Function Optimization Based on Higher-Order Quantum Genetic Algorithm

V.M. Tkachuk, Ph.D. (Phys.-Math.), M.I. Kozlenko, Ph.D (Eng.),
M.V. Kuz Dr.Sc. (Eng.), I.M. Lazarovych Ph.D. (Eng.), M.C. Dutchak
Vasyl Stefanyk Precarpathian National University
(57 Shevchenko str., Ivano-Frankivsk, 76018, Ukraine,
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Èlektron. model. 2019, 41(3):43-58

ABSTRACT

Quantum genetic algorithms (QGA) are typically built using the traditional representation of theQuantum genetic algorithms (QGA) are typically built using the traditional representation of thequantum chromosome in the form of system of independent qubits. This makes it impossible touse a very powerful quantum calculations mechanism, namely quantum state entanglement. Inthis paper we implement a higher-order QGA and illustrate efficiency of the algorithm on the basisof example of optimization problem solved for a test functions set. An adaptive quantum gateoperator, which does not require a lookup table is also proposed. In comparison to traditionalQGA, the transition to higher (more than two) orders in the algorithm implementation showsmuch better results in terms of the running time, convergence speed and solution precision.

KEYWORDS

function optimization, quantum state entanglement, quantum genetic algorithm,function optimization, quantum state entanglement, quantum genetic algorithm,quantum computation, quantum register.

REFERENCES

1. Han, K.-H. and Kim, J.-H. (2000), “Genetic quantum algorithm and its application to combinatorial optimization problem”, Proceedings of the 2000 Congress on Evolutionary Computation,
USA, 2, pp. 1354-1360.
2. Roy, U., Roy, S. and Nayek, S. (2014), “Optimization with quantum genetic algorithm”, International Journal of Computer Applications, Vol. 102, no. 16, pp. 1-7.
3. Zhang, G. (2011), “Quantum-inspired evolutionary algorithms: a survey and empirical study“, Journal of Heuristics, Vol. 2011, no. 17, pp. 303-351.
https://doi.org/10.1007/s10732-010-9136-0
4. Wang, H., Liu, J., Zhi, J. and Fu, C. (2013), “The Improvement of Quantum Genetic Algorithm and Its Application on Function Optimization”, Mathematical Problems in Engineering, Vol. 2013.
https://doi.org/10.1155/2013/730749
5. Wang, L., Kowk, S.K. and Ip, W.H. (2012), “Design of an improved quantum-inspired evolutionary algorithm for a transportation problem in logistics systems”, Journal of Intelligent Manufacturing, pp. 2227-2236.
https://doi.org/10.1007/s10845-011-0568-7
6. Jantos, P., Grzechca, D. and Rutkowski, J. (2012), “Evolutionary algorithms for global parametric
fault diagnosis in analogue integrated circuits”, Bull. Pol. Tech, Vol. 60, pp. 133-142.
https://doi.org/10.2478/v10175-012-0019-4
7. Talbi, H., Batouche, M. and Draa, A. (2007), “A Quantum-Inspired Evolutionary Algorithm for Multiobjective Image Segmentation”, International Journal of Nuclear and Quantum Engineering, Vol. 1, pp. 109-114.
8. Qin, C., Liu, Y. and Zheng, J. (2008), “A real-coded quantum-inspired evolutionary algorithm for global numerical optimization”, 2008 IEEE Conference on Cybernetics and Intelligent Systems, pp. 1160-1164.
https://doi.org/10.1109/ICCIS.2008.4670779
9. Lin, D. and Waller, S. (2009), “A quantum-inspired genetic algorithm for dynamic continuous network design problem”, Transportation Letters: The International Journal of Transportation Research, Vol. 1, pp. 81-93.
https://doi.org/10.3328/TL.2009.01.01.81-93
10. Malossini, A., Blanzieri, E. and Calarco, T. (2008), “Quantum genetic optimization”, IEEE Trans. Evol. Comput, Vol. 12, pp. 231-241.
https://doi.org/10.1109/TEVC.2007.905006
11. SaiToh, A., Rahimi, R. and Nakahara, M. (2014), “A quantum genetic algorithm with quantum crossover and mutation operations”, Quantum Information Process, Vol. 13, pp. 737-755.
https://doi.org/10.1007/s11128-013-0686-6
12. Lahoz-Beltra, R. (2016), “Quantum Genetic Algorithms for Computer Scientists”, Computers, Vol. 5, no. 4.
https://doi.org/10.3390/computers5040024
13. Tkachuk, V. (2018). “Quantum Genetic Algorithm onMultilevel Quantum Systems”, Mathematical Problems in Engineering, Vol. 2018.
https://doi.org/10.1155/2018/9127510
14. Narayanan, A. and Moore, M. (1996), “Quantum-inspired genetic algorithms”, Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC’96), Nagoya, Japan, pp. 61-66.
https://doi.org/10.1109/ICEC.1996.542334
15. Nowotniak, R. and Kucharski, J. (2014), “Higher-Order Quantum-Inspired Genetic Algorithms”, Federated Conference on Annals of Computer Science and Information Systems, Vol. 2, pp. 465-470.
https://doi.org/10.15439/2014F99
16. Ullah, S. and Wahid, M. (2015), “Topology Control of Wireless Sensor Network Using Quantum Inspired Genetic Algorithm”, International Journal of Swarm Intelligence and Evolutionary Computation, Vol. 4.
https://doi.org/10.4172/2090-4908.1000121
17. Tkachuk, V. (2018), “Quantum Genetic Algorithm Based on Qutrits and Its Application”, Mathematical Problems in Engineering, Vol. 2018.
https://doi.org/10.1155/2018/8614073
18. Sun, Y. and Xiong, H. (2014), “Function Optimization Based on Quantum Genetic Algorithm”, Research Journal of Applied Sciences, Engineering and Technology, Vol. 7, no. 1, pp. 144-149, ISSN: 2040-7459; e-ISSN: 2040-7467.
https://doi.org/10.19026/rjaset.7.231
19. Kuo, S.-Y. and Chou, Y.-H. (2017), “Entanglement-Enhanced Quantum-Inspired Tabu Search Algorithm for Function Optimization”, IEEE Access, Vol. 5, pp. 13236-13252.
https://doi.org/10.1109/ACCESS.2017.2723538

Full text: PDF