A%20Comparison%20of%20Simulated%20Annealing%20and%20Genetic%20Algorithm%20Approaches%20for%20Cultivation%20Model%20Identification

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A Comparison of Simulated Annealing and Genetic
Algorithm Approaches for Cultivation Model
Identification

• Olympia Roeva
• Institute of Biophysics and Biomedical
  Engineering Bulgarian Academy of Sciences
• E-mail olympia_at_clbme.bas.bg

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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
competing paradigms in the field of modern
heuristics Genetic Algorithm Simulated
Annealing Algorithm quite close relatives and
much of their difference is superficial
population size ? one population new
solutions by ? a new solution by modifying
only combining two different solutions one
solution with a local move (crossover and
mutation) (only mutation) In this work, both
GA and SA are applied and compared for a
parameter identification of non-linear
mathematical model of E. coli MC4110 fed-batch
cultivation process.
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
A pseudo code of a GA is presented as 1. Set
generation number to zero (t 0) 2. Initialise
usually random population of individuals
(P(0)) 3. Evaluate fitness of all initial
individuals of population 4. Begin major
generation loop in k 4.1. Test for
termination criterion 4.2. Increase the
generation number 4.3. Select a sub-population
for offspring reproduction (select P(i)
from P(i 1)) 4.4. Recombine the genes of
selected parents (recombine
P(i)) 4.5. Perturb the mated population
stochastically (mutate P(i)) 4.6.
Evaluate the new fitness (evaluate P(i)) 5. End
major generation loop
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
Basic GA operators and parameters
Operator Type
encoding binary
fitness function linear ranking
selection function roulette wheel selection
crossover function double point
mutation function bit inversion
reinsertion fitness-based
Parameter Value
ggap 0.97
xovr 0.70
mutr 0.01
nind 100
maxgen 200
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
A pseudo code of SA could be presented as 1.
Find initial solution (by generating it randomly)
2. Set initial value for the control parameter
T T0 3. Set a value for r, the rate of
cooling parameter j 0 Generate (at
random) a new solution S Calculate the
difference in cost ? cost(S) cost(S)
Examine the new solution and decide accept or
reject If accepted, it becomes the current
solution otherwise, keep the old one j j1
Reduce the temperature and generate a new
solution 4. Until some stopping criterion
applies
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
Boltzman distribution with the probability of
acceptance
Temperature update T T0 0.95r
Annealing parameters
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
Parameter identification of E. coli MC4110
fed-batch cultivation model
Real experimental data of the E. coli MC4110
fed-batch cultivation are used.
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
A two stage parameter identification procedure is
used
Objective function
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
GA ?max 0.4796, kS 0.0162, YS/X 2.0137
SA ?max 0.4864, kS 0.0150, YS/X 1.9088
Table 1. Results from parameter identification
second step
GA GA SA SA
average best average best
Execution time, s 213.5737 195.1406 169.2982 88.9688
J value 0.1367 0.11025 0.1494 0.11041
1/ 7.8215 7.3271 8.1277 7.1884
21.1521 20.8503 23.6376 20.5477
pO2 21.2833 21.2879 21.2800 21.2863
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
Best GA result
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
Best SA result
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1. Introduction 2. Outline of the GA 4. Test
problem 3. Outline of the SA 5. Results and
discussion
Cultivation of E. coli MC4110
21.2

GA model
SA model
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Exp. data
20.8
Dissolved oxygen,
20.6

20.9
20.4
20.85
20.8
20.2
20.75
20.0
20.7

8.4
8.5
8.6
8.7
8.8
8.9
9
9.1
9.2
9.3
9.4
19.8

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8
9
10
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Time, h