Progressive Articulation of Preference Information

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Progressive Articulation of Preference Information

• Satisficing Trade-off Analysis part of iSIGHT but
  not iSIGHT-FD (STOM)
• Can manually mimic main features of algorithm in
  iSIGHT-FD with all techniques.
• Basically a variation of min-max and goal
  programming.
• Calculation effort is 3X that of single
  optimization and much less than MOGA

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Satisficing Tradeoff Analysis

• Satisficing - to obtain an outcome that is good
  enough. Satisficing action can be contrasted with
  maximizing action, which seeks the biggest, or
  with optimizing action, which seeks the best.
• Satisficing Tradeoff is a method of evaluating
  tradeoff for multiple objectives
• A compromise approach varying goals and
  objective constraints.
• User explores designs in criterion space without
  worrying about weights
• Interactive

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Satisficing Trade-off Analysis
Utopia Point Reference point for Pareto solution
search

• It does not consider the whole Pareto optimal
  front
• Looks near users desired point
• One Pareto solution is calculated after a
  trade-off trial
• Calculation effort for one trade-off trial
  roughly equals to single-objective optimization
• Intuitive and Quick solution

Aspirant/Request Point Users desired value
A Pareto Solution Near solution by request point
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Satisficing Tradeoff Analysis

• Terminology
• Utopia/Ideal Point a (theoretically
  impossible) set of values for all objective
  parameters (e.g., 127.417 for a parameter Area
  that is minimized, or 0.0059 for a parameter
  StaticDeflection that is minimized).
• Aspirant/Seek Level desired values for all
  objective parameters
• Specify realistic values for Ideal Point
• For more information
• Aspiration Level Approach to Interactive
  Multi-Objective Programming and Its Applications
  by H. Nakayama. 1995.
• Nonlinear Multiobjective Optimization, Miettinen

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Basically a MinMax Formulation
Solve problem interactively by adjusting aspirant
values and possibly adding objective
constraints. Need to add calculation to
calculate constraint values foreach
objective. Need to add a design variable Z
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Problem Formulation

• Z is the objective.
• Z is the maximum value that any objective is from
  the aspiration level.
• Z is also added as a design variable to prevent
  discontinuous derivative if multiple objectives
  have same value.
• Z has an initial value of 100

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Set Tradeoff Parameters

• Utopia (127.417, 0.0059)
• Nadir (850.0, 0.0612)
• Aspirant/Seek Point (500.0, 0.007)

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Model With Calculation
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Problem Formulation
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Calculation
Need to include Z since iSIGHT-FD has
limitedsupport for use of parameters in output
constraint bounds.
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Optimization Results
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User Categories for Each Objective Result

• Improve specify a lower aspirant value
• Relax specify a higher aspirant value
• Satisfied leave unchanged or add a constraint

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Update Tradeoff Parameters

• Utopia (127.417, 0.0059)
• Nadir (850.0, 0.0612)
• Aspirant/Seek Point (500.0, 0.007)
• Actual (540.596, 0.00711)
• New Aspirant (400.000, 0.00736)

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Find Pareto Solution

• The second optimization does not start from where
  the first one ended.
• The optimization begins at the original starting
  point with an updated set of constraints.
• Z is reset to 100.

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Second Problem Formulation
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Second Optimization Complete
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Update Tradeoff Parameters

• Utopia (127.417, 0.0059)
• Nadir (850.0, 0.0612)
• Aspirant/Seek Point 1 (500.0, 0.007)
• Actual (540.596, 0.00711)
• New Aspirant Point 2 (400.000, 0.00736)
• Actual (489.439, 0.00783)
• New Aspirant Point 3 (400.00), 0.00855)

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Third Optimization Complete
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STA Steps

• Calculate the utopian objective.
• Ask the decision maker to specify a aspirant
  point such that aspirantk gt Fkoptimal
• Minimize the scalarizing function. Denote
  solution by xh. Let the objective vector be zh
• Ask the decision maker to classify functions into
  categories Ilt, Igt and I. If Ilt 0 then
  finished.
• Ask the decision maker for new lower aspiration
  levels for Ilt and higher aspiration level for Igt.
  Set h h 1. Go to step 3

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Summary of STA

• Interactive
• Studies indicate 3-8 iterations
• Engineers like dealing in criterion space.

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End of Lecture

• Questions
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