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Optimization Techniquesin
CST STUDIO SUITE
Vratislav Sokol, CST
www.cst.com
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Optimization algorithms in CST STUDIO SUITE
Classic Powell
Interpolated Quasi-Newton
Trust Region Framework
Nelder-Mead Simplex
Genetic Algorithm
Particle Swarm Optimization
General suggestions for optimizer setting
Examples
Waveguide corner
Dual-band matching circuit network
Planar filter tuning
Antenna array side lobes suppression
Agenda
www.cst.com
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Optimizer Window Overview
Solver Selection
Optimizer Choice
Automatically
choose parameter
boundaries
Parameter space
definition
Terminationcriterion
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Goal Function Overview (1)
You can choose to optimize
the sum of all goals or the
maximum of all goals
An arbitrary number of goals
can be defined. The optimizer
will try to satisfy all goals.
Goals are 0D, and can be derived from any 1D or 0D Result Template
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Goal Function Overview (2)
Possible operators are:
>,
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Optimizer - Goal Visualisation
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also in DS
Optimizer - Result Plots
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Local vs. Global Optimizers
local global
Genetic Algorithm
Particle Swarm Optimization
Nelder-Mead Simplex Algorithm
Trust Region Framework
Interpolated Quasi Newton
Classic Powell
Initial parameters already
give a good estimate of the
optimum, parameter ranges
are small
Initial parameters give a
poor estimate of the
optimum, parameter
ranges are large
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Classic Powell
Quasi Newton
Simplex (Nelder-Mead)
Genetic Algorithm
Particle Swarm
Trust Region Framework
Example 1: Waveguide Corner
x
y
Goal Minimize S11
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Classic Powell
A local optimizer that robustly finds an optimum within the given
parameter bounds. Sometimes, many iterations are necessary when
closing in on the optimum. This algorithm is suitable for one-variable
problems.
Optimization terminates
if two consecutive goal
values g1 and g2 yield
Accuracygg
gg
21
21 )(2
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Interpolated Quasi Newton
A Search algorithm for expensive problems: The parameter space issampled in each variable direction. EM simulations are only performed for
these discrete parameter space points. A model is created from these
evaluations and used for optimization. During the search, the model is
updated regularly by real evaluations.
The optimizer allows a restart
of the algorithm within an
automatically chosen smallerparameter range. This range
is determined by the previous
pass.
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Trust Region Framework
A fast and accurate optimizer that converges robustly and finds an
optimum within the given parameter bounds using a low number of
evaluations. It is suitable for 3D EM optimization.
If a normalized variation of
the parameters becomessmaller than this value, the
optimization terminates
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Trust Region Framework Algorithm (1)
Choose initial point
Create a local linear model around that point,and define an initial trust region radius, anarea in which we think the model is good.
Repeat:
Go to the minimizer (predicted optimum) ofthe model inside the trust-region
Verify: Does the error decrease?
If true, and if the model is very good, gofurther until quality gets worse, take last
point as new center. Reduce trust regionradius and calculate new model
Ifjust true, keep trust region radius andcalculate new model
If not true, reduce size of trust region.
0
x
0 10
1
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Trust Region Framework Algorithm (2)
Choose initial point
Create a local linear model around that point,and define an initial trust region radius, anarea in which we think the model is good.
Repeat:
Go to the minimizer (predicted optimum) ofthe model inside the trust-region
Verify: Does the error decrease?
If true, and if the model is very good, gofurther until quality gets worse, take last
point as new center. Reduce trust regionradius and calculate new model
Ifjust true, keep trust region radius andcalculate new model
If not true, reduce size of trust region.
0
x
0 10
1
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Trust Region Framework Algorithm (3)
Choose initial point
Create a local linear model around that point,and define an initial trust region radius, anarea in which we think the model is good.
Repeat:
Go to the minimizer (predicted optimum) ofthe model inside the trust-region
Verify: Does the error decrease?
If true, and if the model is very good, gofurther until quality gets worse, take last
point as new center. Reduce trust regionradius and calculate new model
Ifjust true, keep trust region radius andcalculate new model
If not true, reduce size of trust region.
0
x
0 10
1
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Trust Region Framework Algorithm (4)
Choose initial point
Create a local linear model around that point,and define an initial trust region radius, anarea in which we think the model is good.
Repeat:
Go to the minimizer (predicted optimum) ofthe model inside the trust-region
Verify: Does the error decrease?
If true, and if the model is very good, gofurther until quality gets worse, take last
point as new center. Reduce trust regionradius and calculate new model
Ifjust true, keep trust region radius andcalculate new model
If not true, reduce size of trust region.
0
x
0 10
1
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Trust Region Framework Algorithm (5)
Choose initial point
Create a local linear model around that point,and define an initial trust region radius, anarea in which we think the model is good.
Repeat:
Go to the minimizer (predicted optimum) ofthe model inside the trust-region
Verify: Does the error decrease?
If true, and if the model is very good, gofurther until quality gets worse, take last
point as new center. Reduce trust regionradius and calculate new model
Ifjust true, keep trust region radius andcalculate new model
If not true, reduce size of trust region.
0
x
0 10
1
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Trust Region Framework Algorithm (6)
The algorithm willbe converged once the
trust region radius or
distance to the next
predicted optimum
becomes smaller thanthe specified domain
accuracy.
0 10
1
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Global Optimizer Overview
Nelder Mead
An optimizer for more
complex problem
domains with good
convergence behavior:
Uses relatively few
evaluations if theproblem has a low
number of parameters
(i.e., less than 5 ).
Particle Swarm Genetic Algorithm
A global optimizer that
uses a higher number of
evaluations to explore
the search space, also
suited for larger
numbers of parameters(hint: use distributed
computing).
A global optimizer that
uses a high number of
evaluations to explore
the search space, suited
for large numbers of
parameters or verycomplex problem
domains (hint: use
distributed computing).
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1. Try to use a concise parameterization.
2. Try to keep the number of goal functions low.
3. Monitor parameter changes throughout optimization to gaininsight into convergence behavior.
4. Sometimes, re-formulating your goal function makes thedifference (e.g., min vs. move min).
5. You can use coarse parameter sweeps to determine goodinitial values and boundaries, and to support the right choiceof optimization algorithm.
6. If possible, use face constraints together with sensitivities incombination with the trust region optimizer.
General Suggestions
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Mobile Phone Antenna
Goal: Best impedance matching in bands 890-960 MHz and 1710-1880 MHz.
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Optimisation in CST DS (1)
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Optimisation in CST DS (2)
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Trust Region Framework + Sensitivity
www.cst.com
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TRF + Sensitivity: Results
www.cst.com
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Radiation pattern of 8x1 antennaarray is constructed from thefarfield of one element byapplying so called array factorusing template based post-
processing (TBPP). In the second step the side lobe
level is minimized using pureTBPP optimisation.
Post-Processing Optimisation
8x
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Optimisation of TBPP Steps
Optimise amplitudes and
phases of element excitationsas a post-processing step tominimise vertical plane side-
lobe levels.
vertical plane directivity
a1
a2
a3
a4
a5
a6a7
a8original an=1 SLL = -13.7 dB
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Optimisation of Side Lobe Levels
Optimise amplitudes andphases of element excitationsas a post-processing step tominimise vertical plane side-
lobe levels.
vertical plane directivity
a1
a2
a3
a4
a5
a6a7
a8original an=1 SLL = -13.7 dB
optimised an
SLL = -20 dB
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Optimisation of Side Lobe Levels
Method 3D TBPP
Time per 3D
simulation5 min 5 min
Number of 3Dsimulations
40 8
Time per
TBPP eval.30 sec 30 sec
Optimisation
steps40 40
Total
simulation
time
200
min
60
min
+
a1
a2
a3
a4
a5
a6
a7
a8original an=1 SLL = -13.7 dB
optimised an SLL = -20 dB
vertical plane directivityOptimisationComparison
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1. CST STUDIO SUITE 2011 offers a complete portfolioof optimization methods for various application.
2. A new Trust Region Framework algorithm is veryefficient tool for a direct 3D EM optimization
especially in conjunction with the sensitivityanalysis.
3. New visualization of goals and parameter values
4. Post-processing optimization without a need of any
EM or circuit solver5. A new Minimax goal function definition is now
available.
Summary