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Particle swarm optimization algorithm driven by multichaotic number generator

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Abstract

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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References

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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

    Chapter  Google Scholar 

  • 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 

  • 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

  • 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 

  • 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 

  • 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 

  • 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 

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

    Google Scholar 

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

  • 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 

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

    Article  Google Scholar 

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

  • 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 

  • 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 

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

    Article  MathSciNet  Google Scholar 

  • 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

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

    Google Scholar 

  • 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 

  • 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 

  • 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

  • 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

  • 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

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

    Google Scholar 

  • 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 

  • 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 

  • 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

  • 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

  • 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

  • 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

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

  • 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 

  • 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 

  • 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 

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

    Google Scholar 

  • 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 

  • 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 

  • 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

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

  • 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

  • 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.

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Communicated by M. Pluhacek.

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.

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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). https://doi.org/10.1007/s00500-014-1222-z

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