Optimization Methods for Computer-Aided Design

This paper surveys record automatic optimization methods which either have found or should find useful application in the optimal design of microwave networks by digital computer. Emphasis is given to formulations and methods which can be implemented in situations when the classical synthesis approach (analytic or numerical) is inappropriate. Objectives for network optimization are formulated including minimax and least pth. Detailed consideration is given to methods of dealing with parameter and response constraints by means of transformations or penalties. In particular, the formulation of problems in terms of inequality constraints and their solution by sequential unconstrained minimization is discussed. Several one-dimensional and multidimensional minimization strategies are summarized in a tutorial manner. Included are Fibonacci and Golden Section search, interpolation methods, pattern search, Rosenbrock's method, Powell's method, simplex methods, and the Newton-Raphson, Fletcher-Powell, and least squares methods. Relevant examples of interest to microwave circuit designers illustrating the application of computer-aided optimization techniques are presented. The paper also includes a classified list of references.

[1]  P. A. Macdonald,et al.  Cascaded Noncommensurate Transmission-line Networks as Optimization Problems , 1969 .

[2]  Allan W. Dickinson.  Nonlinear optimization: Some procedures and examples , 1964 .

[3]  D. Goldfarb,et al.  Conjugate Gradient Method for Nonlinear Programming Problems with Linear Constraints , 1968 .

[4]  M. L. Tsetlin,et al.  The Principle of Nonlocal Search in Automatic Optimization Systems , 1961 .

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

[6]  D. Kammler.  The Design of Discrete N-Section and Continuously Tapered Symmetrical Microwave TEM Directional Couplers , 1969 .

[7]  G. R. Hext,et al.  Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation , 1962 .

[8]  R. E. Kalman,et al.  Optimum Seeking Methods. , 1964 .

[9]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[10]  H. S. Hewitt.  A Computer Designed, 720 to 1 Microwave Compression Filter , 1967 .

[11]  J. R. Palmer.  An Improved Procedure for Orthogonalising the Search Vectors in Rosenbrock's and Swann's Direct Search Optimisation Methods , 1969, Comput. J..

[12]  H. Cooke,et al.  Computer design and optimization of UHF and microwave circuits , 1967 .

[13]  Patrick D. Krolak,et al.  An extension of Fibonaccian search to several variables , 1963, CACM.

[14]  J. B. Rosen.  The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints , 1960 .

[15]  Leon S. Lasdon,et al.  Nonlinear Programming Applied to Linear‐Array Design , 1966 .

[16]  L. Lasdon,et al.  Optimal Design of Filters with Bounded, Lossy Elements , 1966 .

[17]  R. Fletcher,et al.  Function Minimization Without Evaluating Derivatives - a Review , 1965, Comput. J..

[18]  Anthony V. Fiacco,et al.  The Sequential Unconstrained Minimization Technique for Nonlinear Programing, a Primal-Dual Method , 1964 .

[19]  M. J. Box,et al.  Non-linear optimization techniques; , 1969 .

[20]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[21]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[22]  G. W. Stewart,et al.  A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives , 1967, JACM.

[23]  B. V. Shah,et al.  Some Algorithms for Minimizing a Function of Several Variables , 1964 .

[24]  R. Crane,et al.  All-Pass Network Synthesis , 1968 .

[25]  John W. Bandler.  Optimum noncommensurate stepped transmission-line transformers , 1968 .

[26]  A. Wexler.  Computation of Electromagnetic Fields , 1969 .

[27]  J. Stoer,et al.  Rational Chebyshev approximation , 1967 .

[29]  Gabor C. Temes,et al.  Computer-aided network optimization the state-of-the-art , 1967 .

[30]  J. B. Rosen.  The gradient projection method for nonlinear programming: Part II , 1961 .

[31]  J. D. Pearson.  ON VARIABLE METRIC METHODS OF MINIMIZATION , 1968 .

[32]  William C. Davidon,et al.  Variance Algorithm for Minimization , 1968, Comput. J..

[33]  P. A. Macdonald,et al.  Optimization of Microwave Networks by Razor Search , 1969 .

[34]  R. Kwan,et al.  Simultaneous Approximations in Filter Design , 1969 .

[35]  V. G. Gelnovatch,et al.  Computer Aided Design of Wide-Band Integrated Microwave Transistor Amplifiers on High Dielectric Substrates , 1968 .

[36]  E. A. Huber.  Letter to the editor: Comments on “review of design optimization techniques” , 1966 .

[37]  Charles W. Carroll.  The Created Response Surface Technique for Optimizing Nonlinear, Restrained Systems , 1961 .

[38]  Gabor C. Temes,et al.  Least pth Approximation , 1969 .

[39]  H. Watanabe,et al.  An Iterative Chebyshev Approximation Method for Network Design , 1968 .

[40]  G. McCormick,et al.  Selected applications of nonlinear programming , 1968 .

[41]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[42]  M. Wells.  Algorithm 251: function minimisation [E4] , 1965, CACM.

[43]  W. McGee,et al.  Numerical Approximation Technique for Filter Characteristic Functions , 1967, IEEE Transactions on Circuit Theory.

[44]  Anthony V. Fiacco,et al.  Computational Algorithm for the Sequential Unconstrained Minimization Technique for Nonlinear Programming , 1964 .

[45]  Douglass J. Wilde,et al.  Foundations of Optimization. , 1967 .

[46]  Willard I. Zangwill,et al.  Minimizing a function without calculating derivatives , 1967, Comput. J..

[47]  G. Zoutendijk.  Nonlinear Programming: A Numerical Survey , 1966 .

[48]  C. Desoer,et al.  Design of Lossy Ladder Filters by Digital Computer , 1961 .

[49]  John W. Bandler,et al.  Computer Optimization of a Stabilizing Network for a Tunnel-Diode Amplifier , 1968 .

[50]  H. Spang.  A Review of Minimization Techniques for Nonlinear Functions , 1962 .

[51]  Ronald A. Rohrer,et al.  Fully automated network design by digital computer: Preliminary considerations , 1967 .

[52]  F. E. Emery,et al.  Optimal Design of Matching Networks for Microwave Transistor Amplifiers , 1966 .

[53]  M. J. Box.  A New Method of Constrained Optimization and a Comparison With Other Methods , 1965, Comput. J..

[54]  Hans P. Künzi,et al.  Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs , 1970, The Mathematical Gazette.

[55]  M. J. D. Powell,et al.  On the calculation of orthogonal vectors , 1968, Comput. J..

[56]  R. Rohrer,et al.  Automated Network Design-The Frequency-Domain Case , 1969 .

[57]  Patrick D. Krolak,et al.  Further Extensions of Fibonaccian Search to Nonlinear Programming Problems , 1968 .

[58]  Cyrus F. Wood,et al.  Review of Design Optimization Techniques , 1965, IEEE Trans. Syst. Sci. Cybern..

[59]  R. Hesse.  Recent Advances in Optimization Techniques , 1968 .

[60]  J. D. Pearson.  Variable metric methods of minimisation , 1969, Comput. J..

[61]  G. Alistair Watson,et al.  An Algorithm for Minimax Approximation in the Nonlinear Case , 1969, Comput. J..

[62]  René de Vogelaere,et al.  Remark on algorithm 178: Direct search , 1968, Commun. ACM.

[63]  Leon S. Lasdon,et al.  Optimization in engineering design , 1967 .

[64]  J. Bingham,et al.  Iterative Chebyshev Approximation Technique for Network Synthesis , 1967, IEEE Transactions on Circuit Theory.

[65]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[66]  John W. Bandler,et al.  Computer Optimization of Inhomogeneous Waveguide Transformers , 1969 .

[67]  M. Aaron,et al.  The Use of Least Squares in System Design , 1956 .

[68]  M. J. D. Powell,et al.  A Method for Minimizing a Sum of Squares of Non-Linear Functions Without Calculating Derivatives , 1965, Comput. J..

[69]  L. Cooper,et al.  Sequential Search: A Method for Solving Constrained Optimization Problems , 1965, JACM.

[70]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[71]  C. G. Broyden.  A New Method of Solving Nonlinear Simultaneous Equations , 1969, Comput. J..

[72]  J. P. Shelton,et al.  Synthesis and Design of Wide-Band Equal-Ripple TEM Directional Couplers and Fixed Phase Shifters , 1966 .