parameter optimization of a bioprocess model using tabu search algorithm olympia roeva, kalin kosev...

Parameter Optimization Parameter Optimization of a Bioprocess Model of a Bioprocess Model

using Tabu Search using Tabu Search

AlgorithmAlgorithm Olympia Roeva, Kalin KosevOlympia Roeva, Kalin Kosev

Institute of Biophysics and Biomedical Institute of Biophysics and Biomedical Engineering Bulgarian Academy of SciencesEngineering Bulgarian Academy of Sciences

105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria105 Acad. G. Bonchev Str., Sofia 1113, BulgariaE-mail: [email protected]: [email protected]

1. Introduction1. Introduction 2. 2. Outline of the Outline of the TS algorithm TS algorithm 3. Test problem3. Test problem 4. Results and discussion4. Results and discussion

BioprocessesBioprocesses → complex→ complex

→ → highly nonlinear highly nonlinear

Mathematical descriptionsMathematical descriptions

→ → hard simplificationshard simplifications

Metaheuristic methodsMetaheuristic methods

→→ new, more adequatenew, more adequate modeling concepts modeling concepts


with Stefka Fidanova


Tabu Search (TS)Tabu Search (TS) →→ Fred Glover, 1986

A pseudo code of a TS is presented as:A pseudo code of a TS is presented as:

Step 1. InitializationStep 1. Initialization Step 3. Next iteration Step 3. Next iteration Set Set k k = 1= 1 Set Set k k = = kk + 1 + 1Generate initial solution Generate initial solution SS00 IF IF kk = N THEN = N THENSet Set SS11 = = SS00, then G(, then G(SS11) = G() = G(SS00)) STOP STOP

Step 2. MovingStep 2. Moving ELSEELSESelect Select SScc from neighborhood of from neighborhood of SSkk GOTO GOTO

Step 2Step 2IF move from IF move from SSkk to to SScc is already in TL THENis already in TL THEN END IFEND IF SSk+1k+1 = = SSkk

GOTO Step 3GOTO Step 3END IFEND IFIF G(IF G(SScc) = G() = G(SS00) THEN) THEN SS00 = = SScc

END IFEND IF

Delete the TL move in the bottom of TLDelete the TL move in the bottom of TL

Add new Tabu Move in the top of TLAdd new Tabu Move in the top of TL

GOTO Step 3GOTO Step 3

1. Introduction1. Introduction 2. 2. Outline of the Outline of the TS algorithmTS algorithm 3. Test problem3. Test problem 4. Results and discussion4. Results and discussion

2

2 2

2 22 2 2

2

1

1

1

inmax

S

inmax in

S / X S

inmax

A / X A

pO * inmax L

pO / X pO

in

FdX S= μ X X

dt k +S V

FdS S= μ X + S S

dt Y k +S V

FdA Aμ X A

dt Y k + A V

FdpO pOμ X k a pO pO pO

dt Y k + pO V

dVF

dt

Parameter identification of Parameter identification of E. coli MC4110E. coli MC4110 fed-batch cultivation model fed-batch cultivation model

Real experimental dataReal experimental data of the of the E. E. coli MC4110 coli MC4110 fed-batch fed-batch cultivationcultivation are used.are used.


1

inmax

S

inmax in

S / X S

in

FdX S= μ X X

dt k +S V

FdS S= μ X + S S

dt Y k +S V

dVF

dt

Case 1Case 1

max S S / Xp μ k Y

Objective functionObjective function

2

1 1

n m

exp mod ji j

J x i x i min


Case 2Case 2

2

2 2

2 22 2 2

2

1

1

1

inmax

S

inmax in

S / X S

inmax

A / X A

pO * inmax L

pO / X pO

in

FdX S= μ X X

dt k +S V

FdS S= μ X + S S

dt Y k +S V

FdA Aμ X A

dt Y k + A V

FdpO pOμ X k a pO pO pO

dt Y k + pO V

dVF

dt

2

2 2 2pO *

max S A pO S / X A / X pO / X Lp μ k k k Y Y Y k a pO


6 7 8 9 10 11 120

0.2

0.4

0.6

0.8

1

Time, [h]

Sub

stra

te, [

g/l]

Experimental data

Model data (TS)

6 7 8 9 10 11 120.02

0.04

0.06

0.08

0.1

0.12

0.14Results from optimization

Time, [h]

Ace

tate

, [g/

l]Time profiles of the process Time profiles of the process variablesvariables


6 7 8 9 10 11 120

2

4

6

8

10

Time, [h]

Bio

mas

s, [g

/l]

Experimental data

Model data (TS)

6 7 8 9 10 11 1220

20.2

20.4

20.6

20.8

21

21.2

Time, [h]

Dis

solv

ed o

xyge

n, [%

]Time profiles of the process Time profiles of the process variablesvariables


TS performs TS performs

equalequal that GA and SA in terms of solution quality and that GA and SA in terms of solution quality and

betterbetter that GA and SAthat GA and SA in terms ofin terms of computation time computation time

for considered here problem.for considered here problem.

Summarized: Summarized:

• TS avoids entrapment in local minima and continues the search TS avoids entrapment in local minima and continues the search to give a near-optimal final solution; to give a near-optimal final solution;

• TS is very general and conceptually much simpler than either SA TS is very general and conceptually much simpler than either SA or GA; or GA;

• TS has no special space requirement and is very easy to TS has no special space requirement and is very easy to implement (the entire procedure only occupies a few lines of implement (the entire procedure only occupies a few lines of code); code);

• TS is a flexible framework of a variety of strategies originating TS is a flexible framework of a variety of strategies originating from artificial intelligence and is therefore open to further from artificial intelligence and is therefore open to further improvementimprovement..

5. Conclusion5. Conclusion

6. Future work6. Future work

parameter optimization of a bioprocess model using tabu search algorithm olympia roeva, kalin kosev...

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