Abstract
An improved multiobjective particle swarm optimization algorithm is developed to get and compare Pareto fronts for constrained and unconstrained optimization test problems, with two objective functions and with a variable number of decision variables, available in literature. A new Minimum Angular Distance Information technique, to assign the best local guide for each particle within the swarm to get the Pareto front in the polar coordinate system, is adopted and verified. An external repository (archive) is used to store the nondominated particles at the end of each iteration, and a crowding distance technique is followed to maintain the archive size and the front diversity for each test problem. A self-adaptive penalty function technique is used to handle the constraint functions through transforming the original objective functions into new penalized functions based on their amount of constraint violation at each iteration. The developed algorithm is coded by Matlab formulas and verified via thirteen well-known test problems. Test results, represented in the regular Pareto fronts and the values of three comparative metrics (GD, S, and ER) calculated to verify the proposed algorithm, show more efficient and realistic agreements compared with that gained from previous studies and algorithms. Applying different engineering design problems to the developed algorithm is suggested as a future work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Coello Coello, A.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. J. Comput. Methods Appl. Mech. Eng. 191(11–12), 1245–1287 (2002)
Coello Coello, A., Pulido, T., Lechugu, M.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 265–279 (2004)
Knowles, J., Corne, W.: Approximating the nondominated front using the Pareto archived evolution strategy. J. Evol. Comput. 8(2), 149–172 (2000)
Coello Coello, A., Pulido, T.: Multiobjective optimization using a micro-genetic algorithm. In: Spector, L., et al. (eds.) Proceedings of Genetic and Evolutionary Computation Conference (GECCO 2001), San Francisco, CA (2001)
Tessema, G.: A self adaptive genetic algorithm for constrained optimization. M. Sc. thesis, Faculty of Graduate College, Oklahoma State University, pp. 29–39, December 2006
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the Fourth IEEE International Conference on Neural Networks, Perth, Australia (1995). IEEE Service Center 1942–1948, 1995
Kumer, V., Minz, S.: Multi-objective particle swarm optimization: an introduction. J. Smart Comput. Rev. 4(5), 335–353 (2014)
Özkaya, U., Güneş, F.: A modified particle swarm optimization algorithm and its application to the multiobjective FET modeling problem. Turk J. Elec. Eng. Comput. Sci. 20(2), 263–271 (2012)
Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. J. Evol. Comput. 4(1), 1–32 (1996)
Courant, R.: Variational methods for the solution of problems of equilibrium and vibration. Bull. Am. Math. Soc. 49(1), 1–23 (1943)
Fiacco, V., McCormick, P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York (1968). 201 p
Coello Coello, A.: comprehensive survey of evolutionary-based multiobjective optimization techniques. Int. J. Knowl. Inf. Syst. 1(3), 269–308 (1999)
Mishra, K., Harit, S.: A fast algorithm for finding the nondominated set in multiobjective optimization. Int. J. Comput. Appl. (0975-8887) 1(25), 35–39 (2010)
Raquel, C., Naval, P.: An effective use of crowding distance in multiobjective particle swarm optimization. In: GECCO 2005 Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation, 25–29 June 2005, Washington DC, USA, pp. 257–264 (2005)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast Elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Schoenauer, M., et al. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45356-3_83
Van Veldhuizen, D.A., Gary, B.: Multiobjective evolutionary algorithm research: a history and analysis. Technical report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1998)
Schott, J.: Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA (1995)
Van Veldhuizen, D.A.: Multiobjective evolutionary algorithm: classification, analysis, and new innovations. Ph.D. thesis, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1999)
Binh, T.: A multi objective evolutionary algorithm: the study cases. Technical report, Institute for Automation and Communication, Barleben, Germany (1999)
Kursawe, F.: A variant of evolution strategies for vector optimization. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 193–197. Springer, Heidelberg (1991). https://doi.org/10.1007/BFb0029752
Deb, K.: Multi-objective genetic algorithms: problem difficulties and construction of test problems. J. Evol. Comput. 7(1), 205–230 (1999)
Chakong, V., Haimes, Y.: Multiobjective Decision Making Theory and Methodology. Elsevier Science, New York (1983)
Fonseca, C., Fleming, P.: Genetic algorithms for multi-objective optimization: formulation, discussion and generalization. In: Proceedings of the 5th International Conference on Genetic Algorithms, San Francisco, CA, USA (1993)
Poloni, C., Giurgevich, A., Onesti, A., Pediroda, V.: Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics. J. Comput. Methods Appl. Mech. Eng. 186(2–4), 403–420 (2000)
Schaffer, J.: Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the First International Conference on Genetic Algorithms, pp. 93–100 (1985)
Zitzler, E., Deb, K., Theile, L.: Comparison of multiobjective evolutionary algorithms: empirical results. J. Evol. Comput. 8(2), 173–195 (2000)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Saleh, I.K., Özkaya, U., Hasan, Q.F. (2018). Improving Multiobjective Particle Swarm Optimization Method. In: Al-mamory, S., Alwan, J., Hussein, A. (eds) New Trends in Information and Communications Technology Applications. NTICT 2018. Communications in Computer and Information Science, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-030-01653-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-01653-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01652-4
Online ISBN: 978-3-030-01653-1
eBook Packages: Computer ScienceComputer Science (R0)