eArtius - ANSYS Optimization Add-in webinar

Boosting Optimization Standards

eArtius and ANSYS Stretch the Limits of
Multi-Objective Design Optimization
Vladimir Sevastyanov
eArtius, Inc., Irvine, CA 92614, USA
vladimir@eartius.com

©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012

Agenda:
 eArtius Technology Overview
 eArtius-ANSYS Optimization Add-in
 Getting Started
 Demo
 Optimization Results
 eArtius Optimization Technology in Detail


eArtius Technology Overview

• eArtius is a company dedicated to development of a new innovative
Design Optimization Technology over last 14 years (US patents #6,417,852,
#7,593,834, #8,041,545):

• Software to Optimize Complex Designs that have predictive
mathematical models
– Hours/days to optimize high value designs
• Aerospace, automotive, turbo machinery, electronics, chemical processing,
ship design, weapons systems
– Main product—a PIDO application Pareto Explorer
– Other products: plug-ins for Simulia Isight, Noesis OPTIMUS, ESTECO
modeFrontier, ANSYS Workbench

• Breakthrough Optimization Algorithms
– Orders of magnitude faster than other algorithms
– Directed optimization on Pareto frontier
– Thousands of design variables

• Partnership with ANSYS since middle of 2011
– Two new products eArtius-ANSYS Optimization Add-in (local and remote)
have been developed for ANSYS users since then


Acknowledgement

Intevac Inc, Santa Clara, CA served as first beta site for eArtius ANSYS Add-
in. Dr. V. Kudriavtsev (Intevac) provided demo problems and valuable inputs
to make plug-in more suitable for ANSYS multi-physics users. Intevac utilized
plug-in for the development of optimal high power heating equipment for its
new c-Si solar cell manufacturing (Lean Solar) and for its hard disk media
deposition product lines.

Intevac c-Si Technology

http://www.intevac.com


Current Computational Design Process

8 threads i7
CPU
Comput DELAY Ingenious
er Solutions

240 cores TESLA Graphic
Processing Unit GPU (x2)
Human Thinking
and Analysis

slowest component

fastest component (meetings, reviews,
and grows exponentially faster
alignments, cancellations)


eArtius Optimization Add-in is Now
Available among Workbench Components
eArtius Optimization
Add-in is now
available as an add-
in to ANSYS
Workbench.
It can be found in the
Design Exploration
toolbox

With little more effort
than for a single
run, you can use
eArtius to drive
ANSYS Workbench

Leverage the parametric and persistent power of ANSYS
Workbench with the eArtius Optimization Add-in

Synergy of ANSYS & eArtius Technologies
 According to a Survey
performed by ANSYS, there
are some obstacles to
optimization (see the diagram)

 ANSYS and eArtius are
focused on removing the
most significant obstacles:
– ANSYS Workbench:
• Allows easily create
parametric models,
• and integrate add-ins
with WB
Optimization Add-in is designed specifically for
ANSYS users, and has excellent ROI value
– eArtius Optimization Add-in:
• Removes all integration issues; looks and behaves like part of WB
• Reduces integration cycle and learning curve to minutes
• Significantly reduces the number of design points required for a given
number of parameters


Multi-Objective Optimization
eArtius optimization algorithms solve optimization tasks with multiple objectives. For
instance, we need to minimize weight and cost, and maximize an engine efficiency.
The solution of the optimization task is a set of trade-offs (set of Pareto optimal points) found by
an optimization algorithm.
Why it is so important to use Pareto optimal designs?
– Because for any non-Pareto optimal design we can find at least one optimal design which
is better with respect to all objectives. It does not make any sense to use non-Pareto
optimal designs.

 Point C is not on the Pareto
Frontier because it is
dominated by both point A
and point B.

 Points A and B are not
dominated by any other, and
hence do lie on the frontier.

Example of a Pareto frontier. Smaller values are preferred to
©Copyright eArtius Inc 2012 All Rights Reserved larger ones. April 30, 2012

eArtius-ANSYS Optimization Add-ins
There are two separate eArtius-ANSYS Optimization Add-ins—local and
remote

Local Add-in is build into ANSYS Workbench GUI, and performs
optimization locally

Remote Add-in is also integrated with ANSYS WB in the same way as local
one, but optimization is performed remotely by eArtius stand alone
software Pareto Explorer (PE)

PE communicates with remote eArtius-ANSYS Optimization Add-in via
Internet, and allows to monitor and plot design points in real time

Remote Add-in is designed for advanced users

This presentation gives and idea about both add-ins, but it is focused
more on the local one


Overall Scheme of Interaction

eArtius Consol
Optimizers
(console
ANSYS
eArtius applications)
Workbench eArtius Add-in Local Add-in
(GUI
application)

eArtius eArtius Pareto Explorer
Remote Add-in
(Desktop Windows
application)


We will demonstrate use of add-in using
Stress and Deformation of Cantilever
Beam problem as a backdrop

Force
width

Fixed height

deformation
length

Min Deformation, Min Max Stress, min Weight
These are conflicting objectives.


Getting Started

1. Install the Add-in

2. Add to project
3. Transfer i/o parameters

After installation eArtius Optimization Add-in
appears in the Design Exploration section

Model Setup
Workbench Parameter
Workbench Main Set Screen
Screen


Optimization Model Setup
4. Define a simulation model and select an optimization algorithm

As follows from the Model Properties screenshot, a
few types of design variables are supported:
Constant/Double/Integer/Shortcut

Output variables can be set as constraints,
minimized/maximized objectives, or as ignored (No
Action) variables

There is an option to formulate an output variable as
an algebraic expression based on existent
input/output parameters—see Formula Editor

Optimization Properties
5. Specify parameters of the algorithm

6. Start optimization by clicking on ‘Update’,
and watch logs and a progress bar


Plot Results
7. Check the optimization results in the local mode
Charts allow to click on a marker, and see all properties of the selected point:

deformation

Mass stress

Grid allows to
see all
evaluated
solutions
and optimal
designs (green):

deformation

Selected point can be set as an initial point for further
improvement in the following optimization session

Selected Results

deformation deformation

Von Mises Stress deformation length

Force

Safety Factor deformation width
deformation

height Force


Getting Started
8. Observe runtime optimization results in the remote mode
eArtius Pareto Explorer is a full featured design optimization tool with a library of optimization
algorithms and powerful post-processing capabilities
Pareto Explorer is
a part of remote
eArtius-ANSYS
Add-in. It performs
optimization and
exchanges data
with ANSYS WB
via an HTTP
connection

Pareto Explorer
has OpenGL-based
interactive 2D/3D
graphics, and
allows observing
and analyzing
optimization
results in runtime.


OPTIMIZATION
EXAMPLES


Case Study 1:
Heat Sink Thermal Optimization

Alpha, heat transfer
Heat Flux coefficient

Convective and
Radiative Cooling

emissivity2 emissivity1

Flat Sheet of Aluminum serves as radiator heat sink, dumps heat via natural
convection and radiation to ambient. Heated locally in a small area by
electronics heat source with load from 50 to 5000W. Need to minimize heat
sink area (mass), determine if it is a suitable solution for high power range.
Max allowable temperature is limited in 70…150 deg. C

Model Setup


Model Setup
COMBI
optimization
algorithm builds
the optimization
strategy based
on available
time resource. It
does not require
any knowledge
or training from
users.

Selected design can be set as an initial point for further improvement by
an optimization algorithm

VIDEO 1

How to setup a model for optimization


Optimization Results

Tmin

Tmax
Heat Flux

deltaTmax



HMGE optimization algorithm has been
used for optimization of the model.
Pareto front looks like an almost linear
curve in the 3-dimensional criteria
space. It is filled by Pareto optimal
points evenly, which allows to choose
the best trade-off precisely.

Pareto front
includes at
least two
disjoint areas
in the design
space


VIDEO 2

How to observe optimization results
locally


Case Study 2:
Multi-Physics Steady State
Thermoelectric Simulation coupled with
Solid Works Shape Optimization and
Transient Radiative Heat Transfer for
Substrate Heat-up

left substrate

right

Design Modeler
(imports geometry parameters
Solid Works from Solid Works, modifies
Workbench+eArtius
model adding symmetry

Complex Multi Physics Problem
Design Modeler Parametric Steady State Thermo- Transient Radiation
Geometry interface with Solid Electric with Surface to with Surface to Surface
Surface Radiation Project folders
Works

Optimization Method
selection (MGE)

WorkBench status Bar
(stop button)

Optimization Messages updates (# of
data points computed)

Optimization Log output


Optimization Parameters
Heater Geometry dimension 1,
from Solid Works

Substrate Temperature
after short term transie
exposure to heater

F1= Tmax-350
F2=Tmin-350
350 =>desired process
temperature we want to
P23=P24 (heating on left reach
Heater Geometry dimension 2, side=heating on right)
from Solid Works
Electrical current runs through 3 separate heating elements creating temperature distribution. Electrical power in each heater equals I*V
and to minimize P18 we need to find optimal ratio of power between center and left/Right elements.



dT,
Deg. C
dT,
Deg. C

(Tmin-350), Deg. C
Heater Geometry dimension 1

dT,
dT,
Deg. C Want to pick best
Deg. C
Values for
geometry
dimensions
1 and 2

(Tmax-350), Deg. C
©Copyright eArtius Inc 2012 All Rights Reserved Heater Geometry dimension 2 April 30, 2012

Most Essential Result

dT,
Deg. C

Optimal Range of 35
interest found 31

(Tmax-350), Deg. C

These are demo results of overnight –run, so study is not complete. However, we instantly see relationship between key
conflicting variables (P18- maximum temperature difference in substrate) vs F1 – deviation from desired maximum
temperature. The larger F1 the lower maximum temperature during heat-up, that means lower thermal ramp (gradient), lower
power and thus lower temperature difference P18.
It is easy to have low temperature difference if you heat less, it means you loose less heat as well and thermal uniformity is
better. In this problem we need to heat more, thus we are interested in Pareto frontier distribution looking for multiple trade-
offs.


Summary Result

Global computational optimization
of heating module and element
designs to minimize temperature
difference on substrate surface
(DeltaT).

Optimization uses state-of-the art
hybrid genetic-multi-gradient
optimization methodology.

Dimension 2
Dimension 1

Plotting by EXCEL using CSV
export from eArtius

Increase in power
reduces
uniformity Optimal power ratio ~2


Conclusions to the ANSYS Add-in Section

 New design improvement technology is now available in ANSYS
 It is simple to use:
- Removes all integration issues; behaves like part of Workbench
- Reduces learning curve to minutes

 eArtius optimization technology finds better designs faster because
it is based on a multi-gradient analysis
 eArtius optimization algorithms:
- COMBI—simple to use, one parameter—builds optimization
strategy based on available time resource
- MGE/MGP/HMGE/HMGE—for advanced users
 Evaluation license is available for all webinar participants—for 2
months, no restrictions


Thank You!

Vladimir Sevastyanov
vladimir@eartius.com phone: 949-375-7647

Evaluation license is available for all webinar
participants—for 2 months, no restrictions

Installation package for the Windows version of
eArtius-ANSYS Optimization Add-in can be
downloaded from
http://www.eartius.com/download.html


Questions regarding ANSYS Add-in?

Next section is about eArtius design
optimization technology


Part II
eArtius Optimization Technology


Fundamental Design Optimization Issues
Study Motivation
The biggest issues of current design optimization
algorithms:
 Low computational efficiency
 Low scalability

Reasons:
 Absence of efficient algorithms for estimating gradients
 Curse of Dimensionality Phenomenon
 Searching for optimal solutions in the entire design space while the search
space can be reduced
 Approximating the entire Pareto frontier while the user only needs a small
part of it

Consequences:
 Artificially reduced task dimensions by arbitrarily excluding design
variables
 Overhead in use of global response surfaces and sensitivity analysis
 Have to rely only on use of brute-force methods such as algorithms’
parallelization


Curse of Dimensionality Phenomenon
and Design Optimization
Example of uniformly distributed points:
 Unit interval—0.01 distance between points—100
points
 10-dimensional unit hypercube, a lattice with 0.01
between neighboring points—1020 sample points
(Richard Bellman)
Adding extra dimensions to the design space
requires an exponential increase in the number of:

- Sample points necessary to build an adequate global surrogate model
- Pareto optimal points to maintain equal distance between neighboring optimal points in
the design space

How eArtius Addresses the Issues:
For Response Surface Methods:
- eArtius DDRSM spends just 0-7 points for local approximations—no global Response
Surfaces
For Approximation of the Entire Pareto Frontier:
- eArtius performs directed search on Pareto Frontier—no global approximation of the entire
Pareto frontier


Dynamically Dimensioned Response Surface
Method (DDRSM)
DDRSM evaluates gradients necessary for any gradient based
optimization algorithms.
Start iteration:
Start iteration: Builds local approximations
Builds local approximations
Determines the most
Determines the most for each response based
for each response based
How DDRSM operates: significant design variables
significant design variables only on the most
only on the most
for each response
for each response significant design variables
significant design variables
variable separately
variable separately

Analytically estimates
Analytically estimates
Performs a gradient
Performs a gradient gradients based on local
gradients based on local
based step
based step approximations
approximations
DDRSM Benefits:
 Equally efficient and accurate for any task dimension
 Requires just 0-7 model evaluations regardless of task dimension
 Fast— it builds a local approximation in 10-30 milliseconds
 Automatic and hidden from users
 Eliminates necessity in global response surface methods
 Eliminates necessity in a sensitivity analysis

Search in the Entire Design Space

Minimize f1  3  (1  x3 )  cos( x1   / 2)  cos( x2   / 2)
Minimize f 2  3  (1  x3 )  cos( x1   / 2)  sin( x2   / 2)
Minimize f 3  3  (1  x3 )  cos( x1   / 2)  sin( x1   / 2)
0  x1  0.65
0  x2  1
0.5  x3  1
2225 green points
visualize Pareto
frontier for the
above task

Pareto frontier
is located
on the flat x3=1
in the design space

Why do we need to search in the entire design space?
The search on the plane x3=1 would be more efficient

Multi-Gradient Pathfinder (MGP) Method

 On the first half-step MGP improves F1
preferable objective (F2)—green arrows

 On the second half-step MGP improves
ALL objectives—blue arrows—to maintain
a short distance to Pareto frontier

 Then MGP starts the next step from the
newly found Pareto optimal point

F2


Directed Optimization on Pareto Frontier

MGP started optimization three times from the same start point {x1=1; x2=1; x3=1},
but with different preferable objectives.
Green trajectory:
Min f1
Min f2
Min+ f3
Red trajectory:
Min+ f1;
Min f2
Min f3
Blue trajectory:
Min+ f1
Min f2
Min+ f3

Light-green small markers visualize entire Pareto frontier, which is located
on the plane x3=1 in the design space


Searching the Entire Design Space
is Not Productive!

ZDT2 Benchmark Problem: multiple Pareto frontiers

Minimize  F1  x1
  F 2 
Minimize F2  g  1   1  
 
 g 
 
 9 n 
g  1 

 xi 
n  1 i 2 
0  xi  1, i  1,..n
n  30

MGP—18 global Pareto optimal points out of 38 model evaluations
Pointer—5 optimal points out of 1500 evaluations
NSGA-II & AMGA—FAILED to find a single Pareto optimal point after
1500 evaluations!

Searching the Entire Design Space
is Not Productive!
g 110 (n 1)  (x2  x3 ... xn ) 10[cos( x2 )  cos( x3 ) ... cos( xn )],n 10
2 2 2
4 4 4
h 1 F / g  F / g  sin( F ); [ X ][0;1]
1 1 10 1
Minimize  F1  x1 MGP spent 185 evaluations, and found exact solutions
Minimize F2  g  h Pointer, NSGA-II, AMGA spent 2000 evaluations each, and failed


Hybrid Multi-Gradient Explorer (HMGE)
Optimization Algorithm

Synergy of the features brings
HMGE on unparalleled level of
efficiency and scalability Genetic Algorithm
Framework
HMGE is believed to be the
first global multi-objective
optimization algorithm which
provides:

- Efficiency in finding the Random Mutation Gradient Mutation
global Pareto frontier

- High convergence
typical for gradient-
based methods

- Scalability: Equal
efficiency optimizing
models with dozens, DDRSM – Super Fast Gradient Estimation
hundreds, and even
thousands of design
variables


COMBI Optimization Algorithm
 COMBI – takes just one
parameter – time
resource available for
optimization, and Time Resource = 8 hours ANSYS Model
dramatically simplifies
using the optimization
technology

 COMBI is a smart HMGE
wrapper for eArtius
optimization algorithms
MGE, MGP, and HMGE MGE MGP

 COMBI decides which
algorithm to use based
on a model analysis and
available time resource DDRSM – Super Fast Gradient Estimation

 COMBI is designed for
the users that need
benefits of optimization,
but do not have time to Output all Optimal Designs Found
learn optimization over 8 hours
technology

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