Exploring Potential Barrier Estimation Mechanism Based on Quantum Dynamics Framework

TANG Quan; WANG Peng

doi:10.23919/cje.2023.00.293

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Quan TANG and Peng WANG, “Exploring Potential Barrier Estimation Mechanism Based on Quantum Dynamics Framework,” Chinese Journal of Electronics, vol. x, no. x, pp. 1–15, xxxx doi: 10.23919/cje.2023.00.293

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Quan TANG and Peng WANG, “Exploring Potential Barrier Estimation Mechanism Based on Quantum Dynamics Framework,” Chinese Journal of Electronics, vol. x, no. x, pp. 1–15, xxxx doi: 10.23919/cje.2023.00.293

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Exploring Potential Barrier Estimation Mechanism Based on Quantum Dynamics Framework

doi: 10.23919/cje.2023.00.293

TANG Quan^{1, 2
,},
WANG Peng^{3
,
,}

1.
Chengdu Institution of Computer Application, China Academy of Science, Chengdu 610041, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Computer Science and Engineering, Southwest Minzu University, Chengdu 610225, China

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Author Bio:
Quan TANG is currently pursuing the Ph.D. degree with the University of Chinese Academy of Sciences, Beijing. She received the M.E. degree in Communication and Information Systems from University of Electronic Science and Technology, in 2006. Her research interests include computational intelligence, swarm intelligence, quantum computing, and wireless sensor network. (Email: tangquan20@mails.ucas.ac.cn)

Peng WANG is currently a Professor with Southwest Minzu University and also with the Chinese Academy of Sciences. Chinese Institute of Electronics. He received the M.S. degree in Nuclear Technology and Applications from Sichuan University, in 2001, and the Ph.D. degree in Computer Science and Technology from the Chinese Academy of Sciences, in 2004. His research interests include quantum mechanics, computational intelligence, and high performance computing. (Email: qhoalab@163.com)
Corresponding author: Email: qhoalab@163.com
Received Date: 2023-08-24
Accepted Date: 2024-05-11

Available Online: 2024-07-01

Abstract

Abstract

Due to the probability characteristics of quantum mechanism, the combination of quantum mechanism and intelligent algorithm has received wide attention. Quantum dynamics theory uses the Schrödinger equation as a quantum dynamics equation. Through three approximation of the objective function, quantum dynamics framework (QDF) is obtained which describes basic iterative operations of optimization algorithms. Based on QDF, this paper proposes a potential barrier estimation (PBE) method which originates from quantum mechanism. With the proposed method, the particle can accept inferior solutions during the sampling process according to a probability which is subject to the quantum tunneling effect, to improve the global search capacity of optimization algorithms. The effectiveness of the proposed method in the ability of escaping local minima was thoroughly investigated through double well function (DWF), and experiments on two benchmark functions sets show that this method significantly improves the optimization performance of high dimensional complex functions. The PBE method is quantized and easily transplanted to other algorithms to achieve high performance in the future.
- quantum dynamics,
- objective function,
- potential barrier estimation,
- local optima

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References(55)

References

[1]	A. Baykasoğlu, A. Hamzadayi, and S. Y. Köse, “Testing the performance of teaching-learning based optimization (TLBO) algorithm on combinatorial problems: Flow shop and job shop scheduling cases,” Information Sciences, vol. 276, pp. 204–218, 2014. doi: 10.1016/j.ins.2014.02.056
[2]	C. Zhang, Z. S. Shi, Z. W. Huang, et al, “Flow shop scheduling with a batch processor and limited buffer,” International Journal of Production Research, vol. 55, no. 11, pp. 3217–3233, 2017. doi: 10.1080/00207543.2016.1268730
[3]	S. Gupta, H. Abderazek, B. S. Yıldız, et al, “Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems,” Expert Systems with Applications, vol. 183, article no. 115351, 2021. doi: 10.1016/j.eswa.2021.115351
[4]	S. P. Gong, M. Khishe, and M. Mohammadi, “Niching chimp optimization for constraint multimodal engineering optimization problems,” Expert Systems with Applications, vol. 198, article no. 116887, 2022. doi: 10.1016/j.eswa.2022.116887
[5]	J. Qin, C. H. Huang, and Y. Luo, “Adaptive multi-swarm in dynamic environments,” Swarm and Evolutionary Computation, vol. 63, article no. 100870, 2021. doi: 10.1016/j.swevo.2021.100870
[6]	J. W. Lu, J. Zhang, and J. A. Sheng, “Enhanced multi-swarm cooperative particle swarm optimizer,” Swarm and Evolutionary Computation, vol. 69, article no. 100989, 2022. doi: 10.1016/j.swevo.2021.100989
[7]	M. N. M. Salleh, K. Hussain, S. Cheng, et al., “Exploration and exploitation measurement in swarm-based metaheuristic algorithms: An empirical analysis,” in Proceedings of the 3rd International Conference on Soft Computing and Data Mining (SCDM), Johor, Malaysia, pp. 24–32, 2018.
[8]	S. Cheng, Y. H. Shi, Q. D. Qin, et al, “Population diversity maintenance in brain storm optimization algorithm,” Journal of Artificial Intelligence and Soft Computing Research, vol. 4, no. 2, pp. 83–97, 2014. doi: 10.1515/jaiscr-2015-0001
[9]	P. A. N. Bosman, J. Grahl, and D. Thierens, “Enhancing the performance of maximum-likelihood Gaussian EDAs using anticipated mean shift,” in Proceedings of the 10th International Conference on Parallel Problem Solving from Nature, Dortmund, Germany, pp. 133–143, 2008.
[10]	T. Friedrich, T. Kötzing, M. S. Krejca, et al., “Escaping local optima with local search: A theory-driven discussion,” in Proceedings of the 17th International Conference on Parallel Problem Solving from Nature, Dortmund, Germany, pp. 442–455, 2022.
[11]	L. L. Liu, S. X. Yang, and D. W. Wang, “Particle swarm optimization with composite particles in dynamic environments,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 40, no. 6, pp. 1634–1648, 2010. doi: 10.1109/TSMCB.2010.2043527
[12]	C. W. Qu and Y. M. Fu, “Crow search algorithm based on neighborhood search of non-inferior solution set,” IEEE Access, vol. 7, pp. 52871–52895, 2019. doi: 10.1109/ACCESS.2019.2911629
[13]	J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Ann Arbor, MI, USA, 1975. (查阅网上资料, 出版信息不确定, 请确认) .
[14]	J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95-International Conference on Neural Networks, Perth, Australia, pp. 1942–1948, 1995.
[15]	J. Sun, W. B. Xu, and B. Feng, “A global search strategy of quantum-behaved particle swarm optimization,” in Proceedings of the IEEE Conference on Cybernetics and Intelligent Systems, 2004, Singapore, Singapore, pp. 111–116, 2004.
[16]	J. Sun, W. Fang, X. J. Wu, et al, “Quantum-behaved particle swarm optimization: Analysis of individual particle behavior and parameter selection,” Evolutionary Computation, vol. 20, no. 3, pp. 349–393, 2012. doi: 10.1162/EVCO_a_00049
[17]	Y. Tan and Y. C. Zhu, “Fireworks algorithm for optimization,” in Proceedings of the 1st International Conference on Advances in Swarm Intelligence, Beijing, China, pp. 355–364, 2010.
[18]	J. Z. Li and Y. Tan, “The bare bones fireworks algorithm: A minimalist global optimizer,” Applied Soft Computing, vol. 62, pp. 454–462, 2018. doi: 10.1016/j.asoc.2017.10.046
[19]	K. V. Price, “Differential evolution: A fast and simple numerical optimizer,” in Proceedings of North American Fuzzy Information Processing, Berkeley, CA, USA, pp. 524–527, 1996.
[20]	R. Storn and K. Price, “Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997. doi: 10.1023/A:1008202821328
[21]	A. A. A. Mohamed, Y. S. Mohamed, A. A. M. El-Gaafary, et al, “Optimal power flow using moth swarm algorithm,” Electric Power Systems Research, vol. 142, pp. 190–206, 2017. doi: 10.1016/j.jpgr.2016.09.025
[22]	A. A. Heidari, S. Mirjalili, H. Faris, et al, “Harris hawks optimization: Algorithm and applications,” Future Generation Computer Systems, vol. 97, pp. 849–872, 2019. doi: 10.1016/j.future.2019.02.028
[23]	S. M. Li, H. L. Chen, M. J. Wang, et al, “Slime mould algorithm: A new method for stochastic optimization,” Future Generation Computer Systems, vol. 111, pp. 300–323, 2020. doi: 10.1016/j.future.2020.03.055
[24]	Y. T. Yang, H. L. Chen, A. A. Heidari, et al, “Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts,” Expert Systems with Applications, vol. 177, article no. 114864, 2021. doi: 10.1016/j.eswa.2021.114864
[25]	I. Ahmadianfar, A. A. Heidari, S. Noshadian, et al, “INFO: An efficient optimization algorithm based on weighted mean of vectors,” Expert Systems with Applications, vol. 195, article no. 116516, 2022. doi: 10.1016/j.eswa.2022.116516
[26]	N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, et al, “Equation of state calculations by fast computing machines,” The Journal of Chemical Physics, vol. 21, no. 6, pp. 1087–1092, 1953. doi: 10.1063/1.1699114
[27]	A. Ghosh and S. Mukherjee, “Quantum annealing and computation: A brief documentary note,” arXiv preprint, arXiv: 1310.1339, 2013.
[28]	L. Stella, G. E. Santoro, and E. Tosatti, “Optimization by quantum annealing: Lessons from simple cases,” Physical Review B, vol. 72, no. 1, article no. 014303, 2005. doi: 10.1103/PhysRevB.72.014303
[29]	D. H. Wolpert and W. G. Macready, “No free lunch theorems for optimization,” IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 67–82, 1997. doi: 10.1109/4235.585893
[30]	J. Branke, M. Cutaia, and H. Dold, “Reducing genetic drift in steady state evolutionary algorithms,” in Proceedings of the Genetic and Evolutionary Computation Conference, Orlando, FL, USA, pp. 68–74, 1999.
[31]	A. Ghosh, S. Tsutsui, and H. Tanaka, “Function optimization in nonstationary environment using steady state genetic algorithms with aging of individuals,” in Proceedings of the 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence, Anchorage, AK, USA, pp. 666–671, 1998.
[32]	D. A. De Jong, “An analysis of the behavior of a class of genetic adaptive systems,” Ph. D. Thesis, University of Michigan, Ann Arbor, MI, USA, 1975.
[33]	S. W. Mahfoud, “Niching methods for genetic algorithms,” Ph. D. Thesis, University of Illinois at Urbana Champaign, Urbana, IL, USA, 1995.
[34]	M. Lozano, F. Herrera, and J. R. Cano, “Replacement strategies to preserve useful diversity in steady-state genetic algorithms,” Information Sciences, vol. 178, no. 23, pp. 4421–4433, 2008. doi: 10.1016/j.ins.2008.07.031
[35]	Y. S. Liang, Z. G. Ren, L. Wang, et al., “Inferior solutions in Gaussian EDA: Useless or useful,” in Proceedings of the 2017 IEEE Congress on Evolutionary Computation (CEC), San Sebastian, Spain, pp. 301–307, 2017.
[36]	I. Kosztin, B. Faber, and K. Schulten, “Introduction to the diffusion Monte Carlo method,” American Journal of Physics, vol. 64, no. 5, pp. 633–644, 1996. doi: 10.1119/1.18168
[37]	N. Siddique and H. Adeli, “Simulated annealing, its variants and engineering applications,” International Journal on Artificial Intelligence Tools, vol. 25, no. 6, article no. 1630001, 2016. doi: 10.1142/S0218213016300015
[38]	E. C. Behrman, J. E. Steck, and M. A. Moustafa, “Learning quantum annealing,” Quantum Information & Computation, vol. 17, no. 5-6, pp. 469–487, 2017.
[39]	P. Wang and Y. Huang, “Physical model of multi-scale quantum harmonic oscillator optimization algorithm,” Journal of Frontiers of Computer Science and Technology, vol. 9, no. 10, pp. 1271–1280, 2015. doi: 10.3778/j.issn.1673-9418.1502003
[40]	G. Xin and P. Wang, “Exploring superposition state in multi-scale quantum harmonic oscillator algorithm,” Applied Soft Computing, vol. 107, article no. 107398, 2021. doi: 10.1016/j.asoc.2021.107398
[41]	G. Xin, P. Wang, and Y. W. Jiao, “Multiscale quantum harmonic oscillator optimization algorithm with multiple quantum perturbations for numerical optimization,” Expert Systems with Applications, vol. 185, article no. 115615, 2021. doi: 10.1016/j.eswa.2021.115615
[42]	J. Jin and P. Wang, “Multiscale quantum harmonic oscillator algorithm with guiding information for single objective optimization,” Swarm and Evolutionary Computation, vol. 65, article no. 100916, 2021. doi: 10.1016/j.swevo.2021.100916
[43]	A. Crispin and A. Syrichas, “Quantum annealing algorithm for vehicle scheduling,” in Proceedings of the 2013 IEEE International Conference on Systems, Man, and Cybernetics, Manchester, UK, pp. 3523–3528, 2013.
[44]	F. Schwabl, Quantum Mechanics, 4th ed. , Springer, Berlin, Germany, 2007.
[45]	G. C. Wick, “Properties of Bethe-salpeter wave functions,” Physical Review, vol. 96, no. 4, pp. 1124–1134, 1954. doi: 10.1103/PhysRev.96.1124
[46]	D. O’Brien, “The wick rotation,” Australian Journal of Physics, vol. 28, no. 1, pp. 7–14, 1975. doi: 10.1071/PH750007
[47]	P. Wang and G. S. Yang, “Using double well function as a benchmark function for optimization algorithm,” in Proceedings of the 2021 IEEE Congress on Evolutionary Computation (CEC), Kraków, Poland, pp. 886–892, 2021.
[48]	L. Stella, G. E. Santoro, and E. Tosatti, “Optimization by quantum annealing: Lessons from simple cases,” Physical Review B, vol. 72, no. 1, article no. 014303, 2005. (查阅网上资料,本条文献与第28条文献重复,请确认) . doi: 10.1103/PhysRevB.72.014303
[49]	B. Morales-Castañeda, D. Zaldívar, E. Cuevas, et al, “A better balance in metaheuristic algorithms: Does it exist,” Swarm and Evolutionary Computation, vol. 54, article no. 100671, 2020. doi: 10.1016/j.swevo.2020.100671
[50]	G. H. Wu, R. Mallipeddi, and P. N. Suganthan, “Problem definitions and evaluation criteria for the CEC 2017 competition on constrained real-parameter optimization,” in press, 2017. (查阅网上资料, 报告所属机构、技术报告名称及报告编号信息不确定, 请确认补充) .
[51]	A. Saxena, R. Kumar, and S. Das, “β-chaotic map enabled grey wolf optimizer,” Applied Soft Computing, vol. 75, pp. 84–105, 2019. doi: 10.1016/j.asoc.2018.10.044
[52]	L. Wang, B. Yang, and J. Orchard, “Particle swarm optimization using dynamic tournament topology,” Applied Soft Computing, vol. 48, pp. 584–596, 2016. doi: 10.1016/j.asoc.2016.07.041
[53]	İ. B. Aydilek, “A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems,” Applied Soft Computing, vol. 66, pp. 232–249, 2018. doi: 10.1016/j.asoc.2018.02.025
[54]	G. G. Wang, S. Deb, and L. Dos S. Coelho, “Elephant herding optimization,” in Proceedings of the 2015 3rd International Symposium on Computational and Business Intelligence, Bali, Indonesia, pp. 1–5, 2015.
[55]	A. Askarzadeh, “A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm,” Computers & Structures, vol. 169, pp. 1–12, 2016. doi: 10.1016/j.compstruc.2016.03.001