Solving ‎‎‎Multi-objective Optimal Control Problems of chemical ‎processes ‎using ‎Hybrid ‎Evolutionary ‎Algorithm

Document Type: Research Paper

Authors

1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

2 Department of Mathematics and Computer Science, Damghan University, Damghan, Iran

3 Department of Mathematics, Payame Noor University, Tehran, Iran

10.22052/ijmc.2018.137247.1370

Abstract

Evolutionary algorithms have been recognized to be suitable for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier‎. ‎This paper applies an evolutionary optimization scheme‎, ‎inspired by Multi-objective Invasive Weed Optimization (MOIWO) and Non-dominated Sorting (NS) strategies‎, ‎to find approximate solutions for multi-objective optimal control problems (MOCPs)‎. ‎The desired control function may be subjected to severe changes over a period of time‎. ‎In response to deficiency‎, ‎the process of dispersal has been modified in the MOIWO‎. ‎This modification will increase the exploration power of the weeds and reduces the search space gradually during the iteration process‎. ‎
‎The performance of the proposed algorithm ‎is compared with conventional Non-dominated Sorting Genetic Algorithm (NSGA-II) and Non-dominated Sorting Invasive Weed Optimization (NSIWO) algorithm‎.The results show that the proposed algorithm has better performance than others in terms of computing time‎, ‎convergence rate and diversity of solutions on the Pareto ‎frontier.

Keywords


 

1. L. Biegler, Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation, Comput. Chem. Eng. 8 (1984) 243248.

2. L. Biegler, An overview of simultaneous strategies for dynamic optimization, Chem. Eng Process: Process Intensif. 46 (11) (2007) 10431053.

3. H. Bock and K. Plitt, A multiple shooting algorithm for direct solution of optimal control problems. In: Proceedings of the 9th IFAC world congress, Budapest. Pergamon Press, 1984, pp. 243-247.

4. C. A. Coello, A comprehensive survey of evolutionary-based multi-objective optimization techniques, Knowl. Inf. Syst.1 (3) (1999) 269−308.

5. C. A. Coello andM. S. Lechuga, MOPSO: A proposal for multiple objective particle swarm optimization, In: Proceeding of Congress on Evolutionary Computation (CEC2002), Honolulu, HI. 1 (2002) 10511056.

6. I. Das and J. E. Dennis, Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multi-criteria optimization problems, SIAM. J.Optimiz. 8 (3) (1998) 631657.

7. K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms,Wiley 2001.

8. K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multi-objective geneticalgorithm: NSGA-II, IEEE. Trans. Evolut. Comput. 6 (2) (2002) 182197.

9. T. Erickson, A. Mayer andJ. Horn, The niched Pareto genetic algorithm 2 applied to the design of ground water remediation systems, Evolutionary Multi-Criterion Optimization: First International Conference, EMO. (2001) 681695.

  1. C. M. Fonseca, Multi-Objective Genetic Algorithms with Application to Control Engineering Problems, Ph.D. Thesis, University of Sheffield. Sheffield, 1995.
  2. S. M. K. Heris and H. Khaloozadeh, Open- and closed-loop multi-objective optimal strategies for HIV therapy using NSGA-II, IEEE. Trans. Biomed. Eng. 58 (6) (2011) 16781685.
  3. J. Knowles andD. Corne, ThePareto archived evolution strategy: A new baseline algorithm for Pareto multi-objective optimization, Proceedings of the 1999 IEEE Congress on Evolutionary Computation 1999.
  4. S. Kukkonen and K. Deb, Improved Pruning of Non-Dominated Solutions Based on Crowding Distance for Bi-Objective Optimization Problems, IEEE Congress on Evolutionary Computation, pp. 9198, 2007.
  5. D. Kundu, K. Suresh, S. Ghosh, S. Das and B. K. Panigrahi, Multi-objective optimization with artificial weed colonies, J. Inf. Sci. 181 (2011) 24412454.
  6. D. Leineweber, I. Bauer, H. Bock and J. Schlder, An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization, Part I: Theoretical aspects, Comput. Chem. Eng. 27 (2003) 157166.
  7. F. Logist, P. M. Van Erdeghem and J. F. Van Impe, Efficient deterministic multiple objective optimal control of (bio)chemical processes, Chem. Eng. Sci. 64 (2009) 25272538.
  8. F. Logist, B. Houska, M. Diehl and J. Van Impe, Fast Pareto set generation for nonlinear optimal control problems with multiple objectives, Struct. Multidisc. Optim. 42 (2010) 591603.
  9. F. Logist, B. Houska, M. Diehl and J. Van Impe, Robust multi-objective optimal control of uncertain (bio)chemical processes, Chem. Eng. Sci. 66 (2011) 46704682.
  10. F. Logist, S. Sager, C. Kirchesand and J. Van Impe, Efficient multiple objective optimal control of dynamic systems with integer controls, J. Process Control 20 (2010) 810822.
  11. F. Logist, M. Vallerio, B. Houska, M. Diehl and J. Van Impe, Multi-objective optimal control of chemical processes using ACADO toolkit, Comput. Chem. Eng. 37 (2012) 191199.
  12. R. Mehrabian and C. Lucas, A novel numerical optimization algorithm inspired from weed colonization, Ecol. Inform. 1 (4) (2006) 355366.
  13. A. Messac, A. Ismail-Yahaya and C. A. Mattson, The normalized normal constraint method for generating the Pareto frontier, Struct. Multidisc. Optim. 25 (2) (2003) 8698.
  14. K. Miettinen, Nonlinear Multi-Objective Optimization, Kluwer, Boston, 1999.
  15. A. H. Nikoofard, H. Hajimirsadeghi, A. Rahimi-Kian and C. Lucas, Multi-objective invasive weed optimization: Application to analysis of Pareto improvement models in electricity markets, Appl. Soft. Comput. 12 (2012) 100112.
  16. H. Modares and M. N. Sistani, Solving nonlinear optimal control problems using a hybrid IPSOSQP algorithm, Eng. Appl. Artif. Intel. 24 (2011) 476−484.
  17. H. Ohno, E. Nakanishi and T. Takamatsu, Optimal control of a semi-batch fermentation, Biotechnol. Bioeng. 18 (1976) 847864.
  18. G. C. Onwubolu and B. V. Babu, New Optimization Techniques in Engineering, Springer Verlag, Heidelberg, Germany 2004.
  19. N. Patel and N. Padhiyar, Modified genetic algorithm using box complex method: Application to optimal control problems, J. Process Control 26 (2015) 3550.
  20. N. Patel and N. Padhiyar, Multi-objective dynamic optimization study of fed-batch bio-reactor, Chem. Eng. Res. Des. 119 (2017) 160170.
  21. S. Panuganti, P. Roselyn John, D. Devraj and S. Sekhar Dash, Voltage stability constrained optimal power flow using NSGA-II, Comput. Water Energy Envir. Eng. 2 (2013) 18.
  22. S. Park and W. Fred Ramirez, Optimal production of secreted protein in fed-batch reactors, AIChE. J. 34 (1988) 15501558.
  23. D. Sarkar and J. Modak, Genetic algorithms with filters for optimal control problems infed-batch bioreactors, Bioprocess Biosyst. Eng. 26 (2004) 295−306.
  24. D. Sarkar and J. M. Modak, Pareto-optimal solutions for multi-objective optimization offed-batch bioreactors using non-dominated sorting genetic algorithm, Chem. Eng. Sci. 60 (2) (2005) 481492.
  25. J. D. Schafier, Multiple objective optimization with vector evaluated genetic algorithms, Proceedings of the First International Conference of Genetic Algorithms, Pittsburgh, pp. 93100, 1985.
  26. N. Srinivas and K. Deb, Multi-objective function optimization using non-dominated sorting genetic algorithms, Evolut.Comput.2 (3) (1995) 221248.
  27. F. Sun, W. Du, R. Qi, F. Qian and W. Zhong, A hybrid improved genetic algorithm and its application in dynamic optimization problems of chemical processes, Chin. J. Chem. Eng. 21 (2013) 144154.
  28. E. Zitzler and L. Thiele, Multi-objective evolutionary algorithms: A comparative case study and the strength Pareto approach, IEEE Trans. Evolut. Comput. 3 (1999) 257271.
  29. E. Zitzler, M. Laumanns and L. Thiele, SPEA2: Improving the strength Pareto evolutionary algorithm, Zurich, Switzerland: Swiss Federal Institute Technology, 2001.
  30. X. Zhang,  J. Xu and G. Cui, Research on invasive weed optimization based on the cultural framework, 3rd International Conference on Bio-Inspired Computing: Theories and Applications, IEEE Conference Publications, pp. 129134, 2008.
  31. P. Zhang, H. Chen, X. Liu and Z. Zhang, An iterative multi-objective particle swarm optimization-based control vector parameterization for state constrained chemical and biochemical engineering problems, Biochem. Eng. J. 103 (2015) 138151.