Abstract
Space mapping (SM) has been one of the most popular surrogate-based optimization techniques in microwave engineering to date. By exploiting the knowledge embedded in the underlying coarse model (e.g., an equivalent circuit), SM allows dramatic reduction of the computational cost while optimizing electromagnetic (EM)-simulated structures such as filters or antennas. While potentially very efficient, SM is not always straightforward to implement and set up, and may suffer from convergence problems. In this chapter, we discuss several variations of an SM optimization algorithm aimed at improving SM performance for design problems involving EM simulations. These include SM with constrained parameter extraction and surrogate model optimization designed to overcome the problem of selecting preassigned parameters for implicit SM, SM with response surface approximation coarse models that maintain SM efficiency when a fast coarse model is not available, and SM with sensitivity which takes advantage of adjoint sensitivity (which has recently become commercially available in EM simulators) to improve the convergence properties and further reduce the computational cost of SM algorithms. Each variation of the SM algorithm presented here is illustrated using a real-world microwave design example.
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References
Bandler, J.W., Biernacki, R.M., Chen, S.H., Grobelny, P.A., Hemmers, R.H.: Space mapping technique for electromagnetic optimization. IEEE Trans. Microw. Theory Tech. 4, 536–544 (1994)
Bakr, M.H., Bandler, J.W., Georgieva, N.K., Madsen, K.: A hybrid aggressive space-mapping algorithm for EM optimization. IEEE Trans. Microw. Theory Tech. 47, 2440–2449 (1999)
Bakr, M.H., Bandler, J.W., Biernacki, R.M., Chen, S.H., Madsen, K.: A trust region aggressive space mapping algorithm for EM optimization. IEEE Trans. Microw. Theory Tech. 46, 2412–2425 (1998)
Amari, S., LeDrew, C., Menzel, W.: Space-mapping optimization of planar coupled-resonator microwave filters. IEEE Trans. Microw. Theory Tech. 54, 2153–2159 (2006)
Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidynathan, R., Tucker, P.K.: Surrogate-based analysis and optimization. Prog. Aerosp. Sci. 41, 1–28 (2005)
Forrester, A.I.J., Keane, A.J.: Recent advances in surrogate-based optimization. Prog. Aerosp. Sci. 45, 50–79 (2009)
Koziel, S., EcheverrÃa-Ciaurri, D., Leifsson, L.: Surrogate-based methods. In: Koziel, S., Yang, X.S. (eds.) Computational Optimization, Methods and Algorithms. Studies in Computational Intelligence, pp. 33–60. Springer, Berlin (2011)
Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Mohamed, A.S., Bakr, M.H., Madsen, K., Sondergaard, J.: Space mapping: the state of the art. IEEE Trans. Microw. Theory Tech. 52, 337–361 (2004)
Koziel, S., Ogurtsov, S.: Rapid design optimization of antennas using space mapping and response surface approximation models. Int. J. RF Microw. Comput.-Aided Eng. 21, 611–621 (2011)
Ouyang, J., Yang, F., Zhou, H., Nie, Z., Zhao, Z.: Conformal antenna optimization with space mapping. J. Electromagn. Waves Appl. 24, 251–260 (2010)
Zhu, J., Bandler, J.W., Nikolova, N.K., Koziel, S.: Antenna optimization through space mapping. IEEE Trans. Antennas Propag. 55, 651–658 (2007)
Schantz, H.: The Art and Science of Ultrawideband Antennas. Artech House, Boston (2005)
Wu, K.: Substrate integrated circuits (SiCs)—a new paradigm for future GHz and THz electronic and photonic systems. IEEE Circuits Syst. Soc. Newsl. 3, 1 (2009)
Koziel, S., Bandler, S.W., Madsen, K.: A space mapping framework for engineering optimization: theory and implementation. IEEE Trans. Microw. Theory Tech. 54, 3721–3730 (2006)
Koziel, S., Bandler, J.W., Madsen, K.: Quality assessment of coarse models and surrogates for space mapping optimization. Optim. Eng. 9, 375–391 (2008)
Bandler, J.W., Cheng, Q.S., Nikolova, N.K., Ismail, M.A.: Implicit space mapping optimization exploiting preassigned parameters. IEEE Trans. Microw. Theory Tech. 52, 378–385 (2004)
Koziel, S., Bandler, J.W.: Space-mapping optimization with adaptive surrogate model. IEEE Trans. Microw. Theory Tech. 55, 541–547 (2007)
Nocedal, J., Wright, S.: Numerical Optimization, 2nd edn. Springer, Berlin (2006)
Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385–482 (2003)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Upper Saddle River (1989)
Koziel, S., Cheng, Q.S., Bandler, J.W.: Space mapping. IEEE Microw. Mag. 9, 105–122 (2008)
Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. MPS-SIAM Series on Optimization. MPS-SIAM, Philadelphia (2009)
Alexandrov, N.M., Dennis, J.E., Lewis, R.M., Torczon, V.: A trust region framework for managing use of approximation models in optimization. Struct. Multidiscip. Optim. 15, 16–23 (1998)
Booker, A.J., Dennis, J.E. Jr., Frank, P.D., Serafini, D.B., Torczon, V., Trosset, M.W.: A rigorous framework for optimization of expensive functions by surrogates. Struct. Optim. 17, 1–13 (1999)
Amari, S., LeDrew, C., Menzel, W.: Space-mapping optimization of planar coupled-resonator microwave filters. IEEE Trans. Microw. Theory Tech. 54, 2153–2159 (2006)
Crevecoeur, G., Sergeant, P., Dupre, L., Van de Walle, R.: Two-level response and parameter mapping optimization for magnetic shielding. IEEE Trans. Magn. 44, 301–308 (2008)
Koziel, S., Cheng, Q.S., Bandler, J.W.: Implicit space mapping with adaptive selection of preassigned parameters. IET Microw. Antennas Propag. 4, 361–373 (2010)
Koziel, S., Bandler, J.W., Cheng, Q.S.: Constrained parameter extraction for microwave design optimization using implicit space mapping. IET Microw. Antennas Propag. 5, 1156–1163 (2011)
Koziel, S., Bandler, J.W.: Coarse and surrogate model assessment for engineering design optimization with space mapping. In: IEEE MTT-S Int. Microwave Symp. Dig., pp. 107–110 (2007)
Koziel, S., Bandler, J.W., Cheng, Q.S.: Robust trust-region space-mapping algorithms for microwave design optimization. IEEE Trans. Microw. Theory Tech. 58, 2166–2174 (2010)
Koziel, S., Bandler, J.W., Cheng, Q.S.: Adaptively constrained parameter extraction for robust space mapping optimization of microwave circuits. In: IEEE MTT-S Int. Microwave Symp. Dig., pp. 205–208 (2010)
Koziel, S., Bandler, J.W., Madsen, K.: Space-mapping based interpolation for engineering optimization. IEEE Trans. Microw. Theory Tech. 54, 2410–2421 (2006)
Lee, H.-M., Tsai, C.-M.: Improved coupled-microstrip filter design using effective even-mode and odd-mode characteristic impedances. IEEE Trans. Microw. Theory Tech. 53, 2812–2818 (2005)
FEKO User’s Manual. Suite 6.0. EM Software & Systems-S.A. (Pty) Ltd, 32 Techno Lane, Technopark, Stellenbosch, 7600, South Africa (2010)
Agilent ADS, Version 2011, Agilent Technologies, 395 Page Mill Road, Palo Alto, CA, 94304 (2011)
Kempbel, L.C.: Computational electromagnetics for antennas. In: Volakis, J.L. (ed.) Antenna Engineering Handbook, 4th edn. McGraw-Hill, New York (2007)
Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edn. Artech House, Boston (2005)
Jin, J.-M.: The Finite Element Method in Electromagnetics, 2nd edn. Wiley-IEEE Press, New York (2002)
CST Microwave Studio, ver. 2012. CST AG, Bad Nauheimer Str. 19, D-64289 Darmstadt, Germany (2012)
Kabir, H., Wang, Y., Yu, M., Zhang, Q.J.: Neural network inverse modeling and applications to microwave filter design. IEEE Trans. Microw. Theory Tech. 56, 867–879 (2008)
Murphy, E.K., Yakovlev, V.V.: Neural network optimization of complex microwave structures with a reduced number of full-wave analyses. Int. J. RF Microw. Comput.-Aided Des. 21 (2010)
Gutiérrez-Ayala, V., Rayas-Sánchez, J.E.: Neural input space mapping optimization based on nonlinear two-layer perceptrons with optimized nonlinearity. Int. J. RF Microw. Comput.-Aided Eng. 20, 512–526 (2010)
Tighilt, Y., Bouttout, F., Khellaf, A.: Modeling and design of printed antennas using neural networks. Int. J. RF Microw. Comput.-Aided Eng. 21, 228–233 (2011)
Kabir, H., Yu, M., Zhang, Q.J.: Recent advances of neural network-based EM-CAD. Int. J. RF Microw. Comput.-Aided Eng. 20, 502–511 (2010)
Siah, E.S., Ozdemir, T., Volakis, J.L., Papalambros, P., Wiese, R.: Fast parameter optimization using kriging metamodeling [antenna EM modeling/simulation]. In: IEEE Antennas and Prop. Int. Symp, pp. 76–79 (2003)
Siah, E.S., Sasena, M., Volakis, J.L., Papalambros, P.Y., Wiese, R.W.: Fast parameter optimization of large-scale electromagnetic objects using DIRECT with kriging metamodeling. IEEE Trans. Microw. Theory Tech. 52, 276–285 (2004)
Shaker, G.S.A., Bakr, M.H., Sangary, N., Safavi-Naeini, S.: Accelerated antenna design methodology exploiting parameterized Cauchy models. Prog. Electromagn. Res. 18, 279–309 (2009)
Xia, L., Meng, J., Xu, R., Yan, B., Guo, Y.: Modeling of 3-D vertical interconnect using support vector machine regression. IEEE Microw. Wirel. Compon. Lett. 16, 639–641 (2006)
Lophaven, S.N., Nielsen, H.B., Søndergaard, J.: DACE: a Matlab kriging toolbox. Technical University of Denmark (2002)
Beachkofski, B., Grandhi, R.: Improved distributed hypercube sampling. American Institute of Aeronautics and Astronautics, Paper AIAA, 2002–1274 (2002)
Petosa, A.: Dielectric Resonator Antenna Handbook. Artech House, Boston (2007)
RO4000 series high frequency circuit materials, data sheet. Publication no. 92-004, Rogers Corporation, Chandler, AZ (2010)
El Sabbagh, M.A., Bakr, M.H., Nikolova, N.K.: Sensitivity analysis of the scattering parameters of microwave filters using the adjoint network method. Int. J. RF Microw. Comput.-Aided Eng. 16, 596–606 (2006)
Koziel, S., Ogurtsov, S., Bandler, J.W., Cheng, Q.S.: Robust space mapping optimization exploiting EM-based models with adjoint sensitivity. In: IEEE MTT-S Int. Microwave Symp. Dig. (2012)
Alexandrov, N.M., Lewis, R.M.: An overview of first-order model management for engineering optimization. Optim. Eng. 2, 413–430 (2001)
Dielectric resonator filter, Examples, CST Microwave Studio, ver. 2011. CST AG, Bad Nauheimer Str. 19, D-64289 Darmstadt, Germany (2011)
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Koziel, S., Leifsson, L., Ogurtsov, S. (2013). Space Mapping for Electromagnetic-Simulation-Driven Design Optimization. In: Koziel, S., Leifsson, L. (eds) Surrogate-Based Modeling and Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7551-4_1
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