Downhill Simplex Added in iSIGHT 9'0

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Downhill Simplex Added in iSIGHT 9.0

• 6/16/05

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References

• Outstanding paper Optimization Methods for Base
  Station Placement in Wireless Applications.
  Margaret Wright. www.bell-labs.com/org/wireless/w
  isepub/vt98_mhw.pdf
• Optimization Concepts and Applications in
  Engineering. Belegundu and Chandrupatila. 1999.
  Prentice Hall.
• Engineering Optimization Theory and Practice.
  Singiresu Rao. 1996. John Wiley and Sons.
• Optimization in Operations Research. Ronald
  Rardin. 1998. Prentice Hall.

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iSIGHT Diagnostics

• None
• Recommend multiple point restart
• Do not make initial step size too small.
• Needs to have explicit bounds set on design
  variables in iSIGHT

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Characteristics

• O order search technique. No gradients
• Works on non smooth landscapes
• Most widely used of direct search techniques
  (e.g. Hooke Jeeves)
• Wright states has solved tens of thousands of
  problems.
• Needs a penalty function formulation.
• Almost no tuning parameters. Parameters used and
  their values universally accepted.

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Characteristics

• Need n1 vertices
• 4 Possible operations
• Reflection
• Expansion
• Contraction
• Shrinkage (rarely invoked)

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Simplex 3D Visualization Concept
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Reflection
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Reflection Process
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Reflection, Expansion and Contraction
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Scaling or Shrinkage
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Algorithm
Key Tuning Parameters Reflection 1 Expansion
2 Contraction .5 Shrinkage .5
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Iteration

• Each iteration
• New vertex generated. If accepted replaces worse
  vertex.
• If not accepted, shrink with new set of best
  point n new points
• Typically only one or two function evaluations
  per iteration

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Termination Criteria
Maximum Function Change at Vertices lt .001 Or
Number of Iterations
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Spring Formulation
Note Need for lower and upper bounds on
design variables
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Basic Tuning Parameters
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No Advanced Parameters
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Final Solution
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Zero Diagnostics in Log File
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Walkthrough
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Downhill Simplex Lab

• Rerun the Spring_Start.desc file using Downhill
  Simplex with the default step size and upper and
  lower bounds on design variables of -10 and 10
  for X1 and X2.
• Does it reach the same optimum?
• How many function calls did it take?
• Is this more or less efficient then Hooke Jeeves?
• Why is this comparison unfair?
• Since there are no diagnostics and to demonstrate
  your knowledge of the algorithm for self
  diagnostics, on the next slide, label the
  algorithm step number from slides 12 and 13 next
  to each row for the first 10 rows. Remember row1
  never counts as iSIGHT evaluates base point
  before invoking optimizer.

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Spring Problem Self Diagnostics