A Modified Particle Swarm Optimization with Elite Archive for Typical Multi-Objective Problems

  • Zheng Li
  • Jinlei QinEmail author
Research Paper
Part of the following topical collections:
  1. Mathematics


The solution to multi-objective optimization problems with conflicting objectives is a Pareto-optimal solution set. It is well known that the critical work in multi-objective particle swarm optimization (MOPSO) is to find the global best guides for each particle in order to obtain satisfied Pareto fronts with high diversity. In this paper, a modified version of MOPSO is proposed, where dense and sparse distance are adopted to determine the global best guides, and Pareto archive with size limit is used to store the non-dominated solutions. In addition, a random number is used to judge whether the crowding distance considered or not, and the inertia weight decreases linearly to improve the speed of convergence and avoid precocity. The proposed approach is applied to several well-known benchmark functions, and the experimental results show that the diversity of swarm and distribution of Pareto fronts are well satisfied.


Multi-objective optimization Particle swarm optimization External archive Convergence Dense distance Sparse distance 



The research was supported by the Fundamental Research Funds for the Central Universities (2018MS076, 2015MS128) and the Hebei Province Natural Science Fund Program (F2014502081).


  1. Abido MA (2009) Multiobjective particle swarm optimization for environmental/economic dispatch problem. Electr Power Syst Res 79(7):1105–1113CrossRefGoogle Scholar
  2. Cai J, Ma X, Li Q (2009) A multi-objective chaotic particle swarm optimization for environmental/economic dispatch. Energy Convers Manag 50(5):1318–1325CrossRefGoogle Scholar
  3. Coello CA, Lechuga MS (2002) A proposal for multiple objective particle swarm optimization. In: IEEE proceedings, world congress on computational intelligence (CEC2002), pp 1051–1056Google Scholar
  4. Coello CAC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceedings of the 2002 congress on evolutionary computationGoogle Scholar
  5. Dhanalakshmi S, Kannan S, Mahadevan K, Baskar S (2011) Application of modified NSGA-II algorithm to combined economic and emission dispatch problem. Electr Power Energy Syst 33(4):992–1002CrossRefGoogle Scholar
  6. Eberhart HA (2002) Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: IEEE proceedings, world congress on computational intelligence (CEC2002)Google Scholar
  7. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human scienceGoogle Scholar
  8. Fieldsend JE, Everson RM, Singh S (2003) Using unconstrained elite archives for multiobjective optimization. IEEE Trans Evol Comput 7(3):305–323CrossRefGoogle Scholar
  9. Fiorentino HO, Cantane DR, Santos FLP, Bannwart BF (2014) Multiobjective genetic algorithm applied to dengue control. Math Biosci 258:77–84MathSciNetCrossRefzbMATHGoogle Scholar
  10. Holzmann T, Smith JC (2018) Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations. Eur J Oper Res 271(2):436–449MathSciNetCrossRefzbMATHGoogle Scholar
  11. Kalyanmoy D, 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
  12. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks Perth, Australia. IEEE, PiscatawayGoogle Scholar
  13. Lin Q, Li J, Du Z, Chen J, Ming Z (2015) A novel multi-objective particle swarm optimization with multiple search strategies. Eur J Oper Res 247(3):732–744MathSciNetCrossRefzbMATHGoogle Scholar
  14. Liu T, Jiao L, Ma W, Ma J, Shang R (2016) A new quantum-behaved particle swarm optimization based on cultural evolution mechanism for multiobjective problems. Knowl Based Syst 101:90–99CrossRefGoogle Scholar
  15. Osman MS, Abo-Sinna MA, Mousa AA (2009) An epsilon-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem. Electr Power Syst Res 79(11):1561–1567CrossRefGoogle Scholar
  16. Ren D, Cai Y, Huang H (2018) Genetic learning particle swarm optimization with diverse selection. In: 14th International Conference on Intelligent Computing, ICIC 2018, August 15, 2018–August 18, 2018, Wuhan, China, SpringerGoogle Scholar
  17. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the 1st international conference on genetic algorithms. Associates Inc., HillsdaleGoogle Scholar
  18. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360)Google Scholar
  19. Wang X, Cai W, Lu J, Sun Y (2014) Optimization of liquid desiccant regenerator with multiobject particle swarm optimization algorithm. Ind Eng Chem Res 53(49):19293–19303CrossRefGoogle Scholar
  20. Zinflou A, Gagne C, Gravel M (2012) GISMOO: A new hybrid genetic/immune strategy for multiple-objective optimization. Comput Oper Res 39(9):1951–1968MathSciNetCrossRefzbMATHGoogle Scholar
  21. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRefGoogle Scholar
  22. Zou W, Zhu Y, Chen H, Zhang B (2011) Solving multiobjective optimization problems using artificial bee colony algorithm. Discrete Dyn Nat Soc 2011:1–37MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of ComputerNorth China Electric Power University (Baoding)BaodingPeople’s Republic of China

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