Improving the PSO method for global optimization problems

  • Ioannis G. TsoulosEmail author
  • Alexandros Tzallas
  • Evaggelos Karvounis
Original Paper


The paper introduces two modifications for the well-known PSO method to solve global optimization problems. The first modification deals with the termination of the method and the second with the bounding of the so-called velocity in order to prevent the method from creating particles outside the domain range of the objective function. The modified method was tested on a series of global optimization problems from the relevant literature and the results are reported.


Particle swarm optimization Stochastic methods Termination rules 



This work is partly funded by the project entitled HuMORIST-Hospital MOnitoRIng SysTem, co-financed by the European Union and Greek national funds through the Operational Program for Research and Innovation Smart Specialization Strategy (RIS3) of Ipeiros (Project Code: ΗΠ1ΑΒ-00260).


  1. Ali MM, Khompatraporn C, Zabinsky ZB (2005) A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J Glob Optimiz 31:635–672MathSciNetCrossRefGoogle Scholar
  2. Angelov P (1994) A generalized approach to fuzzy optimization. Int J Intell Syst 1994:261–268CrossRefGoogle Scholar
  3. Araujo E, Coelho LS (2008) Particle swarm approaches using Lozi map chaotic sequences to fuzzy modelling of an experimental thermal-vacuum system, Appl Soft Comput 8:1354–1364CrossRefGoogle Scholar
  4. Barhen J, Protopopescu V, Reister D (1997) TRUST: a deterministic algorithm for global optimization. Science 16:1094–1097MathSciNetCrossRefGoogle Scholar
  5. de Moura Meneses AA, Machado MD, Schirru R (2009) Particle swarm optimization applied to the nuclear reload problem of a pressurized water reactor. Progr Nuclear Energy 51:319–326CrossRefGoogle Scholar
  6. Duan Q, Sorooshian S, Gupta V (1992) Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resourc Res 28:1015–1031CrossRefGoogle Scholar
  7. Gaing Z-L (2003) Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst 18:1187–1195CrossRefGoogle Scholar
  8. Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Appl Math Comput 274:292–305MathSciNetzbMATHGoogle Scholar
  9. Gaviano M, Ksasov DE, Lera D, Sergeyev YD (2003) Software for generation of classes of test functions with known local and global minima for global optimization. ACM Trans Math Softw 29:469–480MathSciNetCrossRefGoogle Scholar
  10. Goldberg D (1989) Genetic algorithms in search. Optimization and machine learning. Addison-Wesley Publishing Company, ReadingzbMATHGoogle Scholar
  11. Hosseini SA, Hajipour A, Tavakoli H (2019) Design and optimization of a CMOS power amplifier using innovative fractional-order particle swarm optimization. Appl Soft Comput 85:105831CrossRefGoogle Scholar
  12. Isiet M, Gadala M (2019) Self-adapting control parameters in particle swarm optimization. Appl Soft Comput 83:105653CrossRefGoogle Scholar
  13. Kennedy J, Eberhart RC (1999) The particle swarm: social adaptation in information processing systems. In: Corne D, Dorigo M, Glover F (eds) New ideas in optimization. McGraw-Hill, Cambridge, pp 11–32Google Scholar
  14. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680MathSciNetCrossRefGoogle Scholar
  15. Lennard-Jones JE (1924) On the determination of molecular fields. Proc R Soc Lond A 106:463–477CrossRefGoogle Scholar
  16. Lin Y, Stadtherr MA (2004) Advances in interval methods for deterministic global optimization in chemical engineering. J Glob Optimiz 29:281–296MathSciNetCrossRefGoogle Scholar
  17. Liu B, Wang L, Jin YH, Tang F, Huang DX (2005) Improved particle swarm optimization combined with chaos. Chaos Solitons Fractals 25:1261–1271CrossRefGoogle Scholar
  18. Mariani VC, Duck ARK, Guerra FA (2012) Leandro dos Santos Coelho, R.V. Rao, Heat exchanger design, Shell and tube heat exchanger (STHE), Economic optimization, Particle swarm optimization, Quantum particle swarm optimization, Chaos theory. Appl Therm Eng 42:119–128CrossRefGoogle Scholar
  19. Marinakis Y (2008) Magdalene Marinaki, Georgios Dounias, particle swarm optimization for pap-smear diagnosis. Expert Syst Appl 35:1645–1656CrossRefGoogle Scholar
  20. Michaelewizc Z (1996) Genetic algorithms + data structures = evolution programs. Springer, BerlinGoogle Scholar
  21. Pardalos PM, Shalloway D, Xue G (1994) Optimization methods for computing global minima of nonconvex potential energy functions. J Glob Optimiz 4:117–133MathSciNetCrossRefGoogle Scholar
  22. Park J-B, Jeong Y-W, Shin J-R, Lee KY (2010) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25:156–166CrossRefGoogle Scholar
  23. Powell MJD (1989) A tolerant algorithm for linearly constrained optimization calculations. Math Program 45:547–566MathSciNetCrossRefGoogle Scholar
  24. Price WL (1977) Global optimization by controlled random search. Comput J 20:367–370CrossRefGoogle Scholar
  25. Shahzad F, Baig AR, Masood S, Kamran M, Naveed N (2009) Opposition-based particle swarm optimization with velocity clamping (OVCPSO). In: Yu W, Sanchez EN (eds) Advances in computational intelligence. Advances in intelligent and soft computing, vol 116. Springer, Berlin, HeidelbergGoogle Scholar
  26. Shaw R, Srivastava S (2007) Particle swarm optimization: a new tool to invert geophysical data. Geophysics 2007:72Google Scholar
  27. Shi Y, Eberhart RC (1998) Parameter Selection in particle swarm optimization. In: Evolutionary Programming VII. Lecture Notes in Computer Science, vol 1447. Springer, Berlin, pp 591-600Google Scholar
  28. Shi XH, Liang YC, Lee HP, Lu C, Wang LM (2005) An improved GA and a novel PSO-GA based hybrid algorithm. Inf Process Lett 93:255–261MathSciNetCrossRefGoogle Scholar
  29. Sun J, Xu W, Fang W, Algorithm Quantum-Behaved Particle Swarm Optimization, with Controlled Diversity. In: Alexandrov VN, van Albada GD, Sloot PMA, Dongarra J (eds) Computational science–ICCS 2006. ICCS, (2006) Lecture Notes in Computer Science, vol 3993. Springer, Berlin, Heidelberg, p 2006Google Scholar
  30. Tang R-L, Fang Y-J (2015) Modification of particle swarm optimization with human simulated property. Neurocomputing 153:319–331CrossRefGoogle Scholar
  31. Tsoulos IG (2008) Modifications of real code genetic algorithm for global optimization. Appl Math Comput 203:598–607MathSciNetzbMATHGoogle Scholar
  32. Wachowiak MP, Smolikova R, Yufeng Z, Zurada JM, Elmaghraby AS (2004) An approach to multimodal biomedical image registration utilizing particle swarm optimization. IEEE Trans Evol Comput 8:289–301CrossRefGoogle Scholar
  33. Wales DJ, Scheraga HA (1999) Global optimization of clusters, crystals, and biomolecules. Science 27:1368–1372CrossRefGoogle Scholar
  34. Yapo PO, Gupta HV, Sorooshian S (1998) Multi-objective global optimization for hydrologic models. J Hydrol 204:83–97CrossRefGoogle Scholar
  35. Yasuda K, Iwasaki N (2004) Adaptive particle swarm optimization using velocity information of swarm. In: 2004 IEEE international conference on systems, man and cybernetics (IEEE Cat. No.04CH37583), The Hague, pp 3475-3481, vol 4Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  • Ioannis G. Tsoulos
    • 1
    Email author
  • Alexandros Tzallas
    • 1
  • Evaggelos Karvounis
    • 1
  1. 1.Department of Informatics and TelecommunicationsUniversity of IoanninaArtaGreece

Personalised recommendations