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IEEE AP-S International Symposium Albuquerque NM, June 26, 2006. Optimization Using Broyden-Update Self-Adjoint Sensitivities. Dongying Li, N. K. Nikolova, and M. H. Bakr. (e-mail: [email protected] ). McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, CANADA.

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Optimization Using Broyden-Update Self-Adjoint Sensitivities

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Optimization using broyden update self adjoint sensitivities

IEEE AP-S International Symposium

Albuquerque NM, June 26, 2006

Optimization Using Broyden-Update Self-Adjoint Sensitivities

Dongying Li, N. K. Nikolova, and M. H. Bakr

(e-mail:[email protected])

McMaster University, 1280 Main Street West, Hamilton, ON

L8S 4K1, CANADA

Department of Electrical and Computer Engineering

Computational Electromagnetics Laboratory


Outline

Outline

objective & motivation

sensitivity analysis

  • design sensitivity analysis (DSA)

  • finite difference approximation (FD)

  • self-adjoint sensitivity analysis (SASA)

    SASA-based gradient optimization

  • theory: FD-SASA, B-SASA, B/FD-SASA

  • numerical results & comparison

    conclusion and future work


Objective motivation

Objective & Motivation

applications of DSA

gradient based optimization

yield and tolerance analysis

design of experiments and models

p(0)

Specs

p*

Gradient Based Optimizer

F(p(i))

p(i)

Design Sensitivity Analysis

F(p(i))

Numerical EM Solver


Design sensitivity analysis

Design Sensitivity Analysis

Given

FEM system equation

design variables

objective function

find subject to


Design sensitivity analysis via finite differences

Design Sensitivity Analysis via Finite Differences

easy and simple method

overhead: at least N additional system analyses


Design sensitivity analysis via sasa

Design Sensitivity Analysis via SASA

[N. K. Nikolova, J. Zhu, D. Li, M. Bakr, and J. Bandler, IEEE T-MTT. vol. 54, pp. 670-681, Feb, 2006.]

SASA for S-parameters

only original system solution needed


Design sensitivity analysis via sasa1

Design Sensitivity Analysis via SASA

computational overhead


Sasa based gradient optimization

gradient-based algorithms

quasi-Newton

sequential quadratic

programming (SQP)

trust-region

fast convergence vs.

non-gradient based algorithms

pattern search

neural network-based algorithms

genetic algorithms

particle swarm

guaranteed global minimum

SASA-Based Gradient Optimization


Sasa based gradient optimization1

SASA-Based Gradient Optimization

factors affecting efficiency

1. required number of iterations

nature of the algorithm

2. number of simulation calls per iteration

nature of the algorithm

the Jacobian computation


Sasa based gradient optimization2

SASA-Based Gradient Optimization

finite-difference SASA (FD-SASA)

overhead: N matrix fill

Broyden SASA (B-SASA)

overhead: practically zero


Sasa based gradient optimization3

SASA-Based Gradient Optimization

B/FD-SASA

guarantees robust derivative computation with minimum time

switch between B-SASA and FD-SASA

switching criteria from B-SASA to FD-SASA


Example of b fd sasa h plane filter

Example of B/FD-SASA: H-Plane Filter

design parameter

pT=[L1 L2 L3 W1 W2 W3 W4]

initial design

p(0)T = [12 14 18 14 11 11 11] (mm)

design requirement

optimization algorithm

TR-minimax

[G. Matthaei, L. Young and E. M. T. Jones, Microwave Filters, Impedance–Matching Networks, and Coupling Structures. 1980, pp. 545-547.]


Example of b fd sasa h plane filter1

Example of B/FD-SASA: H-Plane Filter

Initial design

FD optimal

B/FD-SASA optimal


Example of b fd sasa h plane filter2

Example of B/FD-SASA: H-Plane Filter

parameter step size with respect to iterations

function value with respect to iterations


Example of b fd sasa h plane filter3

finite difference

optimal design

pT = [12.226 14.042 17.483 14 11 10.922 11.341] (mm)

Iterations: 11

time: 3825 s

B/FD-SASA

optimal design

pT = [12.131 13.855 17.80914.01 11.1 11.098 11.191] (mm)

Iterations: 7

time: 949 s

Example of B/FD-SASA: H-Plane Filter

[switching criterion Itriggeredat 5th iteration]


Conclusion

Conclusion

summary

efficient SASA method for sensitivity analysis

implementation of B/FD-SASA on gradient-based optimization: improving efficiency

future work

further verification of the switching criteria in B/FD-SASA


Optimization using broyden update self adjoint sensitivities

Thank you


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