Abstract
In multiobjective particle swarm optimization (MOPSO) methods, selecting the local best and the global best for each particle of the population has a great impact on the convergence and diversity of solutions, especially when optimizing problems with high number of objectives. This paper presents an approach using two sets of nondominated solutions. The ability of the proposed approach to detect the true Pareto optimal solutions and capture the shape of the Pareto front is evaluated through experiments on well-known non-trivial multiobjective test problems as well as the real-life electric power dispatch problem. The diversity of the nondominated solutions obtained is demonstrated through different measures. The proposed approach has been assessed through a comparative study with the reported results in the literature.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abido MA (2002a) Optimal design of power system stabilizers using particle swarm optimization. IEEE Trans Energy Convers 17(3):406–413
Abido MA (2002b) Optimal power flow using particle swarm optimization. Int J Electrical Power Energy Syst 24(7):563–571
Abido MA (2003) Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans Power Syst 18(4):1529–1537
Abido MA (2006) Multiobjective evolutionary algorithms for electric power dispatch problem. IEEE Trans Evol Comput 10(3):315–329
Abido MA (2007) Two-level of nondominated solutions approach to multiobjective particle swarm optimization. In: Proceedings of the 2007 genetic and evolutionary computation conference, GECCO’2007, 7–11 July 2007, London, UK, pp 726–733
Angeline P (1998) Evolutionary optimization versus particle swarm optimization: philosophy and performance differences. In: Proceedings of the 7th annual conference on evolutionary programming, March 1998, pp 601–610
Branke J, Mostaghim S (2006) About selecting the personal best in multi-objective particle swarm optimization. In: Proceedings of the 9th international conference on parallel problem solving from nature—PPSN IX, Reykjavik, Iceland, 9–13 September 2006, pp 523–532
Coello CAC (1999) A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowl Inf Syst 1(3):269–308
Coello CAC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Congress on evolutionary computation (CEC’2002), vol 2. IEEE Service Center, Piscataway, New Jersey, May 2002, pp 1051–1056
Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279
Das DB, Patvardhan C (1998) New multi-objective stochastic search technique for economic load dispatch. IEE Proc Gener Transm Distrib 145(6):747–752
Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley-interscience series in systems and optimization. Wiley, Chichester
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithms: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Farag A, Al-Baiyat S, Cheng TC (1995) Economic load dispatch multiobjective optimization procedures using linear programming techniques. IEEE Trans Power Syst 10(2):731–738
Fieldsend JE, Singh S (2002) A multi-objective algorithm based upon particle swarm optimization, an efficient data structure and turbulence. In: Proceedings of the 2002 U.K. workshop on computational intelligence, Birmingham, UK, 2–4 September 2002, pp 37–44
Hu X, Eberhart R (2002) Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Congress on evolutionary computation (CEC’2002), vol 2, IEEE Service Center, Piscataway, New Jersey, May 2002, pp 1677–1681
Hu X, Eberhart R, Shi Y (2003) Particle swarm with extended memory for multiobjective optimization. In: Proceedings of 2003 IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003, pp 193–197
Huang VL, Suganthan PN, Liang JJ (2006) Comprehensive learning particle swarm optimizer for solving multiobjective optimization problems. Int J Intell Syst 21(2):209–226
Kennedy J (1997) The particle swarm: social adaptation of knowledge. In: Proceedings of the 1997 IEEE international conference on evolutionary computation ICEC’97, Indianapolis, Indiana, USA, pp 303–308
Kennedy J, Eberhart R (2001) Swarm intelligence. Morgan Kaufmann Publishers, San Francisco, CA
Li X (2003) A nondominated sorting particle swarm optimizer for multiobjective optimization. In: Lecture Notes in Computer Science, Proceedings of genetic and evolutionary computation GECCO 2003, vol 2723, Part I, Berlin, Germany, July 2003, pp 37–48
Lu H (2003) Dynamic population strategy assisted particle swarm optimization in multiobjective evolutionary algorithm design. IEEE Neural Network Society, IEEE NNS Student Research Grants 2002, Final reports 2003
Mishra S (2005) A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation. IEEE Trans Evol Comput 9(1):61–73
Morse JN (1980) Reducing the size of nondominated set: pruning by clustering. Comput Oper Res 7(1–2):55–66
Mostaghim S, Teich J (2003a) Strategies for finding good local guides in multiobjective particle swarm optimization (MOPSO). In: Proceedings of 2003 IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003, pp 26–33
Mostaghim S, Teich J (2003b) The role of ε-dominance in multiobjective particle swarm optimization methods. In: Proceedings of IEEE congress on evolutionary computation CEC’2003, Canberra, Australia, pp 1764–1771
Mostaghim S, Teich J (2004) Covering pareto-optimal fronts by subswarms in multiobjective particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation CEC’2004, Portland, Oregon, USA, 19–23 June 2004, pp 1404–1411
Ozcan E, Mohan C (1998) Analysis of a simple particle swarm optimization system. Intell Eng Syst Artif Neural Netw 8:253–258
Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization method in multiobjective problems. In: Proceedings of the ACM 2002 symposium on applied computing (SAC’2002), pp 603–607
Parsopoulos KE, Tasoulis DK, Vrahatis MN (2004) Multiobjective optimization using parallel vector evaluated particle swarm optimization. In: Proceedings of IASTED international conference on artificial intelligence and applications, as part of the 22nd IASTED international multi-conference on applied informatics, Innsbruck, Austria
Pulido GT, Coello Coello CA (2004) Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer. In: Proceedings of the genetic and evolutionary computation conference, Seattle, Washington, USA, Springer-Verlag, Lecture Notes in Computer Science, vol 3102, June 2004, pp 225–237
Reyes-Sierra M, Coello CAC (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308
Schaffer JD (1984) Multiobjective optimization with vector evaluated genetic algorithms, PhD Thesis, Vanderbilt University, Nashville, USA
Shi Y, Eberhart R (1998) Parameter selection in particle swarm optimization. In: Proceedings of the 7th annual conference on evolutionary programming, March 1998, pp 591–600
Song MP, Gu GC (2004) Research on particle swarm optimization: a review. In: Proceedings of the 3rd international conference on machine learning and cybernetics, Shanghai, Chaina, 26–29 August 2004, pp 2236–2241
Tasgetiren MF, Sevkli M, Liang YC, Gencyilmaz G (2004) Particle swarm optimization algorithm for permutation flowshop sequencing problem. In: Proceedings of the 4th international workshop on ant colony optimization and swarm intelligence, ANTS2004, LNCS 3172. Springer-Verlag, Brussels, Belgium, 5–8 September 2004, pp 382–390
Wachowiak MP, Smolíková R, Zheng Y, Zurada JM, Elmaghraby AS (2004) An approach to multimodal biomedical image registration utilizing particle swarm optimization. IEEE Trans Evol Comput 8(3):289–301
Zhang Y, Huang S (2004) A novel multiobjective particle swarm optimization for Buoys-arrangement design. In: Proceedings of IEEE/WIC/ACM international conference on intelligent agent technology (IAT 2004), Beijing, China, 20–24 Sept 2004, pp 24–30
Zitzler E, http://www.tik.ee.ethz.ch/~zitzler/testdata.html. Accessed 19 July 2009
Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications, Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich
Zitzler E, Thiele L (1998a) An evolutionary algorithm for multiobjective optimization: the strength pareto approach. TIK-Report, No. 43
Zitzler E, Thiele L (1998b) Multiobjective optimization using evolutionary algorithms—a comparative case study. In: Parallel Problem Solving from Nature V, pp 292–301, Amsterdam, September 1998, Springer-Verlag
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271
Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195
Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm. In: Proceedings of EUROGEN 2001, Athens, Greece, September 2001
Acknowledgment
The author would like to acknowledge the support and encouragement of King Fahd University of Petroleum & Minerals.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Abido, M.A. Multiobjective particle swarm optimization with nondominated local and global sets. Nat Comput 9, 747–766 (2010). https://doi.org/10.1007/s11047-009-9171-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-009-9171-7