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Dynamic optimization of fed-batch bioprocesses using flower pollination algorithm

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Abstract

There exist several optimization strategies such as sequential quadratic programming (SQP), iterative dynamic programing (IDP), stochastic-based methods such as differential evolution (DE), genetic algorithm (GA), particle swarm optimization (PSA), and ant colony optimization (ACO) for finding optimal feeding profile(s) during fed-batch fermentations. Here in the present study, flower pollination algorithm (FPA) which is inspired by the pollination process in terrestrial flowering plants has been used for the first time to find the optimal feeding profile(s) during fed-batch fermentations. Single control variable, two control variables and state variable bounded problems were chosen to test the robustness of the FPA for optimal control problems. It was observed that FPA is computationally less intensive in comparison with other stochastic strategies. Thus, obtained results were compared to other studies and it has been found that the FPA converged either to newer optima or closer to the established global optimum for the cases studied.

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Abbreviations

ACO:

Ant colony optimization

ANN:

Artificial neural networks

CPU:

Central processing unit

CVP:

Control vector parameterization

DAE:

Differential algebraic equation

DE:

Differential evolution

DI:

Deviation index

FPA:

Flower pollination algorithm

GA:

Genetic algorithm

IDP:

Iterative dynamic programming

KKT:

Karush–Kuhn–Tucker (conditions)

MODE:

Multi-objective optimization differential evolution

MOFPA:

Multi-objective flower pollination algorithm

NDF:

Numerical differentiation formula

NSGA-II:

Non-dominated sorting genetic algorithm -II

OCP:

Optimal control problem

ODE:

Ordinary differential equation

OFE:

Objective function evaluations

PI:

Performance index

PSA:

Particle swarm algorithm

PSO:

Particle swarm optimization

SQP:

Sequential quadratic programming

VEGA:

Vector evaluated genetic algorithm

References

  1. Yamané T, Shimizu S (1984) Fed-batch techniques in microbial processes. Adv Biochem Eng 30:147–194. https://doi.org/10.1007/BFb0006382

    Article  Google Scholar 

  2. Shioya S (1992) Optimization and control in fed-batch bioreactors. Mod Biochem Eng. In: Fiechter A (ed) Advances in biochemical engineering/biotechnology, vol 46, pp 111–142. https://doi.org/10.1007/BFb0000708

  3. Bellman R (1957) Dynamic programming. University Press, Princeton

    Google Scholar 

  4. Bryson AE, Ho Y-C, Siouris GM (1979) Applied optimal control: optimization, estimation, and control. IEEE Trans Syst Man Cybern 9:366–367. https://doi.org/10.1109/TSMC.1979.4310229

    Article  Google Scholar 

  5. Biegler LT (2010) Nonlinear programming: concepts, algorithms, and applications to chemical processes. SIAM

  6. Rocha M, Mendes R, Rocha O et al (2014) Optimization of fed-batch fermentation processes with bio-inspired algorithms. Expert Syst Appl 41:2186–2195. https://doi.org/10.1016/j.eswa.2013.09.017

    Article  Google Scholar 

  7. Yang XS (2012) Flower pollination algorithm for global optimization. Lect Notes Comput Sci (including Subser Lect Notes Artif Intell Lect Notes Bioinformatics) 7445 LNCS:240–249. https://doi.org/10.1007/978-3-642-32894-7_27

    Chapter  Google Scholar 

  8. Yang X-S (2014) Nature-inspired optimization algorithms. Elsevier, London

    Google Scholar 

  9. Ochoa A, González S, Margain L et al (2014) Implementing flower multi-objective algorithm for selection of university academic credits. In: 2014 6th World Congr Nat Biol Inspired Comput NaBIC 2014, pp 7–11. https://doi.org/10.1109/NaBIC.2014.6921866

  10. Gautam U, Malmathanraj R, Srivastav C (2015) Simulation for path planning of autonomous underwater vehicle using flower pollination algorithm, genetic algorithm and Q-learning. 2015 Int Conf Cogn Comput Inf Process 1–5. https://doi.org/10.1109/CCIP.2015.7100710

    Article  Google Scholar 

  11. Abdelaziz AY, Ali ES, Abd Elazim SM (2016) Flower pollination algorithm for optimal capacitor placement and sizing in distribution systems. Electr Power Comp Syst 44:544–555. https://doi.org/10.1080/15325008.2015.1117540

    Article  Google Scholar 

  12. Prathiba R, Balasingh Moses M, Sakthivel S (2014) Flower pollination algorithm applied for different economic load dispatch problems. Int J Eng Technol 6:1009–1016

    Google Scholar 

  13. Yang XS (2010) Engineering optimization: An introduction with metaheuristic applications. Wiley, New Jersey

    Book  Google Scholar 

  14. Chen X, Du W, Tianfield H et al (2014) Dynamic optimization of industrial processes with nonuniform discretization-based control vector parameterization. IEEE Trans Autom Sci Eng 11:1289–1299. https://doi.org/10.1109/TASE.2013.2292582

    Article  Google Scholar 

  15. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. 2009 World Congr Nat Biol Inspired Comput NABIC 2009—Proc 210–214. https://doi.org/10.1109/NABIC.2009.5393690

  16. Yang XS, Deb S (2013) Multi-objective cuckoo search for design optimization. Comput Oper Res 40:1616–1624. https://doi.org/10.1016/j.cor.2011.09.026

    Article  Google Scholar 

  17. Mantegna RN (1994) Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes. Phys Rev E. https://doi.org/10.1103/PhysRevE.49.4677

    Article  Google Scholar 

  18. Luus R (1993) Application of dynamic programming to differential-algebraic process systems. Comput Chem Eng 17:373–377. https://doi.org/10.1016/0098-1354(93)80029-M

    Article  CAS  Google Scholar 

  19. Sarkar D, Modak JM (2004) Optimization of fed-batch bioreactors using genetic algorithm: multiple control variables. Comput Chem Eng 28:789–798. https://doi.org/10.1016/j.compchemeng.2004.02.018

    Article  CAS  Google Scholar 

  20. Sarker R, Runarsson T, Newton C (2001) Genetic algorithms for solving a class of constrained nonlinear integer programs. Int Trans Oper Res 8:61–74. https://doi.org/10.1111/1475-3995.00006

    Article  Google Scholar 

  21. Luus R (2000) Iterative dynamic programming. Monographs and surveys in pure and applied mathematics. Chapman and Hall/CRC

  22. Sarkar D, Modak JM (2004) Genetic algorithms with filters for optimal control problems in fed-batch bioreactors. Bioprocess Biosyst Eng 26:295–306. https://doi.org/10.1007/s00449-004-0366-0

    Article  CAS  PubMed  Google Scholar 

  23. Kapadi MD, Gudi RD (2004) Optimal control of fed-batch fermentation involving multiple feeds using differential evolution. Process Biochem 39:1709–1721. https://doi.org/10.1016/j.procbio.2003.07.006

    Article  CAS  Google Scholar 

  24. Tholudur A, Ramirez WF (1997) Obtaining smoother singular arc policies using a modified iterative dynamic programming algorithm. Int J Control 68:1115–1128. https://doi.org/10.1080/002071797223235

    Article  Google Scholar 

  25. Park S, Ramirez WF (1988) Optimal production of secreted protein in fed-batch reactors. AIChE J 34:1550–1558. https://doi.org/10.1002/aic.690340917

    Article  CAS  Google Scholar 

  26. Banga JR, Irizarry-Rivera R, Seider WD (1998) Stochastic optimization for optimal and model-predictive control. Comput Chem Eng 22:603–612. https://doi.org/10.1016/S0098-1354(97)00226-3

    Article  CAS  Google Scholar 

  27. Liu P, Li G, Liu X, Zhang Z (2016) Novel non-uniform adaptive grid refinement control parameterization approach for biochemical processes optimization. Biochem Eng J 111:63–74. https://doi.org/10.1016/j.bej.2016.03.006

    Article  CAS  Google Scholar 

  28. Wang L, Liu X, Zhang Z (2017) A new sensitivity-based adaptive control vector parameterization approach for dynamic optimization of bioprocesses. Bioprocess Biosyst Eng 40:181–189. https://doi.org/10.1007/s00449-016-1685-7

    Article  CAS  PubMed  Google Scholar 

  29. Sarkar D, Modak JM (2003) ANNSA: a hybrid artificial neural network/simulated annealing algorithm for optimal control problems. Chem Eng Sci 58:3131–3142. https://doi.org/10.1016/S0009-2509(03)00168-4

    Article  CAS  Google Scholar 

  30. Lee J, Ramirez WF (1994) Optimal fed-batch control of induced foreign protein production by recombinant bacteria. AIChE J 40:899–907. https://doi.org/10.1002/aic.690400516

    Article  CAS  Google Scholar 

  31. Chen C-T, Hwang C (1990) Optimal control computation for differential-algebraic process systems with general constraints. Chem Eng Commun 97:9–26. https://doi.org/10.1080/00986449008911501

    Article  CAS  Google Scholar 

  32. Banga JR, Alonso AA, Singh RP (1997) Stochastic dynamic optimization of batch and semicontinuous bioprocesses. Biotechnol Prog 13:326–335. https://doi.org/10.1021/bp970015&%23x002B;

    Article  CAS  Google Scholar 

  33. Egea J, Balsa-Canto E (2009) Dynamic optimization of nonlinear processes with an enhanced scatter search method. Ind Eng Chem Res 48:4388–4401

    Article  CAS  Google Scholar 

  34. Tremblay M, De Perrier M, Chavarie C, Archambault J (1992) Bioprocess engineering optimization of fed-batch culture of hybridoma cells using dynamic programming: single and multi-feed cases. Comp A J Comp Educ 7:229–234

    Google Scholar 

  35. Roubos JA, Straten G Van (1999) An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance. J Biotechnol 67:173–187

    Article  CAS  Google Scholar 

  36. Bryson AE Jr, Ho YC (1969) Applied optimal control. Blaisdell, London

    Google Scholar 

  37. Logist F, Telen D, Houska B et al (2013) Multi-objective optimal control of dynamic bioprocesses using ACADO Toolkit. Bioprocess Biosyst Eng 36:151–164. https://doi.org/10.1007/s00449-012-0770-9

    Article  CAS  PubMed  Google Scholar 

  38. Patil KR, Rocha I, Förster J, Nielsen J (2005) Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics 6:308. https://doi.org/10.1186/1471-2105-6-308

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Sarkar D, Modak JM (2003) Optimisation of fed-batch bioreactors using genetic algorithms: two control variables. Comput Aided Chem Eng 14:1127–1132. https://doi.org/10.1016/S1570-7946(03)80269-9

    Article  Google Scholar 

  40. Nikumbh S, Ghosh S, Jayaraman VK (2014) In: Valadi J, Siarry P (Eds.) Applications of metaheuristics in process engineering. Springer

  41. Mutturi S (2017) Molecular BioSystems FOCuS: a metaheuristic algorithm for computing knockouts from genome-scale models for strain. Mol Biosyst. https://doi.org/10.1039/C7MB00204A

    Article  CAS  PubMed  Google Scholar 

  42. Nabil E (2016) A modified flower pollination algorithm for global optimization. Expert Syst Appl 57:192–203. https://doi.org/10.1016/j.eswa.2016.03.047

    Article  Google Scholar 

  43. Luus R (1990) Application of dynamic programming to high-dimensional non-linear optimal control problems. Int J Control 52:239–250. https://doi.org/10.1080/00207179008953533

    Article  Google Scholar 

  44. Carrasco EF, Banga JR (1997) Dynamic optimization of batch reactors using adaptive stochastic algorithms. Society 2252–2261

    Article  CAS  Google Scholar 

  45. Mekarapiruk W (2001) Simultaneous optimal parameter selection and dynamic optimization using iterative dynamic programming. Ph.D. thesis, University of Toronto

  46. Jayaraman VK, Kulkarni BD, Gupta K et al (2001) Dynamic optimization of fed-batch bioreactors using the ant algorithm. Biotechnol Prog 17:81–88. https://doi.org/10.1021/bp000133o

    Article  CAS  PubMed  Google Scholar 

  47. Mendes R, Rocha I, Ferreira EC, Rocha M (2006) A comparison of algorithms for the optimization of fermentation processes. 2006 IEEE Int Conf Evol Comput. https://doi.org/10.1109/CEC.2006.1688555

    Article  Google Scholar 

  48. Roubos JA, De Gooijer CD, Van Straten G, Van Boxtel AJB (1997) Comparison of optimization methods for fed-batch cultures of hybridoma cells. Bioprocess Eng 17:99–102. https://doi.org/10.1007/s004490050360

    Article  CAS  Google Scholar 

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Acknowledgements

The Director, CSIR—Central Food Technological Research Institute (CFTRI), Mysore, India, is also acknowledged for supporting this work.

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Correspondence to Sarma Mutturi.

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Mutturi, S. Dynamic optimization of fed-batch bioprocesses using flower pollination algorithm. Bioprocess Biosyst Eng 41, 1679–1696 (2018). https://doi.org/10.1007/s00449-018-1992-2

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