1. Parameter Optimization of a Bioprocess Model using Tabu Search Algorithm Olympia Roeva, Kalin Kosev Institute of Biophysics and Biomedical Engineering Bulgarian Academy of Sciences 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria E-mail: olympia@clbme.bas.bg

2. 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion Bioprocesses→ complex → highly nonlinear → highly nonlinear Mathematical descriptions → hard simplifications Metaheuristic methods →new, more adequate modeling concepts → new, more adequate modeling concepts

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

4. 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion with Stefka Fidanova

5. 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion Tabu Search (TS) → → Fred Glover, 1986

6. A pseudo code of a TS is presented as: A pseudo code of a TS is presented as: Step 1. Initialization Step 3. Next iteration Step 1. Initialization Step 3. Next iteration Set k = 1Set k = k + 1 Generate initial solution S 0 IF k = N THEN Set S 1 = S 0, then G( S 1 ) = G( S 0 ) STOP Step 2. MovingELSE Step 2. MovingELSE Select S c from neighborhood of S k GOTO Step 2 IF move from S k to S c is already in TL THENEND IF S k+1 = S k S k+1 = S k GOTO Step 3 GOTO Step 3 END IF IF G( S c ) = G( S 0 ) THEN S 0 = S c S 0 = S c END IF Delete the TL move in the bottom of TL Add new Tabu Move in the top of TL GOTO Step 3 GOTO Step 3 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion

7. Parameter identification of E. coli MC4110 fed-batch cultivation model Real experimental data of the E. coli MC4110 fed-batch cultivationare used. Real experimental data of the E. coli MC4110 fed-batch cultivation are used. 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion

8. Case 1 Objective function 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion

9. Case 2 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion

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

11. 6789101112 0 0.2 0.4 0.6 0.8 1 Time, [h] Substrate, [g/l] Experimental data Model data (TS) 6789101112 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Results from optimization Time, [h] Acetate, [g/l] Time profiles of the process variables 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion

12. Time profiles of the process variables 1. Introduction 1. Introduction 2. Outline of the TS algorithm 2. Outline of the TS algorithm 3. Test problem 3. Test problem 4. Results and discussion 4. Results and discussion

13. TS performs equal that GA and SA in terms of solution quality and betterthat GA and SAin terms ofcomputation time better that GA and SA in terms of computation time for considered here problem. Summarized: TS avoids entrapment in local minima and continues the search to give a near-optimal final solution;TS avoids entrapment in local minima and continues the search to give a near-optimal final solution; TS is very general and conceptually much simpler than either SA or GA;TS is very general and conceptually much simpler than either SA or GA; TS has no special space requirement and is very easy to implement (the entire procedure only occupies a few lines of code);TS has no special space requirement and is very easy to implement (the entire procedure only occupies a few lines of code); TS is a flexible framework of a variety of strategies originating from artificial intelligence and is therefore open to further improvement.TS is a flexible framework of a variety of strategies originating from artificial intelligence and is therefore open to further improvement. 5. Conclusion 5. Conclusion

14. 6. Future work 6. Future work