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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