Multi-Objective Differential Evolution (MODE) Algorithm for Multi-Objective Optimization: Parametric Study on Benchmark Test Problems

B.V. Babu*, Ashish. M. Gujrathi**
*Professor,Chemical Engineering Department,Birla Institute of Technology and Science(BITS),Pilani,Rajasthan,India.
**Lecturer,Chemical Engineering Department,Birla Institute of Technology and Science(BITS),Pilani,Rajasthan,India.
Periodicity:August - October'2007
DOI : https://doi.org/10.26634/jfet.3.1.697

Abstract

Multi-Objective Differential Evolution (MODE), a multi-population, multi-objective optimization approach using Differential Evolution (DE) has been successfully applied to selected real world problems. This algorithm is equipped with non-dominated population selection combined with basic DE algorithm. In this study, the MODE algorithm is further applied on six different Test problems with/without constraints and extensive simulation runs are carried out for parametric study. Pareto optimal solutions are obtained for each test problems. The Pareto fronts are compared on the basis of various values of key MODE parameters. This work resulted in identifying the sensitivity of various key parameters of the MODE algorithm applied on the hard test problems.

Keywords

Multi-objective optimization, Multi-Objective Differential Evolution (MODE), Pareto optimal front, Evolutionary computation, Population based search algorithms.

How to Cite this Article?

B.V. Babu and Ashish. M. Gujrathi (2007). Multi-Objective Differential Evolution (MODE) Algorithm for Multi-Objective Optimization: Parametric Study on Benchmark Test Problems. i-manager’s Journal on Future Engineering and Technology, 3(1), 47-59. https://doi.org/10.26634/jfet.3.1.697

References

[1]H.A. Abbas, R. Sarkar, and C. Newton, PDE: a Pareto- frontier differential evolution approach for multi-objective optimization problems, In: Proceedings of the 2001 Congress on Evolutionary Computation, Vol, 2 [IEEE, Piscataway, NJ, USA, 2001) 971 -978.
[2]. R. Angira and B.V.Babu, Optimization of Process Synthesis and Design Problems: A Modified Differential Evolution Approach, Chemical Engineering Science, 61 (14), (2006)4707-4721.
[3]. R. Angira and B.V.Babu, Multi-Objective Optimization using Modified Differential Evolution (MDE), International Journal of Mathematical Sciences: Special Issue on Recent Trends in Computational Mathematics and Its Applications, 5 (2), (2006) 371-387.
[4]. R. Angira and B.V.Babu, Performance of Modified Differential Evolution for Optimal Design of Complex and Non-Linear Chemical Processes, Journal of Experimental & Theoretical Artificial Intelligence, 18 (4), (2006) 501 -512.
[5]. B. V. Babu, Improved Differential Evolution for Single- and Multi-Objective Optimization: MDE, MODE, NSDE, and MNSDE,.Advances in Computational Optimization and its Applications, Edited by Kalyanmoy Deb, Partha Chakroborty, N G R Iyengar, and Santosh K Gupta. Universities Press, Hyderabad, (2007) 24-30.
[6]. B.V. Babu and A.S. Chaurasia, Optimization of Pyrolysis of Biomass Using Differential Evolution Approach, in: Proceedings of The Second International Conference on Computational Intelligence, Robotics, and Autonomous Systems (CIRAS- Singapore, 2003).
[7]. B.V. Babu and C. Gaurav, Evolutionary Computation Strategy for Optimization of an Alkylation Reaction, in: Proceedings of International Symposium & 53rd Annual Session of IIChE CHEMCON-2000 (Science City, Calcutta, 2000)
[8]. B. V. Babu and A. M. Gujarathi, Multi-Objective Differential Evolution (MODE) for Optimization of Supply Chain Planning and Management. In Proceedings of IEEE Congress on Evolutionary Computation (CEC-2007), Swissotel The Stamford, Singapore, September 25-28, 2007.
[9]. B. V. Babu and A. M. Gujarathi, £//f/sf-Multi-Objective Differential Evolution (E-MODE) Algorithm for MultiOobjective Optimization. Proceedings of 3rd Indian International Conference on Artificial Intelligence (IICAI- 2007), Pune, December 17-19,2007.
[10]. B.V. Babu and K.K.N. Sastry, Estimation of Heat- transfer Parameters in a Trickle-bed Reactor using Differential Evolution and Orthogonal Collocation, Computers & Chemical Engineering, 23, (1999) 327 339.
[11]. B.V. Babu and R. Angira, Optimization of Thermal Cracker Operation using Differential Evolution, in: Proceedings of International Symposium & 54th Annual Session of IIChE CHEMCON-2001. (CLRI, Chennai, 2001),
[12]. B.V. Babu and R. Angira, Optimization of Non-linear functions using Evolutionary Computation, in: Proceedings of 12th ISME Conference on Mechanical Engineering, Paper No. CT07 (Crescent Engineering College, Chennai, 2001) 153-157.
[13]. B.V. Babu and R. Angira, A Differential Evolution Approach for Global Optimization of MINLP Problems, in: Proceedings of 4th Asia-Pacific conference on Simulated Evolution and Learning (SEAL- 2002), Vol. 2 (Singapore, 2002)880-884.
[14]. B.V. Babu and R. Angira, New Strategies of Differential Evolution for Optimization of Extraction Process, in: Proceedings of International Symposium & 56th Annual Session of IIChE (CHEMCON-2003), (Bhubaneswar, 2003.)
[15]. B.V. Babu and R. Angira, Optimization of Water Pumping System Using Differential Evolution Strategies, in: Proceedings of The Second International Conference on Computational Intelligence, Robotics, and Autonomous Systems (CIRAS, Singapore, 2003).
[16]. B V Babu and R. Angira, Optimization of Industrial Processes using Improved and Modified Differential Evolution, In Soft Computing Applications in Industry, Edited by Bhanu Prasad, Springer-Verlag, 2007.
[17]. B.V. Babu and R.R Singh, Synthesis & optimization of Heat Integrated Distillation Systems Using Differential Evolution, in: Proceedings of All-India seminar on Chemical Engineering Progress on Resource Development: A Vision 2010 and Beyond, (IE (I), Bhuvaneshwar, 2000),
[18]. B. V. Babu and S.A. Munawar, Differential Evolution Strategies for Optimal Design of Shell-and-Tube Heat Exchangers. Chemical Engineering Science, 62 (14), (2007)3720- 3739.
[19]. B.V. Babu and S.A. Munawar, Optimal Design of Shell & Tube Heat Exchanger by Different strategies of Differential Evolution, PreJournal.com - The Faculty Lounge, Article No. 003873, Available online at : http://www.prejournal.com (2001).
[20]. B.V. Babu, Process Plant Simulation, (New York: Oxford University Press, 2004).
[21]. B.V. Babu, J.H. Syed Mubeen and Pallavi G. Chakole, Multi objective optimization using Differential Evolution, TechGenesys-The journal of Information Technology, 2 (2), (2005) 4-12.
[22]. B. V. Babu, J.H. Syed Mubeen, and Pallavi G.Chakole, Simulation and Optimization of Wiped-Film Poly-Ethylene Terephthalate (PET) Reactor using Multiobjective Differential Evolution (MODE), Materials and Manufacturing Processes: Special Issue on Genetic Algorithms in Materials, 22 (5), (2007) 541 -552.
[23]. B.V. Babu, Pallavi Chakole, and J.H.Syed Mubeen, Multiobjective Differential Evolution (MODE) for Optimization of Adiabatic Styrene Reactor, Chemical Engineering Science, 60 (17), (2005) 4822-4837.
[24]. B.V. Babu, R. Angira, and A. Nilekar, Differential Evolution for Optimal Design of an Auto-Thermal Ammonia Synthesis Reactor, in: Proceedings of The Eighth World Multi-Conference on Systemics, Cybernetics and Informatics (SCI-2004), (Orlando, Florida, USA, 2004)
[25]. A.D. Belegundu and T.R. Chandrupatla, Optimization Concepts and Applications in Engineering. (Pearson Education (Singapore) Pte. Ltd., New Delhi, 2002)
[26]. T. T. Binh and Korn, U. (1997). MOBES: A multi objective evolutions strategy for constrained optimization problems, in The third International conference on Genetic Algorithms (Mendel, 1997), 176-182.
[27]. V. Chankong and Haimes, Y. Y., Multiobjective Decision making Theory and Methodology, (New York: North-Holland 1983).
[28]. J. R Chiou and F.S. Wang, Hybrid Method of Evolutionary Algorithms for Static and Dynamic Optimization Problems with Application to a Fed-batch Fermentation Process, Computers & Chemical Engineering, 23, (1999) 1277-1291.
[29]. D. Dasgupta and Z. Michalewicz, Evolutionary algorithms in Engineering Applications, (Germany: Springer, 1997).
[30]. K. Deb, An efficient constraint handling method for genetic algorithms. Computer Methods in applied Mechanics and Engineering, 186(2-4), (2000)311-338.
[31]. K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, (New York: John Wiley & Sons Limited, 2001). .
[32]. D.E. Goldberg, Genetic Algorithms in search. Optimization, and Machine learning, (MA: Addison- Wesley, 1989)
[33]Indraneel Das, 1997, Home page of Multi-objective optimization. Available: http://www- fp.mcs.anl.gov/otc/Guide/OptWeb/multiobj/
[34]. M. H. Lee, C. Han, and K. S. Cheng, Dynamic Optimization of a Continuous Polymer Reactor using a Modified Differential Evolution, Industrial & Engineering Chemistry Research, 38(12), (1999) 4825-4831.
[35]. J. C. Lu and F. S. Wang, Optimization of Low Pressure Chemical Vapor Deposition Reactors Using Hybrid Differential Evolution, Canadian Journal of Chemical Engineering, 79 (2), (2001) 246-254.
[36]. G. C. Onwubolu and B.V. Babu, New Optimization Techniques in Engineering, (Germany: Springer- Verlag, 2004).
[37]. E. G. Pinto, Supply Chain Optimization using Multi- Objective Evolutionary Algorithms, Technical Report, Availableonlineat: http://www.engr.psu.edu/ce/Divisions/Hydro/Reed/Report s.htm
[38]. K. Price and R. Storn, Differential Evolution - A simple evolution strategy for fast optimization. Dr. Dobb's Journal, 22 (4), (1997) 18 24 and 78.
[39]. K. Price and R. Storn, 2003, Home Page of Differential Evolution, Available: http://www. ICSI. Berkeley.edu/~storn/code. html.
[40]. R. Storn, Differential Evolution design of an IIR-filter with requirements for magnitude and group delay. International Computer Science Institute, (1995) TR-95- 026.
[41]. F. S. Wang and W.M. Cheng, Simultaneous optimization of feeding rate and operation parameters for fed-batch fermentation processes. Biotechnology Progress, 15 (5), (1999) 949-952.
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