Skip to main content
Springer Nature Link
Log in

LSFQPSO: quantum particle swarm optimization with optimal guided Lévy flight and straight flight for solving optimization problems

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

As a metaheuristic algorithm, particle swarm optimization (PSO) has two main disadvantages. Firstly, it needs to set many parameters, which is not conducive to finding the optimal parameters of the model to be optimized. Secondly, it is easy to fall into the trap of local optimal. Motivated by concepts in quantum mechanics and PSO, quantum-behaved particle swarm optimization (QPSO) was proposed having better global search ability. However, QPSO is deficient in solving high-dimensional problems and performs poorly in adaptability. In this paper, in order to better solve the high-dimensional problems and more applicable to real-world optimization problems, two strategies of Lévy flight (LF) and straight flight (SF) are introduced. An improved quantum particle swarm optimization with Lévy flight and straight flight (LSFQPSO) is proposed. The proposed LSFQPSO algorithm is tested on 22 classic benchmark functions and three engineering optimization problems. The obtained results are compared with seven metaheuristic algorithms and evaluated according to Friedman rank test. The experiments show that LSFQPSO algorithm provides better results with superior performance in most tests compared with seven well-known algorithms, especially in solving high-dimensional problems. What’s more, the proposed LSFQPSO algorithm also shows good performance in solving real-world engineering design optimization problems.

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

Similar content being viewed by others

References

  1. Wang GG, Tan Y (2019) Improving metaheuristic algorithms with information feedback models. IEEE Trans Cybern 49(2):542–555

    Article  Google Scholar 

  2. Li J, Li YX, Tian SS (2020) An improved cuckoo search algorithm with self-adaptive knowledge learning. Neural Comput Appl 32(16):11967–11997

    Article  Google Scholar 

  3. Wang GG, Cai X, Cui Z, Min G, Chen J (2020) High performance computing for cyber physical social systems by using evolutionary multi-objective optimization algorithm. IEEE Trans Emerg Top Comput 8(1):20–30

    Google Scholar 

  4. Wang F, Li Y, Zhou A (2019) An estimation of distribution algorithm for mixed-variable newsvendor problems. IEEE Trans Evol Comput 24(3):479–493

    Google Scholar 

  5. Gao D, Wang GG, Pedrycz W (2020) Solving fuzzy job-shop scheduling problem using DE algorithm improved by a selection mechanism. IEEE Trans Fuzzy Syst 28(12):3265–3275

    Article  Google Scholar 

  6. Chen S, Chen R, Wang GG, Gao J, Sangaiah AK (2018) An adaptive large neighborhood search heuristic for dynamic vehicle routing problems. Comput Electr Eng 67:596–607

    Article  Google Scholar 

  7. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133

    Article  Google Scholar 

  8. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  9. Li W, Wang GG, Alavi AH (2020) Learning-based elephant herding optimization algorithm for solving numerical optimization problems. Knowl Based Syst 195:105675

    Article  Google Scholar 

  10. Li W, Wang G-G (2021) Elephant herding optimization using dynamic topology and biogeography-based optimization based on learning for numerical optimization. Eng Comput 20(21):1–29

    Google Scholar 

  11. Wang F, Zhang H, Zhou A (2021) A particle swarm optimization algorithm for mixed-variable optimization problems. Swarm Evol Comput 60:100808

    Article  Google Scholar 

  12. Mirjalili S, Jangir P, Mirjalili SZ, Saremi S, Trivedi IN (2017) Optimization of problems with multiple objectives using the multi-verse optimization algorithm. Knowl Based Syst 134:50–71

    Article  Google Scholar 

  13. Mirjalili S, Lewis A (2015) Novel performance metrics for robust multi-objective optimization algorithms. Swarm Evol Comput 21:1–23

    Article  Google Scholar 

  14. Rong M, Gong D, Zhang Y, Jin Y, Pedrycz W (2019) Multidirectional prediction approach for dynamic multiobjective optimization problems. IEEE Trans Cybern 49(9):3362–3374

    Article  Google Scholar 

  15. Sun J, Miao Z, Gong D, Zeng XJ, Li J, Wang GG (2020) Interval multiobjective optimization with memetic algorithms. IEEE Trans Cybern 50(8):3444–3457

    Article  Google Scholar 

  16. Gu ZM, Wang GG (2020) Improving NSGA-III algorithms with information feedback models for large-scale many-objective optimization. Futur Gener Comput Syst 107:49–69

    Article  Google Scholar 

  17. Zhang Y, Wang GG, Li K, Yeh WC, Jian M, Dong J (2020) Enhancing MOEA/D with information feedback models for large-scale many-objective optimization. Inf Sci 522:1–16

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang F, Li Y, Liao F, Yan H (2020) An ensemble learning based prediction strategy for dynamic multi-objective optimization. Appl Soft Comput 96:106592

    Article  Google Scholar 

  19. Cao Y, Zhang H, Li W, Zhou M, Zhang Y, Chaovalitwongse WA (2019) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23(4):718–731

    Article  Google Scholar 

  20. Beni G, Wang J (1989) Swarm intelligence in cellular robotic systems. In: NATO advanced workshop robots biological system, Springer, pp 703–712

  21. Kennedy J, Eberhart R (1995) Particle swarm optimization (PSO). In: IEEE international conference on neural networks, IEEE, pp 1942–1948

  22. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B (Cybern) 26(1):29–41

    Article  Google Scholar 

  23. Wang GG, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Appl 31(7):1995–2014

    Article  Google Scholar 

  24. Li J, Lei H, Alavi AH, Wang GG (2020) Elephant herding optimization: variants, hybrids, and applications. Mathematics 8(9):1415

    Article  Google Scholar 

  25. Robinson J, Samii YR (2004) Particle swarm optimization in electromagnetics. IEEE Trans Antennas Propag 52(2):397–407

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu B, Wang L, Jin YH (2007) An effective PSO-based memetic algorithm for flow shop scheduling. IEEE Trans Syst Man Cybern Part B (Cybern) 37(1):18–27

    Article  Google Scholar 

  27. Sun J, Fang W, Wu X, Palade V, Xu W (2012) Quantum-behaved particle swarm optimization: analysis of individual particle behavior and parameter selection. Evol Comput 20(3):349–393

    Article  Google Scholar 

  28. Xi M, Sun J, Xu W (2008) An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl Math Comput 205(2):751–759

    MATH  Google Scholar 

  29. Sun J, Fang W, Palade V, Wu X, Xu W (2011) Quantum-behaved particle swarm optimization with Gaussian distributed local attractor point. Appl Math Comput 218(7):3763–3775

    MATH  Google Scholar 

  30. Yang S, Wang M (2004) A quantum particle swarm optimization. In: 2004 IEEE congress on evolutionary computation (CEC 2004), IEEE, pp 320–324

  31. Sun J, Feng B, Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: 2004 IEEE congress on evolutionary computation (CEC 2004), IEEE, pp 325–331

  32. Wang GG, Chang B, Zhang Z (2015) A multi-swarm bat algorithm for global optimization. In: 2015 IEEE congress on evolutionary computation (CEC 2015), IEEE, pp 480–485

  33. Wang GG, Gandomi AH, Alavi AH (2014) An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl Math Model 38(9–10):2454–2462

    Article  MathSciNet  MATH  Google Scholar 

  34. Li ZY, Yi JH, Wang GG (2015) A new swarm intelligence approach for clustering based on krill herd with elitism strategy. Algorithms 8(4):951–964

    Article  MathSciNet  MATH  Google Scholar 

  35. Wang GG, Guo L, Gandomi AH, Hao G-S, Wang H (2014) Chaotic krill herd algorithm. Inf Sci 274:17–34

    Article  MathSciNet  Google Scholar 

  36. Wang GG, Deb S, Gandomi AH, Zhang Z, Alavi AH (2015) Chaotic cuckoo search. Soft Comput 20(9):3349–3362

    Article  Google Scholar 

  37. Rameshkumar K, Suresh RK, Mohanasundaram KM (2005) Discrete particle swarm optimization (DPSO) algorithm for permutation flowshop scheduling to minimize makespan. In: International conference on natural computation, Springer, Berlin, pp 572–581

  38. Shi Y, Eberhart RC (1998) Parameter selection in particle swarm optimization. In: International conference on evolutionary programming, Springer, Berlin, pp 591–600

  39. Angeline PJ (1998) Evolutionary optimization versus particle swarm optimization: philosophy and performance differences. In: International conference on evolutionary programming, Springer, Berlin, pp 601–610

  40. Jong-Bae P, Yun-Won J, Joong-Rin S, Lee KY (2010) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25(1):156–166

    Article  Google Scholar 

  41. Jang-Ho S, Chang-Hwan I, Sang-Yeop K, Cheol-Gyun L, Hyun-Kyo J (2008) An improved particle swarm optimization algorithm mimicking territorial dispute between groups for multimodal function optimization problems. IEEE Trans Magn 44(6):1046–1049

    Article  Google Scholar 

  42. Pan M, Thangaraj R, Grosan G (2008) Improved particle swarm optimization with low-discrepancy. In: 2008 IEEE congress on evolutionary computation (CEC 2008), IEEE, pp 3011–3018

  43. Agrawal RK, Kaur B, Agarwal P (2021) Quantum inspired particle swarm optimization with guided exploration for function optimization. Appl Soft Comput 102:107122

    Article  Google Scholar 

  44. dos Coelho LS, Mariani VC (2008) Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects. Energy Convers Manag 49(11):3080–3085

    Article  Google Scholar 

  45. dos Coelho LS (2008) A quantum particle swarm optimizer with chaotic mutation operator. Chaos Solitons Fractals 37(5):1409–1418

    Article  Google Scholar 

  46. Sabat SL, dos Coelho LS, Abraham A (2009) MESFET DC model parameter extraction using quantum particle swarm optimization. Microelectron Reliab 49(6):660–666

    Article  Google Scholar 

  47. Sun J, Wu X, Palade V, Fang W, Lai C-H, Xu W (2012) Convergence analysis and improvements of quantum-behaved particle swarm optimization. Inf Sci 193:81–103

    Article  MathSciNet  Google Scholar 

  48. Mariani VC, Duck ARK, Guerra FA, dos Coelho LS, Rao RV (2012) A chaotic quantum-behaved particle swarm approach applied to optimization of heat exchangers. Appl Therm Eng 42:119–128

    Article  Google Scholar 

  49. Li L, Jiao L, Zhao J, Shang R, Gong M (2017) Quantum-behaved discrete multi-objective particle swarm optimization for complex network clustering. Pattern Recogn 63:1–14

    Article  Google Scholar 

  50. Vaze R, Deshmukh N, Kumar R, Saxena A (2021) Development and application of quantum entanglement inspired particle swarm optimization. Knowl Based Syst 219:106859

    Article  Google Scholar 

  51. Kumar N, Shaikh AA, Mahato SK, Bhunia AK (2021) Applications of new hybrid algorithm based on advanced Cuckoo search and adaptive Gaussian quantum behaved particle swarm optimization in solving ordinary differential equations. Expert Syst Appl 172:114646

    Article  Google Scholar 

  52. Lu X-L, He G (2021) QPSO algorithm based on Lévy flight and its application in fuzzy portfolio. Appl Soft Comput 99:106894

    Article  Google Scholar 

  53. Song W, Cattani C, Chi C-H (2020) Multifractional brownian motion and quantum-behaved particle swarm optimization for short term power load forecasting: an integrated approach. Energy 194:116847

    Article  Google Scholar 

  54. Gölcük İ, Ozsoydan FB (2021) Quantum particles-enhanced multiple harris hawks swarms for dynamic optimization problems. Expert Syst Appl 167:114202

    Article  Google Scholar 

  55. Senthilnath J, Das V, Omkar SN, Mani V (2013) Clustering using levy flight cuckoo search. In: Proceedings of seventh international conference on bio-inspired computing: theories and applications (BIC-TA 2012), Springer, pp 65–75

  56. Yang X (2010) Firefly algorithm, Lévy flights and global optimization. Res Dev Intell Syst 26:209–218

    Google Scholar 

  57. Reynolds AM, Reynolds DR, Smith AD, Svensson GP, Lofstedt C (2007) Appetitive flight patterns of male agrotis segetum moths over landscape scales. J Theor Biol 245(1):141–149

    Article  MathSciNet  MATH  Google Scholar 

  58. Gomes AS, Raposo EP, Moura AL, Fewo SI, Pincheira PI, Jerez V, Maia LJ, de Araujo CB (2016) Observation of Levy distribution and replica symmetry breaking in random lasers from a single set of measurements. Sci Rep 6:27987

    Article  Google Scholar 

  59. Charin C, Ishak D, Zainuri MAAM, Ismail B (2021) Modified levy flight optimization for a maximum power point tracking algorithm under partial shading. Appl Sci 11(3):992

    Article  Google Scholar 

  60. Haklı H, Uğuz H (2014) A novel particle swarm optimization algorithm with levy flight. Appl Soft Comput 23:333–345

    Article  Google Scholar 

  61. Li X, Yin M (2015) Modified cuckoo search algorithm with self adaptive parameter method. Inf Sci 298:80–97

    Article  Google Scholar 

  62. Henderson D, Jacobson SH, Johnson AW (2003) The theory and practice of simulated annealing. Handbook of Metaheuristics. Springer, pp 287–319

    Chapter  Google Scholar 

  63. Wang GG, Gandomi AH, Alavi AH, Deb S (2015) A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput Appl 27(4):989–1006

    Article  Google Scholar 

  64. Tian N, Lai CH (2013) Parallel quantum-behaved particle swarm optimization. Int J Mach Learn Cybern 5(2):309–318

    Article  MathSciNet  Google Scholar 

  65. Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  66. Derrac J, García S, Hui S, Suganthan PN, Herrera F (2014) Analyzing convergence performance of evolutionary algorithms: a statistical approach. Inf Sci 289:41–58

    Article  Google Scholar 

  67. Carrasco J, García S, Rueda MM, Das S, Herrera F (2020) Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: practical guidelines and a critical review. Swarm Evol Comput 54:100665

    Article  Google Scholar 

  68. Kumar A, Misra RK, Singh D (2017) Improving the local search capability of effective butterfly optimizer using covariance matrix adapted retreat phase. In: 2017 IEEE congress on evolutionary computation (CEC 2017), pp 1835–1842

  69. Brest J, Maučec MS, Bošković B (2017) Single objective real-parameter optimization: algorithm jSO. In: 2017 IEEE congress on evolutionary computation (CEC 2017), IEEE, pp 1311–1318

  70. Awad NH, Ali MZ, Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. In: 2017 IEEE congress on evolutionary computation (CEC 2017), IEEE, pp 372–379

  71. Kannan BK, Kramer SN (1994) An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. Trans ASME J Mech Des 116:405–411

    Article  Google Scholar 

  72. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Article  Google Scholar 

  73. Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473

    Article  MathSciNet  MATH  Google Scholar 

  74. Kaveh A, Talatahari S (2010) An improved ant colony optimization for constrained engineering design problems. Eng Comput 27(1):155–182

    Article  MATH  Google Scholar 

  75. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228–249

    Article  Google Scholar 

  76. Kaveh A, Talatahari S (2009) Engineering optimization with hybrid particle swarm and ant colony optimization. Asian J Civ Eng 10:611–628

    Google Scholar 

  77. Akay B, Karaboga D (2012) Artificial bee colony algorithm for large-scale problems and engineering design optimization. J Intell Manuf 23(4):1001–1014

    Article  Google Scholar 

  78. Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inform 26(4):30–45

    Google Scholar 

  79. Coello CAC, Montes EM (2002) Constraint- handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16:193–203

    Article  Google Scholar 

  80. He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99

    Article  Google Scholar 

  81. Raj KH, Sharma RS (2005) An evolutionary computational technique for constrained optimisation in engineering design. J Inst Eng India Part Mech Eng Div 86:121–128

    Google Scholar 

  82. Mezura-Montes E, Carlos A, Coello C, Reyes JV, Dávila LM (2007) Multiple trial vectors in differential evolution for engineering design. Eng Optim 39(5):567–589

    Article  MathSciNet  Google Scholar 

  83. Carlos A, Coello C (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  Google Scholar 

  84. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338

    Article  MATH  Google Scholar 

  85. Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Comput Appl 25(7–8):1569–1584

    Article  Google Scholar 

  86. Yu C, Cai Z, Ye X, Wang M, Zhao X, Liang G, Chen H, Li C (2020) Quantum-like mutation-induced dragonfly-inspired optimization approach. Math Comput Simul 178:259–289

    Article  MathSciNet  MATH  Google Scholar 

  87. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112–113:283–294

    Article  Google Scholar 

  88. Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933

    Article  MATH  Google Scholar 

  89. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  90. Li X, Yin M (2013) Multiobjective binary biogeography based optimization for feature selection using gene expression data. IEEE Trans Nanobiosci 12(4):343–353

    Article  Google Scholar 

Download references

Acknowledgements

This research was funded by National Natural Science Foundation of China (No. U1706218, No. 41576011, and No. 41706010).

Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Ocean University of China, Qingdao, 266100, China

    Xiaoyan Liu & Gai-Ge Wang

  2. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, China

    Gai-Ge Wang

  3. College of Information Technology, Jilin Agricultural University, Changchun, 130118, China

    Gai-Ge Wang

  4. Department of Automation, Tsinghua University, Beijing, 100084, China

    Ling Wang

Authors
  1. Xiaoyan Liu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Gai-Ge Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Ling Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Gai-Ge Wang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Wang, GG. & Wang, L. LSFQPSO: quantum particle swarm optimization with optimal guided Lévy flight and straight flight for solving optimization problems. Engineering with Computers 38 (Suppl 5), 4651–4682 (2022). https://doi.org/10.1007/s00366-021-01497-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01497-2

Keywords