Date post: | 01-Jul-2015 |
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Health & Medicine |
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OPTIMIZATION TECHNIQUESSuraj C.
AACP
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PPT. Package
Concept Of Optimization
Optimization Parameters
Classical Optimization
Statistical Design
Simulation & Search
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INTRODUCTION
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INTRODUCTION
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• In development projects , one generally
experiments by :
a series of logical steps,
carefully controlling the variables &
changing one at a time, until a satisfactory
system is obtained
• It is not a screening technique.
IDEA !
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OPTIMIZATION TECHNIQUES
ParametricNon-
Parametric
FactorialCentral
CompositeMixture
LagrangianMultiple
Regression
FractionalFactorial
Plackett-Burman
Evolutionary methods
EVOP REVOP
CLASSICAL OPTIMIZATION
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• Involves application of calculus to basic
problem for maximum/minimum function.
• One factor at a time (OFAT).
• Restrict attention to one factor at a time.
• Not more than 2 variables.
CLASSICAL OPTIMIZATION
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• Using calculus the graph obtained can be solved.
Y = f (x)
• When the relation for the response y is given as the
function of two independent variables,X1 & X2
Y = f(X1 , X2)
• The above function is represented by contour plots on
which the axes represents the independent variables X1&
X2
Contd…..
CLASSICAL OPTIMIZATION
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Response Variable
Independent Variable
Contd…..
CLASSICAL OPTIMIZATION
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Independent Variable - X2
Independent Variable - X1
Contd…..
OFAT vs DOE
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Properties OFAT DOE
Type Classical- Sequenctial one one factor method
Scientific – simultaneous with multiple factor method
No. of experiments High – Decided by experimenter
Limited – Selected by design
Conclusion Inconclusive – Interaction Interaction unknown
Comprehensive –Interactions studied too.
Precision & Efficiency Poor – sometimes misleading result with errors (4 exp.)
High – Errors are shared evenly (2 exp.)
Consequences One exp. Wrong… all goes goes wrong -Inconclusive
Orthogoanl design –Predictable & conclusive
Information gained Less per experiment High per experiment
STATISTICAL DESIGN
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• Techniques used divided in to two types:
1. Experimentation continues as optimization
proceeds
2. Experimentation is completed before
optimization takes place.
STATISTICAL DESIGN
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• Experimentation is completed before
optimization takes place.
Theoretical approach
Empirical or experimental approach
Contd…..
STATISTICAL TERMS
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• Relationship with single independent variable -
Simple regression analysis or Least squares method.
• Relationship with more than one important variable -
Statistical design of experiment & Multi linear
regression analysis.
• Most widely used experimental plan is Factorial
design.
STATISTICAL DESIGN
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• Optimization: helpful in shortening the experimenting
time.
• DOE: is a structured , organized method used to
determine the relationship between –
the factors affecting a process &
the output of that process.
• Statistical DOE: planning process + appropriate data
collected + analysed statistically.
Contd…..
MATHEMATICAL MODELS
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• Permits the interpretation of RESPONSES more
economically & becomes less ambiguous.
1. First Order: 2 Levels of the factor – Linear
LCL (Lower control limit) - {-ve or -1}
UCL (Upper control limit) - {+ve or +1}
2. Second Order: 3 Levels (Mid-level) – coded as “0” –
Curvature effect
FIRST ORDER
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X1
Response
LOW HIGH
Predictable Response at X1
SECOND ORDER
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X1
Response
LOW HIGH
True Response
SIMULATION & SEARCH
METHODS
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• Search method does not requires CONTINUITY or
DIFFERENTIALITY function.
• Search methods also known as - “Sequential
optimization”.
NOTE: Simulation involves the computability of a
response.
SIMULATION & SEARCH
METHODS
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• A simple inspection of experimental results is
sufficient to choose the desired product.
• If the independent variable is Qualitative – Visual
observation is enough.
• Computer aid not required, but if it there then added
advantage.
• Even 5 variables can be handled at once.
Contd…..
SIMULATION & SEARCH
(types)
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Steepest Ascent Method
Response Surface Methodology (RSM)
Contour Plots
Steepest Ascent Method
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• Procedure for moving sequentially along the path
(or direction) in order to obtain max. ↑ in response.
• Applied to analyze the responses obtained from:
1. Factorial Designs
2. Fractional Factorial Designs
NOTE: Initial estimates of DOE are far from actual, so
method chosen for optimum value.
Response Surface Methodology (RSM)
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• A 3-D geometric representation that establishes an
empirical relationship between responses &
independent variables.
• For:
Determining changes in response surface
Determining optimal set of experimentalconditions
NOTE: Overlap of plots for complete info is possible.
Contour Plots
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• Are 2-D (X1 & X2) graphs in which some variables are
held at one desired level & specific response noted.
• Both axes are in experimental units.
• Sometimes both the contour & RSM plots are drawn
together for better optimum values.
Contour Plots
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RSM & Contour Combined
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