Skip to main content

Advertisement

Springer Nature Link
Log in

An improved hybrid quantum optimization algorithm for solving nonlinear equations

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

This paper proposes a hybrid quantum genetic algorithm (HQGA) and the core is the use of a new quantum revolving gate strategy and population adaptive retention strategy, and with the Quasi-Newton method. HQGA has the characteristics of fast convergence speed, strong global optimization ability and local detailed optimization. Through the typical complex function, tests show that the optimized quality and efficiency of HQGA are better than traditional quantum genetic algorithms. This algorithm has a good effect in training logistic regression (convex problem) in machine learning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Fan, E.: Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277(4–5), 212–218 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Derek, G., Chris, N., Glen, H., Damien, L.G.: Moose: a parallel computational framework for coupled systems of nonlinear equations. Nucl. Eng. Des. 239(10), 1768–1778 (2009)

    Article  Google Scholar 

  3. Wang, M., Zhou, Y., Li, Z.: Application of a ho-mogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A 216(1–5), 67–75 (1996)

    Article  ADS  Google Scholar 

  4. Gen, M., Lin, L.: Genetic algorithms. Wiley Encyclopedia of Computer Science and Engineering, pp. 1–15, (2007)

  5. Such, F.P., Madhavan, V., Conti, E., Lehman, J., Stanley, K.O., Clune, J.: Deep neuroevolu-tion: genetic algorithms are a competitive alternative for training deep neural networks for reinforcement learning. arXiv preprint arXiv:1712.06567, (2017)

  6. Kelley, C.T.: Solving nonlinear equations with Newton’s method, vol. 1. SIAM, (2003)

  7. Qi, L., Sun, J.: A nonsmooth version of Newton’s method. Math. Program. 58(1–3), 353–367 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tinney, W.F., Hart, C.E.: Power flow solution by Newton’s method. IEEE Trans. Power Appar. Syst. 11, 1449–1460 (1967)

    Article  ADS  Google Scholar 

  9. Yasar Özban, A.: Some new variants of Newton’s method. Appl. Math. Lett. 17(6), 677–682 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chun, C.: Iterative methods improving Newton’s method by the decomposition method. Comput. Math. Appl. 50(10–12), 1559–1568 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jinwei, G., Manzhan, G., Cao, C., Xingsheng, G.: A novel competitive co-evolutionary quantum genetic algorithm for stochastic job shop scheduling problem. Comput. Oper. Res. 37(5), 927–937 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lee, J.-C., Lin, W.-M., Liao, G.-C., Tsao, T.-P.: Quantum genetic algorithm for dynamic economic dispatch with valve-point effects and including wind power system. Int. J. Electr. Power Energy Syst. 33(2), 189–197 (2011)

    Article  Google Scholar 

  13. Jinwei, G., Xingsheng, G., Manzhan, G.: A novel parallel quantum genetic algorithm for stochastic job shop scheduling. J. Math. Anal. Appl. 355(1), 63–81 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Laboudi, Z., Chikhi, S.: Comparison of genetic algorithm and quantum genetic algorithm. Int. Arab J. Inf. Technol. 9(3), 243–249 (2012)

    Google Scholar 

  15. Sabahi, F.: Quantum genetic LMI-based h control with time delay. Int. J. Ind. Electron. Control Optim. 3(1), 1–10 (2020)

    Google Scholar 

  16. Li, B., Pingfang, H., Zhu, N., Lei, F., Xing, L.: Performance analysis and optimization of a CCHP-GSHP coupling system based on quantum genetic algorithm. Sustain. Cities Soc. 46, 101408 (2019)

    Article  Google Scholar 

  17. Lizhen Deng, H., Zhu, Q.Z., Li, Y.: Adaptive top-hat filter based on quantum genetic algorithm for infrared small target detection. Multimed. Tools Appl. 77(9), 10539–10551 (2018)

    Article  Google Scholar 

  18. Chen, P., Yuan, L., He, Y., Luo, S.: An improved SVM classifier based on double chains quantum genetic algorithm and its application in analogue circuit diagnosis. Neurocomputing 211, 202–211 (2016)

    Article  Google Scholar 

  19. Zhang, L., Lv, H., Tan, D., Fang, X., Chen, J., Bao, G., Cai, S.: Adaptive quantum genetic algorithm for task sequence planning of complex assembly systems. Electron. Lett. 54(14), 870–872 (2018)

    Article  ADS  Google Scholar 

  20. Li, P.C., Song, K.P., Shang, F.H.: Double chains quantum genetic algorithm with application to neuro-fuzzy controller design. Adv. Eng. Softw. 42(10), 875–886 (2011)

    Article  MATH  Google Scholar 

  21. Li, S., Li, P.: Quantum genetic algorithm based on real encoding and gradient information of object function. J. Harbin Inst. Technol. 38(8), 1216–1223 (2006)

    Google Scholar 

  22. Steane, A.: Quantum computing. Rep. Prog. Phys. 61(2), 117 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  23. O’brien, J.L.: Optical quantum computing. Science 318(5856), 1567–1570 (2007)

    Article  ADS  Google Scholar 

  24. Leuenberger, M.N., Loss, D.: Quantum computing in molecular magnets. Nature 410(6830), 789–793 (2001)

    Article  ADS  Google Scholar 

  25. Qi, X., Palmieri, F.: Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space part II: analysis of the diversification role of crossover. IEEE Trans. Neural Netw. 5(1), 120–129 (1994)

    Article  Google Scholar 

  26. Schmitt, L.M.: Theory of genetic algorithms. Theor. Comput. Sci. 259(1–2), 1–61 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. Abdoun, O., Abouchabaka, J., Tajani C.: Analyzing the performance of mutation operators to solve the travelling salesman problem. arXiv preprint arXiv:1203.3099, (2012)

  28. Wang, Y., Li, Y.-H.: A novel quantum genetic algorithm for tsp. Chin. J. Comput. Chin. Ed. 30(5), 748 (2007)

    MathSciNet  Google Scholar 

  29. Prakash, S., Prakash Vidyarthi, D.: A novel scheduling model for computational grid using quantum genetic algorithm. J. Supercomput. 65(2), 742–770 (2013)

    Article  Google Scholar 

  30. Duan, H., Chun-fang, X., Xing, Z.-H.: A hybrid artificial bee colony optimization and quantum evolutionary algorithm for continuous optimization problems. Int. J. Neural Syst. 20(01), 39–50 (2010)

    Article  Google Scholar 

  31. Li, P., Li, S.: Quantum-inspired evolutionary algorithm for continuous space optimization based on Bloch coordinates of qubits. Neurocomputing 72(1–3), 581–591 (2008)

    Article  Google Scholar 

  32. Panchi, L.I.: Quantum genetic algorithm based on Bloch coordinates of qubits and its application. Control Theory Appl. 25(6), 985–989 (2008)

    MATH  Google Scholar 

  33. Zaitsev-Zotov, S.V.: Classical to quantum crossover in charge density wave creep at low temperatures. Phys. Rev. Lett. 71(4), 605 (1993)

    Article  ADS  Google Scholar 

  34. SaiToh, A., Rahimi, R., Nakahara, M.: A quantum genetic algorithm with quantum crossover and mutation operations. Quantum Inf. Process. 13(3), 737–755 (2014)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Yang, J., Li, B., Zhuang, Z.: Research of quantum genetic algorith and its application in blind source separation. J. Electron. (China) 20(1), 62–68 (2003)

    Article  Google Scholar 

  36. Xiao-fenga, Z.H.A.N.G., Gui-fanga, S.U.I., Rana, Z.H.E.N.G., Zhi-nongb, L.I., Guo-weia, Y.A.N.G.: An improved quantum genetic algorithm of quantum revolving gate. Comput. Eng. 04, 56 (2013)

    Google Scholar 

  37. Hua, T., Chen, J., Pei, D., Zhang, W., Zhou, N.: Quantum image encryption algorithm based on image correlation decomposition. Int. J. Theor. Phys. 54(2), 526–537 (2015)

    Article  MATH  Google Scholar 

  38. Xiaohui, Z., Li, C., Peng, Z.: Simulation of quantum cellular automatas based on quantum genetic algorithm [j]. Micronanoelectronic Technology 1, (2011)

  39. Du, T., Hu, Y., Ke, X. : Improved quantum artificial fish algorithm application to distributed network considering distributed generation. Computational intelligence and neuroscience 2015, (2015)

  40. Guo, Y., Wei, L., Xu, X.: A sonar image segmentation algorithm based on quantum-inspired particle swarm optimization and fuzzy clustering. Neural Comput. Appl. 45, 1–8 (2018). https://doi.org/10.1007/s00521-018-3890-6

    Article  Google Scholar 

  41. Ariyawansa, K.A.: Deriving collinear scaling algorithms as extensions of quasi-newton methods and the local convergence of DFP and BFGS related collinear scaling algorithms. Math. Program. 49(1–3), 23–48 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  42. Güler, O., Gürtuna, F., Shevchenko, O.: Duality in quasi-Newton methods and new variational characterizations of the DFP and BFGS updates. Optim. Methods Softw. 24(1), 45–62 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  43. Powell, M.J.D.: How bad are the BFGS and DFP methods when the objective function is quadratic? Math. Program. 34(1), 34–47 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  44. Contreras, M., Tapia, R.A.: Sizing the BFGS and DFP updates: numerical study. J. Optim. Theory Appl. 78(1), 93–108 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  45. Dennis, J.E., Martinez, H.J., Tapia, R.A.: Convergence theory for the structured BFGS secant method with an application to nonlinear least squares. J. Optim. Theory Appl. 61(2), 161–178 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  46. Powell, M.J.D.: Updating conjugate directions by the BFGS formula. Math. Program. 38(1), 29 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  47. Xiao-fenga, Z., Gui-fanga, S.U.I., Rana, Z., et al.: An improved quantum genetic algorithm of quantum revolving gate [J]. Comput. Eng. 4, 56 (2013)

    Google Scholar 

  48. Rogers, A., Prugel-Bennett, A.: Genetic drift in genetic algorithm selection schemes. IEEE Trans Evolut. Comput. 3(4), 298–303 (1999)

    Article  Google Scholar 

  49. Tang, K.-Z., Sun, T.-K., Yang, J.-Y.: An improved genetic algorithm based on a novel selection strategy for nonlinear programming problems. Comput. Chem. Eng. 35(4), 615–621 (2011)

    Article  Google Scholar 

  50. Li, B.B., Wang, L.: A hybrid quantum-inspired genetic algorithm for multiobjective flow shop scheduling. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 37(3), 576–591 (2007)

    Article  Google Scholar 

  51. CAI, B.B., ZHANG, X.H.: Hybrid quantum genetic algorithm and its application in VRP [j]. Computer Simulation 7, (2010)

  52. Yang, F., Yi-liu, J.I.A.N.G., Zhen-kun, L.I.: Optimal allocation of distributed generation for microgrid based on hybrid quantum genetic algorithm. Power Syst. Prot. Control 41(24), 50–57 (2013)

    Google Scholar 

  53. Juan, D., Liu, Z.G.: A new hybrid quantum genetic algorithm for solving nonlinear equations. Microcomput. Appl. 29(7), 1–5 (2008)

    Google Scholar 

  54. Liu, Z.G., Xu, S.H.: Training method of process neural networks based on hybrid quantum genetic algorithm. Appl. Res. Comput. 26(8), 2898–2901 (2009)

    Google Scholar 

  55. Xianlong, G., Xu, W., Ying, D.: The vehicle routing problem in the case of stochastic demand based on hybrid quantum genetic algorithm. Syst. Eng. 29(3), 53–59 (2011)

    Google Scholar 

  56. Wang, L., Tang, F., Hao, W.: Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Appl. Math. Comput. 171(2), 1141–1156 (2005)

    MathSciNet  MATH  Google Scholar 

  57. Konar, D., Bhattacharyya, S., Sharma, K., Sharma, S., Pradhan, S.R.: An improved hybrid quantum-inspired genetic algorithm (HQIGA) for scheduling of real time task in multiprocessor system. Appl. Soft Comput. 53, 296–307 (2017)

    Article  Google Scholar 

  58. Xiong, Y., Chen, H., Miao, F., Wang, X.: A quantum genetic algorithm to solve combinatorial optimization problem. Acta Electron. Sin. 32(11), 1855–1858 (2004)

    Google Scholar 

  59. Chen, Y.: Research on Quantum Genetic Algorithm Based on Optimization Problems. University of Electronic Science and Technology of China, (2019)

  60. Zhang, G., Li, N., Jin, W., Hu, L.: A novel quantum genetic algorithm and its application and its application. Acta Electron. Sin. 32(3), 476–479 (2004)

    ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61772295,61572270 and 61173056); the PHD foundation of Chongqing Normal University No.19XLB003; Supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No.KJZD-M202000501 ); Chongqing Technology Innovation and application development special general project(cstc2020jscx-lyjsA0063). Chongqing Normal University Graduate Scientific Research Innovation Project Grant YKC20042.

Author information

Authors and Affiliations

  1. Chongqing Normal University, Chongqing, China

    Yumin Dong & Jinlei Zhang

Authors
  1. Yumin Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinlei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yumin Dong.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 15068 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, Y., Zhang, J. An improved hybrid quantum optimization algorithm for solving nonlinear equations. Quantum Inf Process 20, 134 (2021). https://doi.org/10.1007/s11128-021-03067-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03067-3

Keywords

Search

Navigation