This document discusses various optimization techniques, including classical optimization, statistical design of experiments, simulation and search methods. Classical optimization uses calculus to find the maximum or minimum of a function with one or two variables. Statistical design of experiments is a structured method to determine relationships between factors and responses using techniques like factorial designs. Simulation and search methods do not require differentiability, and include methods like steepest ascent, response surface methodology, and contour plots to find optimal values of responses.

1. OPTIMIZATION TECHNIQUES
Suraj C.
AACP

2. 2
PPT. Package
Concept Of Optimization
Optimization Parameters
Classical Optimization
Statistical Design
Simulation & Search

3. 3
INTRODUCTION

4. 4
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
Parametric
Non-
Parametric
Factorial
Central
Composite
Mixture
Lagrangian
Multiple
Regression
Fractional
Factorial
Plackett-
Burman
Evolutionary
methods
EVOP REVOP

7. 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.

8. 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…..

9. CLASSICAL OPTIMIZATION
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Response
Variable
Independent
Variable
Contd…..

10. CLASSICAL OPTIMIZATION
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Independent
Variable - X2
Independent
Variable - X1
Contd…..

11. 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

12. 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.

13. STATISTICAL DESIGN
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• Experimentation is completed before
optimization takes place.
 Theoretical approach
 Empirical or experimental approach
Contd…..

14. 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.

15. 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…..

16. 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

17. FIRST ORDER
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X1
Response
LOW HIGH
Predictable Response at X1

18. SECOND ORDER
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X1
Response
LOW HIGH
True Response

19. 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.

20. 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…..

21. SIMULATION & SEARCH
(types)
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 Steepest Ascent Method
 Response Surface Methodology (RSM)
 Contour Plots

22. 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.

23. 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 experimental
conditions
NOTE: Overlap of plots for complete info is possible.

24. 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.

25. Contour Plots
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RSM & Contour
Combined

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