Optimization techniques

detail information about all optimization technique

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

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

3. 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

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

5. 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. 5

6. 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 6

7. 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 7

8. 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 8

9. 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. 9

10. Graphical Representation - Hardness of tablet – B)Dissolution time(t50%) 20 40 60 80 100 120 140 %starch % Stearic acid (x1) %starch % 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 % 10

11. c)Feasible solution space indicated by crosshatched area – % Starch (X1 ) % Stearic acid (X2) Hardness t50 Feasible space with limits of hardness be 8-10 kg and t50% = 20 -30min. 4 8 12 16 20 24 28 32 38 3 9 15 21 27 33 39 11

12. 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 . 12

13. 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. 13

14. 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. 14

15. 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 15

16. 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. 16

17. 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. 17

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