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Quantum-Inspired Evolutionary Algorithms and Its Application to Numerical Optimization Problems

  • André V. Abs da Cruz
  • Carlos R. Hall Barbosa
  • Marco Aurélio C. Pacheco
  • Marley Vellasco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3316)

Abstract

This work proposes a new kind of evolutionary algorithm inspired in the principles of quantum computing. This algorithm is an extension of a proposed model for combinatorial optimization problems which uses a binary representation for the chromosome. This extension uses probability distributions for each free variable of the problem, in order to simulate the superposition of solutions, which is intrinsic in the quantum computing methodology. A set of mathematical operations is used as implicit genetic operators over those probability distributions. The efficiency and the applicability of the algorithm are demonstrated through experimental results using the F6 function.

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References

  1. 1.
    Shor, P.W.: Algorithms for quantum computation: Discrete log and factoring. In: Proc. 35th Ann. Symp. Foundations of Computer Science, pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)CrossRefGoogle Scholar
  2. 2.
    Shor, P.W.: Quantum computing. Documenta Mathematica, 467–486 (1998)Google Scholar
  3. 3.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACMSymposium on the Theory of Computing (STOC), pp. 212–219. ACM Press, New York (1996)Google Scholar
  4. 4.
    Spector, L., Barnum, H., Bernstein, H.J., Swami, N.: Finding a better-than-classical quantum AND/OR algorithm using genetic programming. In: Proceedings of the Congress on Evolutionary Computation, vol. 3, pp. 2239–2246. IEEE Press, Los Alamitos (1999)Google Scholar
  5. 5.
    Han, K.H., Kirn, J.H.: Genetic quantum algorithm and its application to combinatorial optimization Problem. In: Proceedings of the 2000 Congress on Evolutionary Computation, pp. 1354–1360. IEEE Press, Los Alamitos (2000)Google Scholar
  6. 6.
    Han, K.H., Kirn, J.H.: Quan uminspired t evolutionary algorithm for a class of combinatorial optimization. IEEE Transactions on Evolutionary Computation 6, 580–593 (2002)CrossRefGoogle Scholar
  7. 7.
    Narayanan, A., Moore, M.: Genetic quantum algorithm and its application to combinatorial optimization problem. In: Proceedings of the 1996 IEEE International Conference on Evolutionary Computation (ICEC 1996), pp. 61–66. IEEE Press, Los Alamitos (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • André V. Abs da Cruz
    • 1
  • Carlos R. Hall Barbosa
    • 1
  • Marco Aurélio C. Pacheco
    • 1
  • Marley Vellasco
    • 1
    • 2
  1. 1.ICA – Applied Computational Intelligence Lab, Electrical Engineering DepartmentPontifícia Universidade Católica doRio de Janeiro
  2. 2.Department of Computer ScienceUniversity College of LondonUK

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