Optimal Design of Computationally Expensive EM-Based Systems: A Surrogate-Based Approach

It is quite a challenge to find the optimal design of computationally expensive engineering systems in different areas such as electrical engineering, structural mechanics, fluid dynamics, and electromagnetic-based (EM-based) systems. The optimal design of such systems requires solving huge optimization problems involving a lot of expensive function evaluations. For example, in microwave circuit design, a function evaluation requires running a full-wave electromagnetic simulator which may exhaust hours of CPU time. The total computational overhead makes the optimization of these engineering systems practically prohibitive. Computationally cheap surrogates (Response Surfaces, Space Mapping, Kriging models, Neural Networks, etc.) offer a good solution of such problems. Throughout the optimization process, iteratively updated surrogates are employed to replace the computationally expensive function evaluations.

[1]  Abdel-Karim S.O. Hassan,et al.  Statistical circuit design with the use of a modified ellipsoidal technique , 1997 .

[2]  M. J. Box.  A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems , 1966, Comput. J..

[3]  M. A. Styblinski,et al.  Algorithms and Software Tools for IC Yield Optimization Based on Fundamental Fabrication Parameters , 1986, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[4]  R. Brayton,et al.  Yield maximization and worst-case design with arbitrary statistical distributions , 1980 .

[5]  Sung-Mo Kang,et al.  Convexity-based algorithms for design centering , 1993, ICCAD '93.

[6]  E.A. Soliman,et al.  The Ellipsoidal Technique for Design Centering of Microwave Circuits Exploiting Space-Mapping Interpolating Surrogates , 2006, IEEE Transactions on Microwave Theory and Techniques.

[7]  M. Powell.  The NEWUOA software for unconstrained optimization without derivatives , 2006 .

[8]  S. Koziel,et al.  Space-mapping-based interpolation for engineering optimization , 2006, IEEE Transactions on Microwave Theory and Techniques.

[9]  E. M. Jones,et al.  Microwave Filters, Impedance-Matching Networks, and Coupling Structures , 1980 .

[10]  M. Powell.  A View of Algorithms for Optimization without Derivatives 1 , 2007 .

[11]  Kumaraswamy Ponnambalam,et al.  A unified approach to statistical design centering of integrated circuits with correlated parameters , 1999 .

[12]  Abdel-Karim S.O. Hassan,et al.  Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique , 2004 .

[13]  G. Hachtel,et al.  Computationally efficient yield estimation procedures based on simplicial approximation , 1978 .

[14]  T. Steihaug.  The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[15]  Ahmed Abdel-Naby,et al.  DESIGN CENTERING AND REGION APPROXIMATION USING SEMIDEFINITE PROGRAMMING , 2011 .

[16]  F. Giannessi,et al.  Nonlinear Optimization and Applications , 1996, Springer US.

[17]  Abdel-Karim S.O. Hassan,et al.  Statistical microwave circuit optimization via a non-derivative trust region approach and space mapping surrogates , 2011, 2011 IEEE MTT-S International Microwave Symposium.

[18]  A. A. Rabie,et al.  Non-derivative design centering algorithm using trust region optimization and variance reduction , 2006 .

[19]  Kurt Antreich,et al.  Circuit analysis and optimization driven by worst-case distances , 1994, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[20]  P. Toint,et al.  An Algorithm using Quadratic Interpolation for Unconstrained Derivative Free Optimization , 1996 .

[21]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[22]  John E. Dennis,et al.  A framework for managing models in nonlinear optimization of computationally expensive functions , 1999 .

[23]  Ya-Xiang Yuan,et al.  On the truncated conjugate gradient method , 2000, Math. Program..

[24]  J.W. Bandler,et al.  Space mapping interpolating surrogates for highly optimized EM-based design of microwave devices , 2004, 2004 IEEE MTT-S International Microwave Symposium Digest (IEEE Cat. No.04CH37535).

[25]  Hany L. Abdel-Malek,et al.  A boundary gradient search technique and its applications in design centering , 1999, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[26]  J. Bandler,et al.  Yield optimization for arbitrary statistical distributions: Part I-Theory , 1980 .

[27]  N. J. Elias.  Acceptance sampling: An efficient, accurate method for estimating and optimizing parametric yield , 1993, Proceedings of IEEE Custom Integrated Circuits Conference - CICC '93.

[28]  K. Singhal,et al.  Statistical design centering and tolerancing using parametric sampling , 1981 .

[29]  N. J. Elias.  Acceptance sampling: an efficient, accurate method for estimating and optimizing parametric yield /spl lsqb/IC manufacture/spl rsqb/ , 1994 .

[30]  Abdel-Karim S.O. Hassan,et al.  Surrogate-Based Circuit Design Centering , 2013 .

[31]  Abdel-Karim S.O. Hassan,et al.  A new hybrid method for optimal circuit design using semi-definite programming , 2012 .

[32]  Timothy N. Trick,et al.  An Extrapolated Yield Approximation Technique for Use in Yield Maximization , 1984, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[33]  Jacob Søndergaard.  Optimization using surrogate models - by the space mapping technique , 2003 .

[34]  Slawomir Koziel,et al.  Surrogate-Based Modeling and Optimization , 2013 .

[35]  Leszek J. Opalski,et al.  Design centering using an approximation to the constraint region , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  A. K. Ray.  DESIGN AND DEVELOPMENT OF 30 MEV, 3 KW RF ELECTRON LINAC , 2007 .

[37]  Abdel-Karim S.O. Hassan.  Normed Distances and Their Applications in Optimal Circuit Design , 2003 .

[38]  M. J. D. Powell,et al.  UOBYQA: unconstrained optimization by quadratic approximation , 2002, Math. Program..

[39]  Sung-Mo Kang,et al.  Statistical Performance Modeling and Parametric Yield Estimation of MOS VLSI , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[40]  Hany L. Abdel-Malek,et al.  The ellipsoidal technique for design centering and region approximation , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[41]  N Pichoff.  Introduction to RF linear accelerators , 2006 .

[42]  Michel Nakhla,et al.  A neural network modeling approach to circuit optimization and statistical design , 1995 .

[43]  R. Kielbasa,et al.  A study of stratified sampling in variance reduction techniques for parametric yield estimation , 1998 .

[44]  Helmut Graeb,et al.  Analog Design Centering and Sizing , 2007 .

[45]  Thomas Wangler,et al.  Principles of RF linear accelerators , 1998 .

[46]  S. Koziel,et al.  Space-Mapping Optimization With Adaptive Surrogate Model , 2007, IEEE Transactions on Microwave Theory and Techniques.

[47]  J. Bandler,et al.  Optimal centering, tolerancing, and yield determination via updated approximations and cuts , 1978 .

[48]  Thomas P. Wangler,et al.  Principles RF Linear Accelerators: Wangler/Principles , 2008 .

[49]  Jirí Vlach,et al.  Ellipsoidal method for design centering and yield estimation , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[50]  M. Roma,et al.  Large-Scale Nonlinear Optimization , 2006 .