Optimization techniques

1
Presented by – Pradnya shinde.
M . Pharm- I
Dept . P’ceutics
R.C.P.Kasegaon.

CONTENTS -
A]Introduction
B]Optimization techniques
1)EVOP method
2)Statistical design
3)Contour design
4)Response surface method
5)Factorial design
2

INTRODUCTION
The term optimize is defined as “To make perfect”
According to Merriam Webster dictionary,-
“Optimization means,An act, process or methodology
of making something as a fully perfect, functional or
possible ; specially the mathematical procedure.”
3

Optimization
techniques/Methods-
1)EVOP Method (Evolutionary operation)
2)Statistical Design :-
a)Basic Simplex Method
b)Modified Simplex Method
3)Contour Design
4)Response Surface Method
5)Factorial Design
4

EVOP Method :-
Make very small changes in formulation repeatedly.
The result of changes are statistically analyzed.
ADVANTAGES -
1)Generates information on product development.
2)Predict direction of improvement.
DISADVANTAGES –
1)More repetitions required.
2)Time consuming.
3)Expensive to use.
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2)Statistical Method -
a)Basic simplex method –
- It is to understand and apply.
- Optimization begins with initial trials.
- The shapes of simplex in a one ,two, three variables
search space are a line ,a triangle or tetrahedron
respectively.
Line for 1 variable triangle for 2 variables
tetrahedron for 3 variables
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b)Modified Simplex Method -
It can adjust its shape and size depending on
response in each step . This method is also called as
variable –size simplex method.
Example :-
Special cubic simplex design for a component mixture.
Each point represent a different formulation as –
SA = Stearic acid
DCP = Dicalcium Phosphate
ST = Starch
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Constraints –
With restriction that sum of their total wt. must equal to 350mg,
from which ,Active ingredient is = 50mg
SA= 180mg
ST = 4mg
DCP =166mg
SA=100mg
ST = 4mg
DCP =
246mg
SA = 20mg
ST = 4mg
DCP = 326mg
SA = 20mg
ST =84mg
DCP =
246mg
SA =28mg
ST =164mg
DCP
=166mg
SA = 100mg
ST = 164mg
DCP =166mg SA =50mg
ST =180mg
DCP
=120mg
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3) Contour Design –
Constrained optimization problem is to locate the levels of
stearic acid (X1) and starch (X2).
This minimize the time of invitro release (Y2),average
friability (Y3), average tablet volume (Y4).
To apply statistical method , problem must be expressed
as :-
Y2 = f2 (X1,X2) ----- invitro release -- 1
Y3 = f3 (X1,X2) ----- friability -- 2
Y4 = f4 (X1,X2) ------ tablet volume -- 3
5 ≤ X1 ≤ 45 -- 4
1 ≤ X2 ≤ 41 -- 5
Equation 4 and 5 serve to keep solution within
experimental range.
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Graphical Representation -
A) Hardness of tablet – B)Dissolution time(t50%)
20
40
60
80
100
120
140
%starch
% Stearic acid (x1) % Stearic
acid
6.1
12.1
33.1
34.6
88.2
148.4
It shows contours for tablet hardness as the levels of
independent variables are changed.
It shows similar contours for dissolution response
t50 %
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c)Feasible solution space indicated by
crosshatched area –
%Starch(X1)
% Stearic acid (X2)
Hardness
Feasible space with limits of hardness be 8-10 kg and t50% = 20 -
30min.
4 8 12 16 20 24 28
32 38
3915212733
39
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Response Surface Method –
It is a set of techniques used in the experimental study of relationship.
RSM is a collection of mathematical and statistical techniques for
empirical model building in which a response of interest is influenced by
several variables and the objectives is to optimize this response.
RSM is useful in 3 different techniques –
1)Statistical experimental design, in particular 2 level factorial
design.
2)Regression modeling techniques.
3)Optimization methods
The most common APPLICATION –
in industrial , biological and clinical science , food science and
physical and engineering science.
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The essential steps in response surface
methodology –
1)A possible mathematical model is selected.
2)An experimental design that is appropriate to the model is chosen.
3)The experiments are carriedout and values of the factors and the
response fitted
to mathematical model.
4)The model is validated.
5)If model does not represent the data in satisfactory manner, then
another model
equation or new experimental design is selected .Stages 1,2,3 and 4
are repeated
using models and design of increasing complexity until a model
is obtained ,
which is an acceptable representation of data.
6)If required , graphical representation of surface is generated.
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5)Factorial Design -
Factorial designs are used in Experiments of different ,or conditions on
experimental results are to be elucidated.
“Intervention studies with two or more categorical explanatory variables
leading to a numerical outcome variables are called as Factorial design”
Objectives –
1)Try to obtain the maximum amount of information about a system for a
given level of available resources.
2)Determine the effects of each individual input parameter.
3)determine the effects due to interactions of the input parameters.
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Types of Factorial Design -
Factorial Designs are classified into two parts –
1. Full factorial design
2. Fractional factorial design
1)Full factorial design -
Definition – “A design in which every setting of every factor appears
with every other factor is a full factorial design .”
Full factorial design is again classified depending on the no.
of levels as follows :-
a)Two level full factorial design –
Here, the number of levels are kept constant i.e. 2 and no. of
factors are variable (2,3,4……).
E.g.-
22 = Here, No. of levels are 2 and no. of factors are 2
23 = Here, no. of levels are 2 and no. of factors are 3
24 = no. of levels are 2 and no. of factors are 4
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b)Three level full factorial design
-
Here, the number of levels are kept constant i.e. 3 and no. of factors are
variable
(2,3,4,…….).These levels are called ‘high’, ‘medium’, ‘low’ .
E.g. –
32 = here ,levels are 3 and no. of factors are 2
33 = here, levels are 3 and no. of factor are 3
2)Fractional factorial design –
“A factorial experiment in which only an adequately chosen fraction of the
treatment
combinations required for the complete factorial experiment is selected to be
run.”
Even if the number of factors, K, in a design is small, the 2k runs specified for a
full
factorial can quickly become very large.
E.g. –
26 = 64 runs are for a two –level ,full factorial design with six factors.
We pick a fraction such as 1/2, 1/4 etc. of the runs called for by the full
factorial.
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Application of Factorial design-
1 )To optimize animal experiments and reduce animal
use.
2)Development and characterization of insecticidal soap
from
Neem oil.
3)To study and assess the single and combined benefits
of drug interventions in a controlled clinical trial.
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Optimization techniques

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