No Articulation of Preferences

1
No Articulation of Preferences

• Global Criterion or Weighted Metric (simple
  programming required)
• Unweighted
• Weighted (falls into Prior Articulation but will
  cover here).
• Can work in nonconvex spaces depending on value
  of exponent.
• MinMax (simple programming required)
• Unweighted
• Weighted
• Works in nonconvex objective spaces
• Benson (simple programming required)
• Works in nonconvex objective spaces

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No Preference Articulation
Most frequent values of p are 1 and 2 Obtains a
single point.
Figure from Anderson
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iSIGHT Steps Evaluate No Preference Articulation

• Added a Calculation Block to calculate the No
  Preference Objective
• Set a value for p
• Execute
• Perhaps change p and run again.

4
Add Calculation
5
No Preference Problem Formulation
6
Optimization Results with GRG
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Standard Tradeoff Curve
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Trying Other Values of P

• Could manually change values of p and rerun to
  explore impact of p.
• Alternatively, create a parent DOE task to
  automatically vary p.
• DOE parameter study will aggregate results
• Display with new EDM tool.

9
Create a Parent Task to Vary P
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Parameter Mapping
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Create a DOE Parameter Study for Parent Task to
Vary P
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Parameter Study to Vary P
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Must Clear Best Solution for Each Subtask Entry
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Solution Monitor of Parameter Study
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Standard Tradeoff Curve updated with 6 Points for
varying P
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EDM Data Configuration Specification
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EDM Parallel Coordinates
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Scatter Plot Matrix
19
Weighted No Preference

• User supplied weighting of each objective
• Can add a top level DOE to vary weights
• For p1 can get all solutions in a convex space
• For p 1 cannot get all solutions in non convex
  space.
• For large p can get all solutions in non convex
  space
• Uniform varying of weight does not guarantee
  uniform distribution

Belongs in Prior Articulation Category but
introduced here since on topic.
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DOE Driven Weight Variance
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DOE Values From Data File
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Sample of Data File
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Remember to Unset Best Run Info in Child Task
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Solution Monitor
25
Standard Tradeoff Curve
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Nonconvex Objective Space
27
Simple Nonconvex Problem
Minimize f1(x) x1 Minimize f2(x) 1 x2 x2
x1 a sin( b p x1) Subject to 0 lt x1
lt 1 -2 lt x2 lt 2 a .1 and b
3.0
Deb page 50
28
Non convex

• P 1 does not perform well in nonconvex spaces
  (essentially is just a weighted sum)
• As P increases the performance in nonconvex
  spaces gets better. Try P 5
• P infinity will be demonstrated with MinMax
  approach shown shortly.

29
Scatter Plot Matrix
P 1
P 5
NSGA 2
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MinMax Approach p -gt infinity
First will assume that weights are 1.
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MinMax Approach p -gt infinity
32
MinMax Problem Formulation
33
Optimization Results with GRG
34
Standard Tradeoff Curve
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Weighted MinMax

• Add weights to calculation
• Add an upper level DOE to vary weights
• Insure you call api_UnsetBestRunInfo in child
  task Optimization Prolog
• Can discover all points in convex and non convex
  space.
• Implementation issues

36
Add Weights to Calculation
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Add a DOE Parent Task
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Clear Run Info Before Each Optimization
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Solution Monitor
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Standard Tradeoff Curve
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Nonconvex Objective Space
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Standard Tradeoff Curve
43
Scatter Plot Matrix
Weighted MinMax
NSGA 2
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Vanderplaats Recommendation
Minimize Z Subject to abs(F1Weight
(F1 F1Optimal)/F1Optimal) lt Z
abs(F2Weight (F2
F2Optimal)/F2Optimal) lt Z
Z gt 0 Design Variables X1, X2, Z
45
Bensons Method

• M
• Maximize S m1 max(0, (zm0 - fm(x))) m
  1,2,,M
• Subject to fm(x) lt zm0 , m1,2,,M
• gj(x) lt 0, j 1,2,.,J
• hk(x) 0, k 1,2,.,K
• xi(L) lt xi lt xi(U) , i 1,2, , n
• Need to normalize each objective for weights to
  be meaningful. Normalize with z0

46
Bensons Method

• Advantages
• Can find pareto solutions in convex and non
  convex regions.
• Disadvantage
• Requires additional constraints

47
Benson Approach
Figure from Deb
48
iSIGHT Formulation

• First time we have Maximize Objective
• Initial feasible design point is 72,45,2,2
• Select a point in the feasible region as a
  reference solution. Some suggest nadir point (see
  next slide)
• Nadir point for IBeam is (850, .0613)

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Utopian Objective Vector
Figure from Deb p. 27
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Calculation for BensonObjective
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Problem Formulation for Benson
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Optimization with GRG
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Standard Tradeoff Curve
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Summary of No Articulation of Preferences

• Global Criterion or Weighted Metric (simple
  programming required)
• Unweighted
• Weighted (falls into Prior Articulation but will
  cover her.
• Can work in nonconvex spaces depending on value
  of exponent.
• MinMax programming
• Unweighted
• Weighted
• Works in noncovex objective spaces
• Benson programming
• Works in nonconvex objective spaces