Basics of MOO

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Multi-Attribute OptimizationBased on Conjoint
Analysis
Hemanth Amarchinta, Ramana Grandhi
Computational Design and Optimization Center
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Outline

• Conjoint Analysis
• Combining Marketing and Engineering
• Engineering Applications
• Conclusions

• Understanding Multi-Attribute Optimization
• Methods available

? Constrained Method ? Weighted Sum Method
? Camera Example
? Cantilever Beam Example
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Solving MAO
STEP1
S T E P 2
Higher level Information is needed
Multiple tradeoffs obtained
Choosing one solution
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Methods

• Constraint Method
• Weighted Sum Method
• Value function Method
• Evolutionary Methods

Constraint Method Weighted Sum Method
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Constrained Method
Subject to

• Preference is set by maximum levels, No real
  trade-offs
• If ,

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Weighted sum method
Here Constraints are converted into an objective
function by assigning weights to each function

• Pay 10 for each increase in comfort level,
  regardless
• of current comfort level which may not be
  true

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Conjoint Analysis (CA)
Conjoint analysis is a technique to break down
attributes for deriving Part Worth associated
with attributes for each level of a product based
on the overall preferences of choice alternatives
by a group of respondents.
Buying a Car Make Two door or Four
Door Engine Color
How much importance is given to each attribute ?
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CA Camera Example
Quality Price
Attributes
Levels for Each attribute
Quality ? High, Medium, Low Price ? 200, 400,
600
Combinations
3 x 3 9 Combinations
Questionnaire Rank based
Preferences
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CA Camera Example
Dummy variable method and Least Squares are used
to calculate Part Worth

• We know which attribute is important
• We know range of importance
• Part Worth provides valuable information in
  developing a new product

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Combining Marketing and Engineering
Marketing
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Cantilever Beam
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Displacement Study
Aim Minimize mass and tip displacement
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Displacement Study Contd
Conjoint-based Approach
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Displacement Study Contd
Result Obtained Mass 1.7963 lb Max Disp 0.1104
in Width 0.5in, Height 1.7963in
For a 11 increase in Mass, there is a 26
decrease in Displacement
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Disp Stress Study
Aim Minimize mass, displacement and stress
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Disp Stress Study contd..
4 levels for each attribute are considered Total
of 64 combinations are possible, Only 30
combinations are considered and ranking based
preference is followed
Calculated Part Worths
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Disp Stress Study contd..
f1
f2
f3
Min f1f2f3
Results obtained Mass 2.3094 lb Stress
9000.08 psi Displacement 0.052 in Width 0.5 in
, Height 2.3094 in
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Conclusions

• Preference - based optimization is needed
• Conjoint Analysis provides a trade-off solution
• Techniques from other fields can be used as
  shown
• Applications to Engineering are shown by solving
  cantilever
• beam example

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Thank for your time
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• Cutting the slides as time is not enough for
  presentation

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Understanding MAO
Aim Minimize Cost and Maximize Comfort

• We have multiple optimum solutions
• For Comfort as criterion Solution 2 is best
• For Cost as criterion Solution 1 is best
• Sacrifices--a, b, c, d are candidate
• solutions
• No solution is superior

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Flow Chart for CA