Montgomery, D.C., Peck, E.A., Vining, G.G. [2001], Introduction to linear regression analysis, 3rd edition,
Wiley, New York.
Morris, M.D. [1991], Factorial sampling plans for preliminary computational experiments, Technometrics, 33, pp. 161-174.
Morris, M.D., Mitchell, T.J. [1995], Exploratory designs for computer experiments, Journal of Statistical Planning and Inference, 43, pp. 381-402.
Nelder, J.A., Mead, R. [1965], A simplex method for function minimization, Computer Journal, 7, pp. 308-313.
Niederreiter, H. [1992], Random number generation and quasi Monte Carlo methods, SIAM CBMS-NSF, 63, Philadelphia.
Nowacki, H. [2003], Design synthesis and optimization - A historical perspective, In: WEGEMT’03: Optimistic - Optimization in Marine Design, pp.1-26, Mensch & Buch Verlag, Berlin. Oden, J.T., [2006], Revolutionizing engineering science through simulation, National Science Foundation
(NSF), Blue Ribbon Panel on Simulation-Based Engineering Science.
Ölcer, A.I., Tuzcu, C., Turan, O. [2003], Internal hull subdivision optimisation of ro-ro vessels in multiple criteria decision making environment, In: Proceedings of the 8th International Marine Design Conference, 1, pp. 339-351, Athens.
Owen, A.B. [1992], Orthogonal arrays for computer experiments, integration and visualization, Statistica Sinica, 2, pp. 439-452.
Park, J.S. [1994], Optimal Latin-hypercube designs for computer experiments, Journal of Planning and Inference, 39, pp. 95-111.
Parry, J., Bornoff, R., Stehouwer, H.P., Driessen, L.T., Stinstra, E.D. [2003], Simulation-based design optimization methodologies applied to CFD, In: Proceedings of the SEMITHERM conference 2003, San José.
Pintér, J.D. [1996], Global optimization in action, Kluwer Academic Publishers, Dordrecht.
Powell, M. J. D. [1987], Radial basis functions for multivariable interpolation: A review, In: Algorithms for Approximation of Functions and Data, pp. 143–167, Oxford University Press, Oxford. Powell, M.J.D. [1994], A direct search optimization method that models the objective and constraint functions by linear interpolation, In: Advances in Optimization and Numerical Analysis, Proceedings of the Sixth Workshop on Optimization and Numerical Analysis, Oaxaca, Me xico, 275, pp. 5-67, Kluwer Academic Publishers, Dordrecht.
Putko, M.M., Newman, P.A., Green, L.L. [2001], Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives, AIAA 2001-2528, pp. 1-14.
Rajagopal, R, Del Castillo, E. [2005], Model-robust process optimization using Bayesian model averaging, Technometrics, 47 (2), pp. 152-163.
Regis, R.G., Shoemaker, C.A. [2005], Constrained global optimization of expensive black box functions using radial basis functions, Journal of Global Optimization, 31 (1), pp. 153-171.
Sacks, J., Schiller, S. [1988], Spatial designs, In: Statistical Decision Theory and Related Topics IV, 2, pp. 385-399, Springer-Verlag, New York.
Sacks, J., Welch W.J., Mitchell T.J., Wynn H.P. [1989a], Design and analysis of computer experiments, Statistical Science, 4, pp. 409-435.
Sacks, J., Schiller, S., Welch, W.J. [1989b], Designs for computer experiments, Technometrics, 31, pp. 41-47.
Sanchez, S.M. [2000], Robust design: seeking the best of all possible worlds, In: Proceedings of the 2000 Winter Simulation Conference, pp. 69-76.
Seidel, R. [1991], Exact upper bounds for the number of faces in d-dimensional Voronoi diagram, In: Applied Geometry and Discrete Mathematics - The Victor Klee Festschrift, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 517-529.
Shannon, C.E. [1948], A mathematical theory of communication, Bell System Technical Journal, 27, pp. 379-423, pp. 623-656.
Shewry, M.C. Wynn, H.P. [1987], Maximum entropy sampling, Journal of Applied Statistics, 14, pp. 165-170.
Siem, A.Y.D., De Klerk, E., Den Hertog, D. [2005], Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions, CentER Discussion Paper 2005- 73, Tilburg University, Tilburg.
Simpson, T.W., Booker, A.J., Ghosh, D., Giunta, A.A., Koch, P.N., Yang, R.J. [2004], Approximation methods in multidisciplinary analysis and optimization: a panel discussion, Structural and Multidisciplinary Optimization, 27 (5), pp. 302-313.
Smith, K.I., Everson, R.M., Fieldsend J.E. [2004], Dominance measures for multi-objective simulated annealing, In: Proceedings of the 2004 IEEE Congress on Evolutionary Computation, pp. 23- 30, IEEE Press.
Smits, G., Kotanchek, M. [2004], Pareto-front exploitation in symbolic regression, In: Genetic Programming Theory and Practice II, pp. 283-299, Springer, Ann Arbor.
Sobieszczanski-Sobieski J., Haftka R.T. [1997], Multidisciplinary aerospace design optimization: survey of recent developments, Structural Optimization, 14 (1), pp. 1-23.
Sobieski, I.P., Manning, V.M., Kroo, I.M. [1998], Response surface estimation and refinement in collaborative optimization, In: Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1, pp. 359-370.
Sommersel, T. [1997], Application of genetic algorithms in practical ship design, In: Proceedings of the 6th International Marine Conference, pp. 611-626, Newcastle.
Stamatis, D.H. [2002], Six Sigma and Beyond: Design for Six Sigma , Volume VI, CRC Press.
Stehouwer, H.P. , Hertog, D. den [1999], Simulation-based design optimisation: methodology and applications, In: Proceedings of the first ASMO-UK/ISSMO conference on Engineering Design Optimization, MCB University Press, Ilkley.
Stern, H. S. [1996], Neural networks in applied statistics, Technometrics, 38 (3), pp. 205-214.
Stinstra, E.D., Driessen, L.T., Stehouwer, H.P. [2001], Design optimization: Some pitfalls and their remedies, In: Proceedings of the third ASMO-UK/ISSMO conference on Engineering Design Optimization, Harrogate.
Sturm, J.F. [2002], Implementation of interior point methods for mixed semidefinite and second order cone optimization problems, Optimization Methods & Software, 17 (6), pp. 1105-1154. Su, J., Renaud, J.E. [1997], Automatic Differentiation in Robust Optimization, AIAA 35, pp. 1072-1079. Taguchi, G. [1993], Taguchi on Robust Technology Development: Bringing Quality Engineering Upstream,
ASME Press, New York.
Tang, B. [1993], Orthogonal array-based latin hypercubes, Journal of the American Statistical Association, 88, pp. 1392-1387.
Toropov. V.V. [1999], Multipoint approximations based on response surface fitting: a summary of recent developments. In: Proceedings of the first ASMO-UK/ISSMO Conference on Engineering Design Optimization, pp. 371-380, MCB University Press, Ilkley.
Toropov, V.V. [2005], Design optimization and stochastic analysis based on the moving least squares method, In: Proceedings of the 6th WCSMO conference, Rio de Janeiro.
Tosserams S., Etman, L.F.P., Papalambros, P.Y., Rooda, J.E. [2006], An augmented Lagrangian relaxation for analytical target cascading using the alternating directions method of multipliers, Structural and Multidisciplinary Optimization, 31, pp. 176-189.
Trocine, L., Malone, L.C. [2000], Finding important independent variables through screening designs: a comparison of methods, In: Proceedings of the Winter Simulation Conference 2000, pp. 749- 754.
Trosset, M.W. [1999], Approximate maximin distance designs, In: Proceedings of the Section on Physical and Engineering Sciences, pp. 223-227, Alexandria.
Vanderplaats, G. N. [1984], Numerical Optimization Techniques for Engineering Design, with Applications, McGraw-Hill, New York.
Vapnik, V., Golowich, S.E., Smola, A. [1997], Support vector method for function approximation, regression estimation, and signal processing. In: Advances in Neural IA Processings Systems, pp. 281-287, MIT Press, Cambridge.
Voncken, R.M.J., Van der Sluis, O., Post, J., Huétink, J. [2004], FEM calculations on a three stage metal forming process of Sandvik Nanoflex™, In: Proceedings of NumiForm 2004, Columbus. Wackernagel, H. [2003], Multivariate Geostatistics: An Introduction with Applications, 3rd edition, Springer-
Verlag, Berlin.
Waldron, S. [1998], Multipoint Taylor formulae, Numerische Mathematik, 80 (3), pp. 461-494.
Watson, G.A. [2004], Robust solutions to a general class of approximation problems, SIAM Journal on Scientific Computing, 25, pp. 1448-1460.
Welch, W.J., Buck, R.J., Sacks, J., Wynn, H.P. , Mitchell, T.J., Morris, M.D. [1992], Screening, predicting, and computer experiments, Technometrics, 34 (1), pp. 15-25.
Xu, D., Albin, S.L. [2003], Robust optimization of experimentally derived objective functions, IIE Transactions, 35 (9), pp. 793-802.
Yang, El-Haik [2003], Design for Six Sigma, McGraw-Hill, New York.
Zaraphonitis, G., Boulougouris, E., Papanikolaou, A. [2003], An integrated optimization procedure for the design of ro-ro passenger ships of enhanced safety and efficiency, In: Proceedings of the 8th Interanational Marine Design Conference, 1, pp. 313-324, Athens.
SAMENVATTING
Dit proefschrift gaat over optimalisatie methoden die special geschikt zijn voor optimalisatie rondom tijdrovende computer simulaties. Dergelijke methoden worden veelvuldig gebruikt bij het