Share This Article:

Quantum Inspired Differential Evolution Algorithm

Abstract Full-Text HTML XML Download Download as PDF (Size:290KB) PP. 31-39
DOI: 10.4236/ojop.2015.42004    7,356 Downloads   7,994 Views   Citations
Author(s)    Leave a comment

ABSTRACT

To enhance the optimization performance of differential evolution algorithm, by studying the implementation mechanism of differential evolution algorithm, a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper. In the proposed approach, the individuals are encoded by qubits described on Bloch sphere, and the rotation angles of qubits in current individual are obtained by differential strategy. The axis of rotation is designed by using vector product theory, and the rotation matrixes are constructed by using Pauli matrixes. Taking the corresponding qubits in current best individual as targets, the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere. The Hadamard gates are used to mutate individuals. The simulation results of optimizing the minimum value of functions indicate that, for an iterative step, the average time of the proposed approach is 13 times as long as that of the classical differential evolution algorithm. When the same limited steps are applied in two approaches, the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm; when the same running time is applied in two approaches, the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm. These results suggest that the proposed approach is inefficient in computational ability; however, it is obviously efficient in optimization ability, and the overall optimization performance is better than that of the classical differential evolution algorithm.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Li, B. and Li, P. (2015) Quantum Inspired Differential Evolution Algorithm. Open Journal of Optimization, 4, 31-39. doi: 10.4236/ojop.2015.42004.

References

[1] Price, K., Storn, R. and Lampinen, J. (2004) Differential Evolutionary: A Practical Approach to Global Optimization. Springer, Heidelberg, 183-187.
[2] Uday, K. (2008) Advance in Differential Evolution. Springer, Heidelberg, 287-293.
[3] Zhou, Y.Z., Li, X.Y. and Gao, L. (2013) A Differential Evolution Algorithm with Intersect Mutation Operator. Applied Soft Computing, 13, 390-401.
http://dx.doi.org/10.1016/j.asoc.2012.08.014
[4] Zhu, W., Tang, Y., Fang, J.A. and Zhang, W.B. (2013) Adaptive Population Tuning Scheme for Differential Evolution. Information Sciences, 223, 164-191.
http://dx.doi.org/10.1016/j.ins.2012.09.019
[5] Zhang, D.X., Wang, J.H., Gao, L.Q. and Steven, L. (2013) A Modified Differential Evolution Algorithm for Unconstrained Optimization Problems. Neurocomputing, 120, 469-481.
http://dx.doi.org/10.1016/j.neucom.2013.04.036
[6] Musrrat, A., Millie, P. and Ajith, A. (2013) Unconventional Initialization Methods for Differential Evolution. Applied Mathematics and Computation, 219, 4474-4494.
http://dx.doi.org/10.1016/j.amc.2012.10.053
[7] Adam, P.P. (2013) Adaptive Memetic Differential Evolution with Global and Local Neighborhood-Based Mutation Operators. Information Sciences, 241, 164-194.
http://dx.doi.org/10.1016/j.ins.2013.03.060
[8] Cao, A.H., Li, W.C. and Li, L.P. (2009) A Passive Location Algorithm Based on Differential Evolution and Genetic Algorithm Using the Doppler Frequency. Signal Processing, 25, 1644-1648.
[9] Wang, Y., Cai, Z.X. and Zhang, Q.F. (2012) Enhancing the Search Ability of Differential Evolution through Orthogonal Crossover. Information Sciences, 185, 153-177.
http://dx.doi.org/10.1016/j.ins.2011.09.001
[10] Dilip, D. and Jose, R.F. (2013) A Real-Integer-Discrete-Coded Differential Evolution. Applied Soft Computing, 13, 3384-3393.
[11] Ali, W.M., Hegazy, Z.S. and Motaz, K. (2012) An Alternative Differential Evolution Algorithm for Global Optimization. Journal of Advanced Research, 3, 149-165.
http://dx.doi.org/10.1016/j.jare.2011.06.004
[12] Ali, W.M. and Hegazy, Z.S. (2012) Constrained Optimization Based on Modified Differential Evolution Algorithm. Information Sciences, 194, 171-208.
http://dx.doi.org/10.1016/j.ins.2012.01.008
[13] Cheng, J.X., Zhang, G.X. and Ferrante, N. (2013) Enhancing Distributed Differential Evolution with Multicultural Migration for Global Numerical Optimization. Information Sciences, 247, 72-93.
http://dx.doi.org/10.1016/j.ins.2013.06.011
[14] Fang, W., Sun, J., Xie, Z.P. and Xu, W.B. (2010) Convergence Analysis of Quantum-Behaved Particle Swarm Optimization Algorithm and Study on Its Control Parameter. Acta Physica Sinica, 59, 3686-3694.
[15] Li, P.C. and Li, S.Y. (2008) Quantum-Inspired Evolutionary Algorithm for Continuous Spaces Optimization Based on Bloch Coordinates of Qubits. Neurocomputing, 72, 581-591.
http://dx.doi.org/10.1016/j.neucom.2007.11.017
[16] Duan, H.B., Zhang, X.Y. and Xu, C.F. (2011) Bio-Inspired Computing. Science Press, Beijing.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.