Constrained optimization involving expensive function evaluations: A sequential approach

European Journal of Operational Research

Volumn 160, Issue 1, 2005, Pages 121-138

  Brekelmans, Ruud ^a   Driessen, Lonneke ^b   Hamers, Herbert ^a   Den Hertog, Dick ^a  

^a TILBURG UNIVERSITY   (Netherlands)

^b Centre for Quantitative Methods   (Netherlands)

Author keywords

Derivative free optimization; Filter; Nonlinear programming; Trust region

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; EVALUATION; FINITE ELEMENT METHOD; FUNCTIONS; OPTIMIZATION;

DERIVATION FREE OPTIMIZATION; FILTERS; TRUST REGIONS;

NONLINEAR PROGRAMMING;

EID: 3943089779     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2003.10.009     Document Type: Conference Paper

References (28)

1. Audet C., Dennis J.E., Moore D.W., Booker A., Frank P.D. A surrogate-model-bases method for constrained optimization. American Institute of Aeronautics and Astronautics. 2000;1-10.
2. Balabanov V., Giunta A., Golovidov O., Grossman B., Mason W., Watson L., Haftka R. Reasonable design space approach to response surface approximation. Journal of Aircraft. 36(1):1999;308-315.
3. Bergveld, H., 2001. Battery Management Systems - Design by Modelling. PhD thesis, Technische Universiteit Twente.
4. Booker A.J., Dennis J.E., Frank P.D., Serafinni D.B., Torczon V., Trosset M.W. A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization. 17:1999;1-13.
5. Brekelmans, R., Driessen, L., Hamers, H., den Hertog, D., 2001. A new sequential optimization approach to product and process design involving expensive simulations. In: Querin, O.M. (Ed.), Proceedings of the Third ASMO UK/ISSMO Conference on Engineering Design Optimization: Product and Process Improvement. pp. 49-52.
6. Conn A.R., Gould N.I.M., Toint P.L. Trust-Region Methods. MPS/SIAM Series on Optimization. 2000;SIAM, Philadelphia.
7. Conn A.R., Scheinberg K., Toint P.L. Recent progress in unconstrained nonlinear optimization without derivatives. Mathematical Programming. 79(3):1997;397-414.
8. den Hertog D., Stehouwer H.P. Optimizing color picture tubes by high-cost non-linear programming. European Journal of Operational Research. 140(2):2002;197-211.
9. Dennis, J.E., Torczon, V., 1994. Derivative-free pattern search methods for multidisciplinary design problems. In: Proceedings of the AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL.
10. Driessen, L., Brekelmans, R., Hamers, H., den Hertog, D., 2001. On D-optimality based trust regions for black-box optimization problems. CentER Discussion Paper 2001-69, Tilburg University, The Netherlands.
11. Driessen, L., Parry, J., Stinstra, E., Stehouwer, P., 2003. Defining cooling strategies of electronic systems using dedicated derivative-free optimization. In: Proceedings of the Fifth World Congress of Structural and Multidisciplinary Optimization (WCSMO5), Lido di Jesolo, Italy.
12. Dykstra O. Jr. The augmentation of experimental data to maximize. |X′X| Technometrics. 13(3):1971;682-688.
13. Etman, L.F.P., 1997. Optimization of Multibody Systems Using Approximation Concepts. PhD thesis, Technische Universiteit Eindhoven.
14. Fletcher, R., Leyffer, S., 1998. Nonlinear programming without a penalty function. Numerical Analysis Report NA/171, University of Dundee, UK.
15. Glover, F., Kelly, J.P., Laguna, M., 1996. New advances and applications of combining simulation and optimization. In: Charnes, J.M., Morrice, D.J., Brunner, D.T., Swain, J.J. (Ed.), Proceedings of the 1996 Winter Simulation Conference. pp. 144-152.
16. Jones D.R., Schonlau M., Welch W.J. Efficient global optimization of expensive black-box functions. Journal of Global Optimization. 13:1998;455-492.
17. Jones D.R. A taxonomy of global optimization methods bases on response surfaces. Journal of Global Optimization. 21:2001;345-383.
18. Lewis, R.M., Torczon, V., Trosset, M.W. 1999. Direct search methods: Then and now. Working paper.
19. Marazzi M., Nocedal J. Wedge trust region methods for derivative free optimization. Mathematical Programming. 91(2):2002;289-306.
20. Powell, M.J.D., 1992. A direct search optimization method that models the objective and constraint function by linear interpolation. Numerical Analyses Report DAMTP 1992/NA5, University of Cambridge.
21. Powell, M.J.D., 2000. UOBYQA: Unconstrained optimization by quadratic approximation. Numerical Analysis Report DAMTP 2000/NA14, University of Cambridge.
22. Powell, M.J.D., 2002. Least Frobenius norm updating of quadratic models that satisfy interpolation conditions. Numerical Analyses Report DAMTP 2002/NA8, University of Cambridge.
23. Powell, M.J.D., 2003. On the use of quadratic models in unconstrained minimization without derivatives. Numerical Analyses Report DAMTP 2003/NA3, University of Cambridge.
24. Schittkowski K. More Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems. vol. 282:1987;Springer- Verlag, New York.
25. Schoofs, A.J.G., Roozen-Kroon, P.J.M., Campen, D.H.V., 1994. Optimization of structural and acoustical parameters of bells. In: Proceedings of the AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL.
26. The Mathworks, Inc., 2000. Optimization Toolbox For Use with MATLAB: User's Guide, Version 2.
27. Torczon, V., 1992. PDS: Direct search methods for unconstrained optimization on either sequential or parallel machines. Technical Report 92-09, Department of Computational and Applied Mathematics, Rice University, Houston, TX.
28. Toropov V.V., Filatov A.A., Polynkin A.A. Multiparameter structural optimization using FEM and multipoint explicit approximations. Structural Optimization. 6:1993;7-14.