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©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
eArtius and ANSYS Stretch the Limits of Multi-Objective Design Optimization
Vladimir SevastyanoveArtius, Inc., Irvine, CA 92614, USA
Boosting Optimization Standards
©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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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.
http://www.intevac.com
Acknowledgement
Intevac c-Si Technology
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Current Computational Design Process
Comput er
8 threads i7 CPU
240 cores TESLA Graphic Processing Unit GPU (x2)
slowest component
(meetings, reviews, alignments, cancellations)
Ingenious
Solutions
Human Thinking
and Analysis
fastest component and grows exponentially faster
D E L A Y
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
– 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
Optimization Add-in is designed specifically for ANSYS users, and has excellent ROI value
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Multi-Objective OptimizationeArtius 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 larger ones.
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
eArtius-ANSYS Optimization Add-ins
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
eArtius Consol Optimizers
(consoleapplications)
eArtius Pareto Explorer(Desktop Windows
application)
eArti
us A
dd-in
ANSYS Workbench(GUI application)
eArtiusLocal Add-in
eArtiusRemote Add-in
Overall Scheme of Interaction
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
We will demonstrate use of add-in using Stress and Deformation of Cantilever
Beam problem as a backdrop
Min Deformation, Min Max Stress, min Weight These are conflicting objectives.
deformation
Force
length
height
width
Fixed
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Getting Started
1. Install the Add-in
2. Add to project3. Transfer i/o parameters
After installation eArtius Optimization Add-in appears in the Design Exploration section
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Model SetupWorkbench Parameter Set ScreenWorkbench Main
Screen
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4. Define a simulation model and select an optimization algorithm
Optimization Model Setup
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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
5. Specify parameters of the algorithm
6. Start optimization by clicking on ‘Update’, and watch logs and a progress bar
Optimization Properties
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
7. Check the optimization results in the local mode
Grid allows to see all evaluated solutions and optimal designs (green):
Charts allow to click on a marker, and see all properties of the selected point:
Plot Results
Selected point can be set as an initial point for further improvement in the following optimization session
deformation
stressMass
deformation
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Safety Factor
Force
Von Mises Stress
deformation deformation
deformation
deformation
length
height
width
Force
deformation
Selected Results
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
8. Observe runtime optimization results in the remote modeeArtius 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.
Getting Started
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
OPTIMIZATION EXAMPLES
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
Case Study 1: Heat Sink Thermal Optimization
Heat Flux
Convective and Radiative Cooling
emissivity1emissivity2
Alpha, heat transfer coefficient
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Model Setup
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Model Setup
Selected design can be set as an initial point for further improvement by an optimization algorithm
Combi optimization algorithm builds the optimization strategy based on available time resource. It does not require any knowledge or training from users.
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
VIDEO 1
How to setup a model for optimization
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Optimization Results
Tmax
Tmin
deltaTmax
Heat Flux
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Optimization Results
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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
VIDEO 2
How to observe optimization results locally
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Case Study 2: Multi-Physics Steady State
Thermoelectric Simulation coupled with Solid Works Shape Optimization and Transient Radiative Heat Transfer for
Substrate Heat-up
Solid WorksDesign Modeler (imports geometry parameters from Solid Works, modifies model adding symmetry
Workbench+eArtius
substrateleft
right
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Complex Multi Physics Problem
Optimization Log output
Optimization Messages updates (# of data points computed)
Optimization Method selection (MGE)
WorkBench status Bar (stop button)
Steady State Thermo- Electric with Surface to Surface Radiation
Transient Radiation with Surface to Surface
Design Modeler Parametric Geometry interface with Solid Works
Project folders
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Optimization Parameters
Heater Geometry dimension 2, from Solid Works
Heater Geometry dimension 1, from Solid Works
P23=P24 (heating on left side=heating on right)
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.
Substrate Temperature after short term transie exposure to heater
F1= Tmax-350 F2=Tmin-350350 =>desired process temperature we want to reach
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Optimization Results
Heater Geometry dimension 1
Heater Geometry dimension 2
dT,Deg. C
dT,Deg. C
dT,Deg. C
dT,Deg. C
(Tmax-350), Deg. C
(Tmin-350), Deg. C
Want to pick bestValues for geometry dimensions 1 and 2
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Most Essential Result
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.
dT,Deg. C
(Tmax-350), Deg. C
3135Optimal Range of
interest found
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Summary Result
Global computational optimizationof 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.
Optimal power ratio ~2Increase in power reducesuniformity
Plotting by EXCEL using CSV export from eArtius
Dimension 1Dimension 2
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Thank You!
Vladimir [email protected] 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
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Questions regarding ANSYS Add-in?
Next section is about eArtius design optimization technology
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Part II eArtius Optimization Technology
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
Fundamental Design Optimization Issues Study Motivation
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
- 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
SurfacesFor Approximation of the Entire Pareto Frontier:- eArtius performs directed search on Pareto Frontier—no global approximation of the entire
Pareto frontier
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:
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
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
DDRSM evaluates gradients necessary for any gradient based optimization algorithms.
How DDRSM operates:Start iteration:
Determines the most significant design variables
for each responsevariable separately
Start iteration:Determines the most
significant design variablesfor each responsevariable separately
Builds local approximations for each response based
only on the most significant design variables
Builds local approximations for each response based
only on the most significant design variables
Analytically estimates gradients based on local
approximations
Analytically estimates gradients based on local
approximations
Performs a gradient based step
Performs a gradient based step
Dynamically Dimensioned Response Surface Method (DDRSM)
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
2225 green points visualize Pareto frontier for the above task
Pareto frontier is located on the flat x3=1in the design space
Search in the Entire Design Space
15.0 3 x10 2 x
65.00 1 x
)2/sin()2/cos()1(3 1133 xxxfMinimize
)2/sin()2/cos()1(3 2132 xxxfMinimize
)2/cos()2/cos()1(3 2131 xxxfMinimize
Why do we need to search in the entire design space? The search on the plane x3=1 would be more efficient
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
On the first half-step MGP improvespreferable objective (F2 )—green arrows
On the second half-step MGP improvesALL objectives—blue arrows—to maintaina short distance to Pareto frontier
Then MGP starts the next step from the newly found Pareto optimal point
Multi-Gradient Pathfinder (MGP) Method
F1
F2
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
MGP started optimization three times from the same start point {x1=1; x2=1; x3=1},but with different preferable objectives. Green trajectory:Min f1Min f2Min+ f3Red trajectory: Min+ f1; Min f2Min f3Blue trajectory:Min+ f1 Min f2Min+ f3
Light-green small markers visualize entire Pareto frontier, which is located on the plane x3=1 in the design space
Directed Optimization on Pareto Frontier
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
MGP—18 global Pareto optimal points out of 38 model evaluations Pointer—5 optimal points out of 1500 evaluationsNSGA-II & AMGA—FAILED to find a single Pareto optimal point after
1500 evaluations!
Searching the Entire Design Space is Not Productive!
30,..1,10
191
1
2
2
12
11
nnix
xn
g
gFgFMinimize
xFMinimize
i
n
ii
ZDT2 Benchmark Problem: multiple Pareto frontiers
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
MGP spent 185 evaluations, and found exact solutionsPointer, NSGA-II, AMGA spent 2000 evaluations each, and failed
Searching the Entire Design Space is Not Productive!
hgFMinimizexFMinimize
XFgFgFh
nxxxxxxng nn
2
11
111
3222
322
]1;0[][);10sin(//1
10)],4cos(...)4cos()4[cos(10)...()1(101
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Hybrid Multi-Gradient Explorer (HMGE) Optimization Algorithm
Synergy of the features brings HMGE on unparalleled level of efficiency and scalability
HMGE is believed to be the first global multi-objective optimization algorithm which provides:
- Efficiency in finding the global Pareto frontier
- High convergence typical for gradient- based methods
- Scalability: Equal efficiency optimizing models with dozens, hundreds, and even thousands of design variables
Genetic Algorithm Framework
Random Mutation Gradient Mutation
DDRSM – Super Fast Gradient Estimation
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
COMBI Optimization Algorithm
MGE
DDRSM – Super Fast Gradient Estimation
HMGE
MGP
Output all Optimal Designs Found over 8 hours
ANSYS ModelTime Resource = 8 hours
COMBI – takes just one parameter – time resource available for optimization, and dramatically simplifies using the optimization technology
COMBI is a smart wrapper for eArtius optimization algorithms MGE, MGP, and HMGE
COMBI decides which algorithm to use based on a model analysis and available time resource
COMBI is designed for the users that need benefits of optimization, but do not have time to learn optimization technology
©Copyright eArtius Inc 2012 All Rights Reserved April 30, 2012
Thank You!
Vladimir [email protected] 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