1. E-mail: olympia@clbme.bas.bg
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

2. competing paradigms in the field of modern heuristics
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.

3. 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

4. Basic GA operators and parameters
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

5. 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 = j+1
Reduce the temperature and generate a new solution
4. Until some stopping criterion applies

6. 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:

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

8. A two stage parameter identification procedure is used
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

9. 1. Introduction 2. Outline of the GA 4. Test problem
3. Outline of the SA 5. Results and discussion

10. 1. Introduction 2. Outline of the GA 4. Test problem
3. Outline of the SA 5. Results and discussion
GA max = , kS = , YS/X =
SA max = , kS = , YS/X =
Table 1. Results from parameter identification – second step GA SA
average
best
Execution time, s
J value
0.1367
0.1494 1/
7.8215
7.3271
8.1277
7.1884
pO2*

11. Best GA result 1. Introduction 2. Outline of the GA 4. Test problem
3. Outline of the SA 5. Results and discussion
Best GA result 1 2 3 5 10 15 20 25
Number of variables (3)
Current best individual
Current Best Individual 40 60 80
100 50
150
Generation
Fitness value
Best: Mean:
200
400
600
800
Best, Worst, and Mean Scores
0.11
0.12
0.13
0.14
0.15 30
Score Histogram
Score (range)
Number of individuals
Best fitness
Mean fitness

12. Best SA result 1. Introduction 2. Outline of the GA 4. Test problem
3. Outline of the SA 5. Results and discussion
Best SA result 1 2 3 5 10 15 20 25
Best point
Number of variables (3)
1000
2000
3000
4000
Iteration
Function value
Best Function Value:
Current Point
Current point 30 40
Current Function Value:

13. 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 21
Exp. data
20.8
Dissolved oxygen, [%]
20.6
20.9
20.4
20.85
20.2
20.8
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 6 7 8 9 10 11 12
Time, [h]