An Improved VEPSO Algorithm for Multi-objective Optimisation Problems

  • Kian Sheng Lim
  • Salinda Buyamin
  • Anita Ahmad
  • Sophan Wahyudi Nawawi
  • Zuwairie Ibrahim
  • Faradila Naim
  • Kamarul Hawari Ghazali
  • Norrima Mokhtar
Conference paper


Multi-objective optimisation problem is the problem which contains more than one objective that needs to be solved simultaneously. The vector evaluated particle swarm optimisation algorithm is widely used for such purpose, where this algorithm optimised one objective using one swarm of particles by the guidance from the best solution found by another swarm. However, this best solution is only updated when a solution is better with respect to the optimised objective and results in poor performance. Therefore, the vector evaluated particle swarm optimisation algorithm is improved by incorporating the non-dominated solutions for guiding the particle movement during optimisation. The performance of the improved algorithm is analysed with several performance measures and simulated on various test functions. The results suggest that the improved algorithm outperformed the performance of the original algorithm.


Particle Swarm Optimisation Test Problem Pareto Front Particle Swarm Optimisation Algorithm Single Objective Function 



This work is supported by the Research University Grant (VOT 04J99) from Universiti Teknologi Malaysia, Exploratory Research Grant Scheme (RDU130605), Research Acculturation Grant Scheme (RDU121403) and MyPhD Scholarship from Ministry of Higher Education of Malaysia.


  1. 1.
    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):287MathSciNetGoogle Scholar
  2. 2.
    Coello CA, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Congress on evolutionary computation (CEC 2002), vol 2. IEEE, pp 1051–1056Google Scholar
  3. 3.
    Coello Coello CA, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279CrossRefGoogle Scholar
  4. 4.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  5. 5.
    Li X (2003) A non-dominated sorting particle swarm optimizer for multiobjective optimization. In: Cantú-Paz E et al (eds) Genetic and evolutionary computation. Springer, Berlin/Heidelberg, pp 198–198Google Scholar
  6. 6.
    Reyes-Sierra M, Coello Coello CA (2005) Improving PSO-based multi-objective optimization using crowding, mutation and ε-dominance. In: Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization. Springer, Berlin/Heidelberg, pp 505–519CrossRefGoogle Scholar
  7. 7.
    Abido M (2010) Multiobjective particle swarm optimization with nondominated local and global sets. Nat Comput 9(3):747–766CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization method in multiobjective problems. In: Proceedings of the ACM symposium on applied computing, ACM, Madrid, pp 603–607Google Scholar
  9. 9.
    Gies D, Rahmat-Samii Y (2004) Vector evaluated particle swarm optimization (VEPSO): optimization of a radiometer array antenna. In: IEEE antennas and propagation society international symposium, vol 3. IEEE, pp 2297–2300Google Scholar
  10. 10.
    Rao SMV, Jagadeesh G (2010) Vector evaluated particle swarm optimization of supersonic ejector for hydrogen fuel cells. J Fuel Cell Sci Tech 7(4):041014–041017CrossRefGoogle Scholar
  11. 11.
    Omkar SN, Mudigere D, Naik GN, Gopalakrishnan S (2008) Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures. Comput Struct 86(1–2):1–14CrossRefGoogle Scholar
  12. 12.
    Vlachogiannis JG, Lee KY (2009) Review: multi-objective based on parallel vector evaluated particle swarm optimization for optimal steady-state performance of power systems. Expert Syst Appl 36(8):10802–10808CrossRefGoogle Scholar
  13. 13.
    Grobler J (2009) Particle swarm optimization and differential evolution for multi objective multiple machine scheduling in Department of industrial and systems engineering. University of Pretoria, PretoriaGoogle Scholar
  14. 14.
    Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. The Morgan Kaufmann series. In: Fogel DB (ed) Evolutionary computation. Morgan Kaufmann Publishers, San Francisco, p 512Google Scholar
  15. 15.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, vol 4, pp 1942–1948Google Scholar
  16. 16.
    El-Sayed H, Belal M, Almojel A, Gaber J (2006) Swarm intelligence. In: Olariu S, Zomaya AY (eds) Handbook of bioinspired algorithms and applications. Taylor and Francis Group, Boca Raton, pp 55–63Google Scholar
  17. 17.
    Schaffer JD (1984) Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition), in Faculty of Graduate School. Vanderbilt University, Nashville, p 166Google Scholar
  18. 18.
    Özcan E, Yılmaz M (2007) Particle swarms for multimodal optimization. In: Beliczynski B et al (eds) Adaptive and natural computing algorithms. Springer, Berlin/Heidelberg, pp 366–375CrossRefGoogle Scholar
  19. 19.
    Schoeman I, Engelbrecht A (2005) A parallel vector-based particle swarm optimizer. In: Ribeiro B et al (eds) Adaptive and natural computing algorithms. Springer, Vienna, pp 268–271CrossRefGoogle Scholar
  20. 20.
    Van Veldhuizen DA (1999) Multiobjective evolutionary algorithms: classifications, analyses, and new innovations, in Air Force Institute of Technology. Air University, Wright-Patterson AFB, Ohio, USA, p 249Google Scholar
  21. 21.
    Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271CrossRefGoogle Scholar
  22. 22.
    Zitzler E, Deb K, Thiele L (2000) Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evol Comput 8(2):173–195CrossRefGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Kian Sheng Lim
    • 1
  • Salinda Buyamin
    • 1
  • Anita Ahmad
    • 1
  • Sophan Wahyudi Nawawi
    • 1
  • Zuwairie Ibrahim
    • 2
  • Faradila Naim
    • 2
  • Kamarul Hawari Ghazali
    • 2
  • Norrima Mokhtar
    • 3
  1. 1.Faculty of Electrical EngineeringUniversiti Teknologi MalaysiaJohor BahruMalaysia
  2. 2.Faculty of Electrical and Electronic EngineeringUniversiti Malaysia PahangPekanMalaysia
  3. 3.Department Of Electrical Engineering, Faculty of EngineeringUniversiti MalayaKuala LumpurMalaysia

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