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An improved quantum-behaved particle swarm optimization algorithm

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Abstract

In this paper, we propose some improvements that enhance the optimization ability of quantum-behaved particle swarm optimization algorithms. First, we propose an encoding approach based on qubits described on the Bloch sphere. In our approach, each particle contains three groups of Bloch coordinates of qubits, and all three groups of coordinates are regarded as approximate solutions describing the optimization result. Our approach updates the particles using the rotation of qubits about an axis on the Bloch sphere. This updating approach can simultaneously adjust two parameters of qubits, and can automatically achieve the best matching of two adjustments. To avoid premature convergence, the mutation is performed with Hadamard gates. The optimization process is performed in the n-dimensional hypercube space [−1,1]n, so the proposed approach can be easily adapted to a variety of optimization problems. The experimental results show that the proposed algorithm is superior to the original one in optimization ability.

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References

  1. Kennedy J, Eberhart RC (1995) Particle swarms optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948

    Chapter  Google Scholar 

  2. Guo WZ, Chen GL, Xiong NX, Peng SJ (2011) Hybrid particle swarm optimization algorithm for VLSI circuit partitioning. J Softw 22(5):833–842

    Article  MATH  Google Scholar 

  3. Hamid M, Saeed J, Seyed M et al (2013) Dynamic clustering using combinatorial particle swarm optimization. Appl Intell 38(3):289–314

    Article  Google Scholar 

  4. Lin SW, Ying KC, Chen SC (2008) Particle swarm optimization for parameter determination and feature selection of support vector machines. Expert Syst Appl 35(4):1817–1824

    Article  Google Scholar 

  5. Yamina M, Ben A (2012) Psychological model of particle swarm optimization based multiple emotions. Appl Intell 36(3):649–663

    Article  Google Scholar 

  6. Cai XJ, Cui ZH, Zeng JC (2008) Dispersed particle swarm optimization. Inf Process Lett 105(6):231–235

    Article  MATH  MathSciNet  Google Scholar 

  7. Bergh F, Engelbrecht AP (2005) A study of particle swarm optimization particle trajectories. Inf Sci 176(8):937–971

    Google Scholar 

  8. Chatterjee A, Siarry P (2007) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33(3):859–871

    Article  Google Scholar 

  9. Lu ZS, Hou ZR (2004) Particle swarm optimization with adaptive mutation. Acta Electron Sin 32(3):416–420

    Google Scholar 

  10. Liu Y, Qin Z, Shi ZW (2007) Center particle swarm optimization. Neurocomputing 70(4–6):672–679

    Article  Google Scholar 

  11. Liu B, Wang L, Jin YH (2005) Improved particle swarm optimization combined with chaos. Chaos Solitons Fractals 25(5):1261–1271

    Article  MATH  Google Scholar 

  12. Luo Q, Yi DY (2008) A co-evolving framework for robust particle swarm optimization. Appl Math Comput 199(2):611–622

    Article  MathSciNet  Google Scholar 

  13. Zhang YJ, Shao SF (2011) Cloud mutation particle swarm optimization algorithm based on cloud model. Pattern Recognition & Artificial Intelligence 24(1):90–95

    MathSciNet  Google Scholar 

  14. Zhu HM, Wu YP (2010) A PSO algorithm with high speed convergence. Control Decis 25(1):20–24

    MATH  Google Scholar 

  15. Wang K, Zheng YJ (2012) A new particle swarm optimization algorithm for fuzzy optimization of armored vehicle scheme design. Appl Intell 37(4):520–526

    Article  Google Scholar 

  16. Salman AK, Andries PE (2012) A fuzzy particle swarm optimization algorithm for computer communication network topology design. Appl Intell 36(1):161–177

    Article  Google Scholar 

  17. Mohammad SN, Mohammad RA, Maziar P (2012) LADPSO: using fuzzy logic to conduct PSO algorithm. Appl Intell 37(2):290–304

    Article  Google Scholar 

  18. Zheng YJ, Chen SY (2013) Cooperative particle swarm optimization for multi-objective transportation planning. Appl Intell 39(1):202–216

    Article  Google Scholar 

  19. Jose GN, Enrique A (2012) Parallel multi-swarm optimizer for gene selection in DNA microarrays. Appl Intell 37(2):255–266

    Article  Google Scholar 

  20. Benioff P (1980) The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by turing machines. J Stat Phys 22(5):563–590

    Article  MathSciNet  Google Scholar 

  21. Benioff P (1982) Quantum-mechanical Hamiltonian models of turing machines that dissipate no energy. Phys Rev Lett 48:1581–1585

    Article  MathSciNet  Google Scholar 

  22. Deutsch D (1989) Quantum computational networks. In: Proceedings of the Royal Society, pp 73–90

    Google Scholar 

  23. Deutsch D, Jozsa R (1992) Rapid solution of problems by quantum computation. In: Proceedings of the Royal Society, pp 553–558

    Google Scholar 

  24. Simon D (1994) On the power of quantum computation. In: Proceedings of the 35th annual symposium on foundations of computer science, pp 116–123

    Chapter  Google Scholar 

  25. Steane AM (1997) In: Quantum computation, arXiv:Quant-ph/9708022

    Google Scholar 

  26. Sun J, Feng B, Xu WB (2004) Particle swam optimization with particles having quantum behavior. In: Proceedings of IEEE conference on evolutionary computation, pp 325–331

    Google Scholar 

  27. Sun J, Feng B, Xu WB (2004) A global search strategy of quantum-behaved particle swarm optimization. In: Proceedings of IEEE conference on cybernetics and intelligent systems, pp 111–116

    Google Scholar 

  28. Sun J, Xu WB, Feng B (2005) Adaptive parameter control for quantum-behaved particle swarm optimization on individual level. In: Proceedings of IEEE conference on cybernetics and intelligent systems, pp 3049–3054

    Google Scholar 

  29. Said MM, Ahmed AK (2005) Investigation of the quantum particle swarm optimization technique for electromagnetic applications. In: Proceedings of IEEE antennas and propagation society international symposium, pp 45–48

    Google Scholar 

  30. Sun J, Xu WB, Fang W (2006) Quantum-behaved particle swarm optimization algorithm with controlled diversity. In: Proceedings of international conference on computational science, pp 847–854

    Google Scholar 

  31. Xia ML, Sun J, Xu WB (2008) An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl Math Comput 205(2):751–759

    Article  Google Scholar 

  32. Fang W, Sun J, Xie ZP, Xu WB (2010) Convergence analysis of quantum-behaved particle swarm optimization algorithm and study on its control parameter. Acta Phys Sin 59(6):3686–3693

    MATH  Google Scholar 

  33. Said MM, Ahmed AK (2006) Quantum particle swarm optimization for electromagnetic. IEEE Trans Antennas Propag 54(10):2765–2775

    Google Scholar 

  34. Clerc M, Kennedy J (2002) The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  35. Gao WF, Liu SY, Huang LL (2012) A global best artificial bee colony algorithm for global optimization. J Comput Appl Math 236:2741–2753

    Article  MATH  MathSciNet  Google Scholar 

  36. Adam PP, Jaroslaw J, Napiorkowski AK (2012) Differential evolution algorithm with separated groups for multi-dimensional optimization problems. Eur J Oper Res 216:33–46

    Article  MATH  Google Scholar 

  37. Liu G, Li YX, Nie X, Zheng H (2012) A novel clustering-based differential evolution with 2 multi-parent crossovers for global optimization. Appl Soft Comput 12:663–681

    Article  Google Scholar 

  38. Suganthan PN, Hansen N, Liang JJ (2005) Problem definitions and evaluation criteria for the CEC2005 special session on realparameter optimization. http://www.ntu.edu.sg/home/EPNSugan

  39. Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12(1):107–125

    Article  Google Scholar 

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Acknowledgements

We sincerely thank the three anonymous reviewers for their many constructive comments and suggestions, which have tremendously improved the presentation and quality of this paper. This work was supported by the National Natural Science Foundation of China (Grant no. 61170132).

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Authors and Affiliations

  1. School of Computer & Information Technology, Northeast Petroleum University, Daqing, 163318, China

    Panchi Li & Hong Xiao

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  1. Panchi Li
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  2. Hong Xiao
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Correspondence to Panchi Li.

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Li, P., Xiao, H. An improved quantum-behaved particle swarm optimization algorithm. Appl Intell 40, 479–496 (2014). https://doi.org/10.1007/s10489-013-0477-x

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