Posteriori Articulation of Preferences

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Posteriori Articulation of Preferences

• Weighted Sum Driven By DOE - programming
• eConstraint Tradeoff Study no programming
• Multiobjective Genetic Algorithm no programming
• Weighted Goal Programming (not demonstrated)
• Weighted Min Max (previously demonstrated)
• Weighted Benson (not demonstrated)

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Weighted Sum Approach With iSIGHT Automatically
Varying Wgts

• Minimize f(x) S wmfm(x)
• Subject to gj(x) lt 0, j 1,2,.,J
• hk(x) 0, k 1,2,.,K
• M
• S m1 wm 1
• xi(L) lt xi lt xi(U) , i 1,2, , n
• Need to normalize each objective for weights to
  be meaningful.

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Weighed Sum Formulation For Pareto Curve

• Add a Calculation to calculate weighted sum.
• Insure add api_UnsetBestRunInfo tcl api to
  Optimization Step Prologue
• Add a parent DOE from file task with 2 parameters
  to vary weight 1 (CrossSectionAreaWeight) and
  weight 2 (StaticDeflectionWeight) in .1
  increments (e.g.weight 1 .1 weight 2
  .9weight 1 .2 weight 2 .8
• .

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Add Calculation to Beam Task
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Add Parent Task With Parameter Mapping
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Create DOE for Parent Task
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DOE Study from Datafile
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Problem Formulation
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Solution Monitor
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Standard Tradeoff Curve
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EDM Parallel Coordinates Plot
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Scatter Plot Matrices
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Summary of Weighted Sum

• Simplest and perhaps most widely used
• If convex objective space then every point can be
  found.
• A uniformly distributed set of weight vectors
  will not necessarily get a uniform distributed
  set of pareto-optimal solutions.

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e-Constraint Approach
Idea is to have a single objective and make the
others constraints.
Figure from Deb
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e-Constraint
Figure from Deb
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e-Constraint

• Advantages
• Works in convex and non convex spaces
• Can find all points on pareto optimal front
• Fully supported without programming in iSIGHT.
• Disadvantage
• Requires user to select appropriate values of
  constraints

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iSIGHT Implementation

• Single task single level
• Single objective Minimize StaticDeflection
• Additional constraint for upper bound to
  CrossSectionArea
• Vary CrossSectionArea using iSIGHT Tradeoff Study

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Single Objective to Min StaticDeflection
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Tradeoff Analysis in 100 increments for Cross
Section Area
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Make Tradeoff Study the Task Plan
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Solution Monitor Tradeoff Study
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Standard Tradeoff Curve With eConstraint
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MOGA Multi Objective Genetic Algorithms

• New GA methods to create entire pareto optimal
  set on one run, NSGA2 or NCGA.
• Both do the same thing.
• Decision to choose one over the other is one
  based solely on preference.
• Works on NLP, INLP and MINLP problems
• For this portion, I will focus on NSGA 2
• No programming is required. Fully supported
  within GUI.

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Genetic and Evolutionary Algorithms

• Citations per year (from Coello)
• 1992 6
• 1995 - 60
• 1998 - 145
• 2001 120
• Many interesting 2nd generational approaches
  PAES, SPEA, NSGA-II, micro-GA

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Difference in Single Objective GA and
Multi-Objective GA
Difference in Single Objective GA and
Multiobjective GA
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Desirable Features in Multi-objective GA
1. Strong approach to the Pareto Front
2. Wide coverage area of Pareto front
3. Uniform distribution on Pareto front
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NSGA 2 Features
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NSGA2

• User selects multiple objectives in parameter
  window in normal fashion.
• When NSGA completed the file, Ibeam_NSGA_pareto_p
  rofile.txt, contains pareto optimal set in
  standard iSIGHT DB format.
• Analyze results using EDM. Use this file
  directly instead of db file.

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Problem Formulation (Straightforward)
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Technique Selection
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Basic Tuning Parameters
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Advanced Tuning Parameters Rarely need to modify
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EDM Select Pareto Txt File
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Scatter Plot Matrix
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(No Transcript)
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NSGA Modeling
Can optimize a single objective as you do
now. Can truly optimize multiple objectives for
an entire paretoset. Consider removing
constraints and treating as objectives.Likely
candidates are active constraints. Consider
having a parameter constrained and also part
ofobjective. A major advantage of NSGA2 is that
it works with convexand non convex spaces and
with mixed integer problems.
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Summary of Posteriori Articulation of Preferences

• Weighted Sum Driven By DOE - programming
• eConstraint Tradeoff Study no programming
• Multiobjective Genetic Algorithm no programming
• Weighted Goal Programming (not demonstrated)
• Weighted Min Max (previously demonstrated)
• Weighted Benson (not demonstrated)