Improved Quantum Particle Swarm Optimization by Bloch Sphere

  • Yu Du
  • Haibin Duan
  • Renjie Liao
  • Xihua Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6145)


Quantum Particle Swarm Optimization (QPSO) is a global convergence guaranteed search method which introduces the Quantum theory into the basic Particle Swarm Optimization (PSO). QPSO performs better than normal PSO on several benchmark problems. However, QPSO’s quantum bit(Qubit) is still in Hilbert space’s unit circle with only one variable, so the quantum properties have been undermined to a large extent. In this paper, the Bloch Sphere encoding mechanism is adopted into QPSO, which can vividly describe the dynamic behavior of the quantum. In this way, the diversity of the swarm can be increased, and the local minima can be effectively avoided. The proposed algorithm, named Bloch QPSO (BQPSO), is tested with PID controller parameters optimization problem. Experimental results demonstrate that BQPSO has both stronger global search capability and faster convergence speed, and it is feasible and effective in solving some complex optimization problems.


Quantum Particle Swarm Optimization (QPSO) Bloch Sphere Bloch QPSO(BQPSO) global search 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: Proc. IEEE Conf. On Neural Network, pp. 1942–1948 (1995)Google Scholar
  2. 2.
    Angeline, P.J.: Evolutionary Optimization Versus Particle Swarm Optimization. In: Philosophy and Performance Differences. Evolutionary Programming VIII. LNCS, vol. 1477, pp. 601–610. Springer, Heidelberg (1998)Google Scholar
  3. 3.
    Eberhart, R.C., Shi, Y.H.: Comparison between Genetic Algorithm and Particle Swarm Optimization. In: Porto, V.W., Waagen, D. (eds.) EP 1998. LNCS, vol. 1447, pp. 611–616. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Krink, T., Vesterstorm, J., Riget, J.: Particle Swarm Optimization with Spatial Particle Extension. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 2, pp. 1474–1479 (2002)Google Scholar
  5. 5.
    Van den Bergh, F.: An Analysis of Particle Swarm Optimizers. PhD Thesis. University of Pretoria, South Africa (2001)Google Scholar
  6. 6.
    Li, P.C., Li, S.Y.: Quantum particle swarms algorithm for continuous space optimization. Journal of Quantum Electronics 24(4), 463–468 (2007)Google Scholar
  7. 7.
    Al-Rabadi, A.N.: New dimensions in non-classical neural computing, part II: quantum, nano, and optical. International Journal of Intelligent Computing and Cybernetics 2(3), 513–573Google Scholar
  8. 8.
    Xing, Z., Duan, H.: An Improved Quantum Evolutionary Algorithm with 2 crossovers. In: Yu, W., He, H., Zhang, N. (eds.) ISNN 2009. LNCS, vol. 5551, pp. 735–744. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Eberhart, R.C., Shi, Y.H.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the International Congress on Evolutionary Computation, Piscataway, pp. 84–88. IEEE Press, Los Alamitos (2000)Google Scholar
  10. 10.
    Li, P.C., Li, S.Y.: Quantum Computation and Quantum Optimization Algorithm, pp. 113–117. Harbin Institute of Technology Press (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yu Du
    • 1
  • Haibin Duan
    • 1
    • 2
  • Renjie Liao
    • 1
  • Xihua Li
    • 1
  1. 1.National Key Laboratory of Science and Technology on Holistic Control, School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina
  2. 2.Provincial Key Laboratory for Information Processing TechnologySuzhou UniversitySuzhouChina

Personalised recommendations