Particle swarm optimization algorithm driven by multichaotic number generator


In this paper, the utilization of different chaotic systems as pseudo-random number generators (PRNGs) for velocity calculation in the PSO algorithm are proposed. Two chaos-based PRNGs are used alternately within one run of the PSO algorithm and dynamically switched over when a certain criterion is met. By using this unique technique, it is possible to improve the performance of PSO algorithm as it is demonstrated on different benchmark functions.

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  1. Aydin I, Karakose M, Akin E (2010) Chaotic-based hybrid negative selection algorithm and its applications in fault and anomaly detection. Exp Syst Appl 37(7):5285–5294

    Article  Google Scholar 

  2. Aziz-Alaoui MA, Robert C, Grebogi C (2001) Dynamics of a Henon-Lozi-type map. Chaos Solitons Fract 12(12):2323–2341

    Article  MATH  MathSciNet  Google Scholar 

  3. Caponetto R, Fortuna L, Fazzino S, Xibilia MG (2003) Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans Evol Comput 7(3):289–304

    Article  Google Scholar 

  4. Coelho LdS, Mariani VC (2009) A novel chaotic particle swarm optimization approach using Hnon map and implicit filtering local search for economic load dispatch. Chaos Solitons Fract 39(2):510–518

    Article  Google Scholar 

  5. Coelho LdS, Mariani VC (2012) Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning. Comput Mathem Appl 64(8):2371–2382

    MATH  MathSciNet  Google Scholar 

  6. Davendra D, Zelinka I, Senkerik R, Bialic-Davendra M (2010) Chaos driven evolutionary algorithm for the traveling salesman problem. In: Davendra D (ed) Travel salesman problem. Theory and applications. InTech, London

    Google Scholar 

  7. Davendra D, Zelinka I, Senkerik R (2010) Chaos driven evolutionary algorithms for the task of PID control. Comput Mathem Appl 60(4):1088–1104

    MATH  MathSciNet  Google Scholar 

  8. Davendra D, Bialic-Davendra M, Senkerik R (2013) Scheduling the lot-streaming flowshop scheduling problem with setup time with the chaos-induced enhanced differential evolution. In: 2013 IEEE Symposium on Differential Evolution (SDE), pp 119–126

  9. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. Proc Sixth Intern Sympos Micro Mach Human Sci 95:39–43

    Article  Google Scholar 

  10. Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Firefly algorithm with chaos. Commun Nonlin Sci Numer Simul 18(1):89–98

    Article  MATH  MathSciNet  Google Scholar 

  11. Hong W-C (2009) Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model. Ener Conv Manag 50(1):105–117

    Article  Google Scholar 

  12. Ickabadi A, Ebadzadeh MM, Safabakhsh R (2011) A novel particle swarm optimization algorithm with adaptive inertia weight. Appl Soft Comput 11(4):3658–3670

    Article  Google Scholar 

  13. Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE Intern Conf Neural Netw 4:1942–1948

    Google Scholar 

  14. Kennedy J, Mendes R (2002) Population structure and particle swarm performance. Proc 2002 Congr Evolut Comput CEC ’02 2:1671–1676.

  15. Kominkova Oplatkova Z, Senkerik R, Zelinka I, Pluhacek M (2013) Analytic programming in the task of evolutionary synthesis of a controller for high order oscillations stabilization of discrete chaotic systems. Comput Mathem Appl 66(2):177–189

    MathSciNet  Google Scholar 

  16. Lee JS, Chang KS (1996) Applications of chaos and fractals in process systems engineering. J Proc Cont 6(23):71–87

    Article  Google Scholar 

  17. Liang JJ, Suganthan PN (2005) Dynamic multiswarm particle swarm optimizer (DMS-PSO)”, IEEE Swarm Intell Symp, pp 124–129

  18. Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evolut Comput 10(3):281–295

    Article  Google Scholar 

  19. Liang W, Zhang L, Wang M (2011) The chaos differential evolution optimization algorithm and its application to support vector regression machine. J Softw 6(7):1297–1304

    Article  Google Scholar 

  20. Lozi R (2012) Emergence of randomness from chaos. Intern J Bifurcat Chaos 22(02):1250021

    Article  MathSciNet  Google Scholar 

  21. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) “Differential evolution algorithm with ensemble of parameters and mutation strategies” Applied Soft Computing, 11( 2): 1679–1696. doi:10.1016/j.asoc.2010.04.024

  22. Narendra KP, Vinod P, Krishan KS (2010) A random bit generator using chaotic maps. Intern J Netw Sec 10(1):32–38

    Google Scholar 

  23. Persohn KJ, Povinelli RJ (2012) Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation. Chaos Solitons Fract 45(3):238–245

    Article  Google Scholar 

  24. Pluhacek M, Senkerik R, Davendra D, Oplatkova ZK, Zelinka I (2013) On the behavior and performance of chaos driven PSO algorithm with inertia weight. Comput Mathem Appl 66(2):122–134

    Google Scholar 

  25. Pluhacek M, Senkerik R, Davendra D, Zelinka I (2013a) Designing PID controller for DC motor by means of enhanced PSO algorithm with dissipative chaotic map. In: Snel V, Abraham A, Corchado ES (eds) Soft computing models in industrial and environmental applications. Advances in intelligent systems and computing, vol 188. Springer, Berlin, pp 475–483

  26. Pluhacek M, Senkerik R, Zelinka I, Davendra D (2013b) Chaos PSO algorithm driven alternately by two different chaotic maps - An initial study. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp 2444–2449

  27. Pluhacek M, Senkerik R, Zelinka I (2014) Multiple choice strategy based PSO algorithm with chaotic decision making a preliminary study. In: Herrero, Baruque B, Klett F (eds) International Joint Conference SOCO13-CISIS13-ICEUTE13. Advances in intelligent systems and computing, vol 239. Springer International Publishing, pp 21–30

  28. Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Natural computing series. Springer, Berlin

    Google Scholar 

  29. Senkerik R, Zelinka I, Davendra D, Oplatkova Z (2010) Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation. Comput Mathem Appl 60(4):1026–1037

    MATH  MathSciNet  Google Scholar 

  30. Senkerik R, Oplatkova Z, Zelinka I, Davendra D (2013) Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: analytic programming. Mathem Comput Model 57(12):57–67

    Article  MathSciNet  Google Scholar 

  31. Senkerik R, Davendra D, Zelinka I, Pluhacek M, Oplatkova Z (2012a) An investigation on the differential evolution driven by selected discrete chaotic systems. In: 18th International Conference on Soft Computing, MENDEL 2012, pp 157–162

  32. Senkerik R, Davendra D, Zelinka I, Pluhacek M, Oplatkova Z (2012b) An Investigation on the Chaos driven differential evolution: an initial study. In: 5th International Conference on Bioinspired Optimization Methods and Their Applications, BIOMA 2012, pp 185–194

  33. Senkerik R, Pluhacek M, Oplatkova ZK, Davendra D, Zelinka I (2013) Investigation on the Differential Evolution driven by selected six chaotic systems in the task of reactor geometry optimization. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp 3087–3094

  34. Senkerik R, Pluhacek M, Zelinka I, Oplatkova Z, Vala R, Jasek R (2014) Performance of chaos driven differential evolution on shifted benchmark functions set. In: Herrero, Baruque B, Klett F (eds) International Joint Conference SOCO13-CISIS13-ICEUTE13. Advances in intelligent systems and computing, vol 239. Springer International Publishing, pp 41–50

  35. Sprott JC (2003) Chaos and time-series analysis. Oxford University Press, New York

  36. Wang X-y, Qin X (2012) A new pseudo-random number generator based on CML and chaotic iteration. Nonlin Dyn 70(2):1589–1592

    Google Scholar 

  37. Wu J, Lu J, Wang J (2009) Application of chaos and fractal models to water quality time series prediction. Environ Model Softw 24(5):632–636

    Article  Google Scholar 

  38. Yang L, Wang X-Y (2012) Design of pseudo-random bit generator based on chaotic maps. Intern J Mod Phys B 26(32):1250208

    Article  Google Scholar 

  39. Yuhui S, Eberhart R (1998) A modified particle swarm optimizer. IEEE World Congr Comput Intell 4–9:69–73

    Google Scholar 

  40. Zelinka I (2004) SOMA self-organizing migrating algorithm. New optimization techniques in engineering. Studies in fuzziness and soft computing, vol 141. Springer, Berlin, pp 167–217

    Google Scholar 

  41. Zelinka I (2009) Real-time deterministic chaos control by means of selected evolutionary techniques. Eng Appl Artif Intell 22(2):283–297

    Article  Google Scholar 

  42. Zelinka I, Chadli M, Davendra D, Senkerik R, Pluhacek M, Lampinen J (2013a) Do evolutionary algorithms indeed require random numbers? Extended study. In: Zelinka I, Chen G, Rssler OE, Snasel V, Abraham A (eds) Nostradamus 2013: prediction, modeling and analysis of complex systems. Advances in intelligent systems and computing, vol 210. Springer International Publishing, pp 61–75

  43. Zelinka I, Senkerik R, Pluhacek M (2013b) Do evolutionary algorithms indeed require randomness? In: Evolutionary Computation (CEC), 2013 IEEE Congress on, pp 2283–2289

  44. Zhenyu G, Bo C, Min Y, Binggang C (2006) Self-adaptive chaos differential evolution. In: Jiao L, Wang L, Gao X-B, Liu J, Wu F (eds) Advances in natural computation. Lecture notes in computer science, vol 4221. Springer, Berlin, pp 972–975

  45. Zhi-Hui Z, Jun Z, Yun L, Yu-hui S (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evolut Comput 15(6):832–847

    Article  Google Scholar 

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Correspondence to Michal Pluhacek.

Additional information

This work was supported by the Grant Agency of the Czech Republic-GACR P103/13/08195S, by the Development of human resources in research and development of latest soft computing methods and their application in practice project, reg. no. CZ.1.07/2.3.00/20.0072 funded by Operational Programme Education for Competitiveness, co-financed by ESF and state budget of the Czech Republic, partially supported by Grant of SGS No. SP2013/114, VB-Technical University of Ostrava.; by European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089; and by Internal Grant Agency of Tomas Bata University under the project No. IGA/FAI/2013/012.

Communicated by M. Pluhacek.

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Pluhacek, M., Senkerik, R. & Zelinka, I. Particle swarm optimization algorithm driven by multichaotic number generator. Soft Comput 18, 631–639 (2014).

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  • Particle swarm
  • Optimization
  • Swarm intelligence
  • Chaos
  • Evolutionary algorithms