Skip to main content
Log in

Quantum-inspired metaheuristic algorithms: comprehensive survey and classification

  • Published:
Artificial Intelligence Review Aims and scope Submit manuscript

Abstract

Metaheuristic algorithms are widely known as efficient solutions for solving problems of optimization. These algorithms supply powerful instruments with significant engineering, industry, and science applications. The Quantum-inspired metaheuristic algorithms were developed by integrating Quantum Computing (QC) concepts into metaheuristic algorithms. The QC-inspired metaheuristic algorithms solve combinational and numerical optimization problems to achieve higher-performing results than conventional metaheuristic algorithms. The QC is used more than any other strategy for accelerating convergence, enhancing exploration, and exploitation, significantly influencing metaheuristic algorithms’ performance. The QC is a new field of research that includes elements from mathematics, physics, and computing. QC has attracted increasing attention among scientists, technologists, and industrialists. During the current decade, it has provided a research platform for the scientific, technical, and industrial areas. In QC, metaheuristic algorithms can be improved by the parallel processing feature. This feature helps to find the best solutions for optimization problems. The Quantum-inspired metaheuristic algorithms have been used in the optimization fields. In this paper, a review of different usages of QC in metaheuristics has been presented. This review also shows a classification of the Quantum-inspired metaheuristic algorithms in optimization problems and discusses their applications in science and engineering. This review paper’s main aims are to give an overview and review the Quantum-inspired metaheuristic algorithms applications.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  1. Gharehchopogh FS, Gholizadeh H (2019) A comprehensive survey: Whale Optimization Algorithm and its applications. Swarm Evol Comput 48:1–24

    Google Scholar 

  2. Shayanfar H, Gharehchopogh FS (2018) Farmland fertility: A new metaheuristic algorithm for solving continuous optimization problems. Appl Soft Comput 71(2):728–746

    Google Scholar 

  3. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549

    MathSciNet  MATH  Google Scholar 

  4. Nadimi-Shahraki MH et al (2021) Migration-based moth-flame optimization algorithm. Processes 9(12):2276

    MathSciNet  Google Scholar 

  5. Gharehchopogh FS, Shayanfar H, Gholizadeh H (2020) A comprehensive survey on symbiotic organisms search algorithms. Artif Intell Rev 53(3):2265–2312

    Google Scholar 

  6. Nadimi-Shahraki MH et al (2022) Gaze cues learning-based grey wolf optimizer and its applications for solving engineering problems. J Comput Sci 61:101636

    Google Scholar 

  7. Koyuncu H, Ceylan R (2019) A PSO based approach: Scout particle swarm algorithm for continuous global optimization problems. J Comput Des Eng 6(2):129–142

    Google Scholar 

  8. Niu P et al (2019) The defect of the Grey Wolf optimization algorithm and its verification method. Knowl Based Syst 171:37–43

    Google Scholar 

  9. Tian X, Li J (2019) A novel improved fruit fly optimization algorithm for aerodynamic shape design optimization. Knowl Based Syst 179:77–91

    Google Scholar 

  10. García-Ródenas R, Linares LJ, López-Gómez JA (2019) A Memetic Chaotic Gravitational Search Algorithm for unconstrained global optimization problems. Appl Soft Comput 79:14–29

    Google Scholar 

  11. Zamani H, Nadimi-Shahraki MH, Gandomi AH (2019) CCSA: Conscious neighborhood-based crow search algorithm for solving global optimization problems. Appl Soft Comput 85:105583

    Google Scholar 

  12. Chen H et al (2019) A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model 71:45–59

    MathSciNet  MATH  Google Scholar 

  13. Long W et al (2019) Solving high-dimensional global optimization problems using an improved sine cosine algorithm. Expert Syst Appl 123:108–126

    Google Scholar 

  14. Garg H (2019) A hybrid GSA-GA algorithm for constrained optimization problems. Inf Sci 478:499–523

    Google Scholar 

  15. Can E, VARIABLE DETERMINED FOR OPTIMIZATION OF(2021) ALTERNATING ENERGY ON THE LOAD BY THE ADAPTIVE TAGUCHI METHOD.Journal of Engineering Research,

  16. Chen X, Tianfield H, Li K (2019) Self-adaptive differential artificial bee colony algorithm for global optimization problems. Swarm Evol Comput 45:70–91

    Google Scholar 

  17. Dhiman G, Kumar V (2019) Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowl Based Syst 165:169–196

    Google Scholar 

  18. Nadimi-Shahraki MH, Zamani H (2022) DMDE: Diversity-maintained multi-trial vector differential evolution algorithm for non-decomposition large-scale global optimization. Expert Systems with Applications, 198: p. 116895

  19. Zamani H, Nadimi-Shahraki MH, Gandomi AH (2022) Starling murmuration optimizer: A novel bio-inspired algorithm for global and engineering optimization. Comput Methods Appl Mech Eng 392:114616

    MathSciNet  MATH  Google Scholar 

  20. Liu J, Liu J (2019) Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems. Appl Soft Comput 74:167–189

    Google Scholar 

  21. Mohammadzadeh H, Gharehchopogh FS (2020) A novel hybrid whale optimization algorithm with flower pollination algorithm for feature selection: Case study Email spam detection. Comput Intell 37(1):176–209

    MathSciNet  Google Scholar 

  22. Zamani H, Nadimi-Shahraki MH, Gandomi AH (2021) QANA: Quantum-based avian navigation optimizer algorithm. Eng Appl Artif Intell 104:104314

    Google Scholar 

  23. Gharehchopogh FS(2022) An Improved Tunicate Swarm Algorithm with Best-random Mutation Strategy for Global Optimization Problems.Journal of Bionic Engineering, : p.1–26

  24. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optim Simulated Annealing Sci 220(4598):671

    Google Scholar 

  25. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: A Gravitational Search Algorithm. Inf Sci 179(13):2232–2248

    MATH  Google Scholar 

  26. Kaveh A, Talatahari S (2010) Charged system search for optimum grillage system design using the LRFD-AISC code. J Constr Steel Res 66(6):767–771

    Google Scholar 

  27. Du H, Wu X, Zhuang J (2006) Small-World Optimization Algorithm for Function Optimization. in Advances in Natural Computation. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  28. Zheng Y-J (2015) Water wave optimization: A new nature-inspired metaheuristic. Comput Oper Res 55:1–11

    MathSciNet  MATH  Google Scholar 

  29. Holland J (1975) Adaptation in Natural and Artificial Systems. University of Michigan, Michigan, USA

    Google Scholar 

  30. Storn R, Price K (1996) Minimizing the real functions of the ICEC’96 contest by differential evolution. in Proceedings of IEEE International Conference on Evolutionary Computation.

  31. Ramezani F, Lotfi S (2013) Social-Based Algorithm (SBA). Appl Soft Comput 13(5):2837–2856

    Google Scholar 

  32. Boussaïd I et al (2012) Biogeography-based optimization for constrained optimization problems. Comput Oper Res 39(12):3293–3304

    MathSciNet  MATH  Google Scholar 

  33. Wari E, Zhu W (2016) A survey on metaheuristics for optimization in food manufacturing industry. Appl Soft Comput 46:328–343

    Google Scholar 

  34. Agrawal RK, Kaur B, Sharma S (2020) Quantum based Whale Optimization Algorithm for wrapper feature selection. Appl Soft Comput 89(2):106092

    Google Scholar 

  35. Hong W-C Hybridizing Meta-heuristic Algorithms with CMM and QCM for SVR’s Parameters Determination. In Hybrid Intelligent Technologies in Energy Demand Forecasting, 2020(2): p. 69–133

  36. Ajagekar A, Humble T, You F (2020) Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems. Computers & Chemical Engineering, 132: p. 106630

  37. Nayyar A, Puri V, Suseendran G (2019) Artificial Bee Colony Optimization—Population-Based Meta-Heuristic Swarm Intelligence Technique. in Data Management, Analytics and Innovation. Springer Singapore, Singapore

    Google Scholar 

  38. Naik B, Nayak J (2018) Crow Search Optimization-Based Hybrid Meta-heuristic for Classification: A Novel Approach. in Progress in Computing, Analytics and Networking. Springer Singapore, Singapore

    Google Scholar 

  39. Hussain A, Muhammad YS (2020) Trade-off between exploration and exploitation with genetic algorithm using a novel selection operator. Complex & Intelligent Systems 6(1):1–14

    Google Scholar 

  40. Sayed GI, Khoriba G, Haggag MH (2018) A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48(10):3462–3481

    Google Scholar 

  41. Deutsch D (1985) Quantum theory, the Church–Turing principle and the universal quantum computer. Proceedings of the Royal Society of London Series A, 400: p. 97–117

  42. Cao B et al (2020) Quantum-enhanced multiobjective large-scale optimization via parallelism. Swarm Evol Comput 57(1):100697

    Google Scholar 

  43. Lin C-J, Chung IF, Chen C-H (2007) An entropy-based quantum neuro-fuzzy inference system for classification applications. Neurocomputing 70(13):2502–2516

    Google Scholar 

  44. Singh HR, Biswas SK, Purkayastha B (2019) A Neuro-Fuzzy Classification System Using Dynamic Clustering. in Machine Intelligence and Signal Analysis. Springer Singapore, Singapore

    Google Scholar 

  45. Miandoab EE, Gharehchopogh FS (2016) A novel hybrid algorithm for software cost estimation based on cuckoo optimization and k-nearest neighbors algorithms, vol 6. Engineering, Technology & Applied Science Research, pp 1018–1022. 3

  46. Abedi M, Gharehchopogh FS (2020) An improved opposition based learning firefly algorithm with dragonfly algorithm for solving continuous optimization problems. Intell Data Anal 24:309–338

    Google Scholar 

  47. Tritschler M, Naber A, Kolisch R (2017) A hybrid metaheuristic for resource-constrained project scheduling with flexible resource profiles. Eur J Oper Res 262(1):262–273

    MathSciNet  MATH  Google Scholar 

  48. Blum C et al (2011) Hybrid metaheuristics in combinatorial optimization: A survey. Appl Soft Comput 11(6):4135–4151

    Google Scholar 

  49. Rahnema N, Gharehchopogh FS, An improved artificial bee colony algorithm based on whale optimization algorithm for data clustering.Multimedia Tools and Applications, 2020(2): p.1–26

  50. Zhang T, Geem ZW (2019) Review of harmony search with respect to algorithm structure. Swarm Evol Comput 48(1):31–43

    Google Scholar 

  51. Menon PS, Ritwik M (2014) A Comprehensive but not Complicated Survey on Quantum Computing. IERI Procedia 10:144–152

    Google Scholar 

  52. Savchuk MM, Fesenko AV (2019) Quantum Computing: Survey and Analysis. Cybernetics and Systems Analysis 55(1):10–21

    MathSciNet  MATH  Google Scholar 

  53. Manju A, Nigam MJ (2014) Applications of quantum inspired computational intelligence: a survey. Artif Intell Rev 42(1):79–156

    Google Scholar 

  54. Zhang G (2011) Quantum-inspired evolutionary algorithms: a survey and empirical study. J Heuristics 17(3):303–351

    MATH  Google Scholar 

  55. Sahu AK, Mahapatra SS, Prediction and optimization of performance measures in electrical discharge machining using rapid prototyping tool electrodes.Journal of Intelligent Manufacturing, 2020(1): p.1–21

  56. Yuan S, Li T, Wang B, A discrete differential evolution algorithm for flow shop group scheduling problem with sequence-dependent setup and transportation times.Journal of Intelligent Manufacturing, 2020(4): p.1–13

  57. Feynman RP (1982) Simulating physics with computers. Int J Theor Phys 21(6):467–488

    MathSciNet  Google Scholar 

  58. Alajmi MS, Alfares FS, Alfares MS (2019) Selection of optimal conditions in the surface grinding process using the quantum based optimisation method. J Intell Manuf 30(3):1469–1481

    Google Scholar 

  59. Wang L, Kowk S, Ip W (2012) Design of an improved quantum-inspired evolutionary algorithm for a transportation problem in logistics systems. J Intell Manuf 23(6):2227–2236

    Google Scholar 

  60. website1 (2019) i>https://www.cbinsights.com/research/report/quantum-computing.

  61. Rao RV, Rai DP, Balic J (2018) Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm. J Intell Manuf 29(8):1715–1737

    Google Scholar 

  62. Karmakar S, Dey A, Saha I(2017) Use of quantum-inspired metaheuristics during last two decades. in 7th International Conference on Communication Systems and Network Technologies (CSNT). 2017

  63. Kuk-Hyun H, Jong-Hwan K (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6(6):580–593

    Google Scholar 

  64. Li J-Y et al (2022) Quantum evolutionary algorithm based power optimization control strategy for China initiative accelerator driven subcritical system. Ann Nucl Energy 166(1):108678

    Google Scholar 

  65. Xiong H et al (2018) Quantum rotation gate in quantum-inspired evolutionary algorithm: A review, analysis and comparison study. Swarm Evol Comput 42:43–57

    Google Scholar 

  66. Jagatheesan K et al(2018) Quantum Inspired Evolutionary Algorithm in Load Frequency Control of Multi-area Interconnected Thermal Power System with Non-linearity, in Quantum Computing:An Environment for Intelligent Large Scale Real Application, A.E. Hassanien, M. Elhoseny, and J. Kacprzyk, Editors. Springer International Publishing: Cham. p. 389–417

  67. Samanta S et al (2017) Chap. 9 - Quantum-inspired evolutionary algorithm for scaling factor optimization during manifold medical information embedding. Quantum Inspired Computational Intelligence. Morgan Kaufmann, Boston, pp 285–326. S. Bhattacharyya, U. Maulik, and P. Dutta, Editors

    Google Scholar 

  68. da Silveira LR, Tanscheit R, Vellasco MMBR (2017) Quantum inspired evolutionary algorithm for ordering problems. Expert Syst Appl 67(5):71–83

    Google Scholar 

  69. Gupta S et al (2017) Parallel quantum-inspired evolutionary algorithms for community detection in social networks. Appl Soft Comput 61:331–353

    Google Scholar 

  70. Wright J, Jordanov I (2019) Convergence properties of quantum evolutionary algorithms on high dimension problems. Neurocomputing 326–327:82–99

    Google Scholar 

  71. Tirumala SS (2018) A Quantum-Inspired Evolutionary Algorithm Using Gaussian Distribution-Based Quantization. Arab J Sci Eng 43(2):471–482

    MATH  Google Scholar 

  72. Talbi H, Draa A (2017) A new real-coded quantum-inspired evolutionary algorithm for continuous optimization. Appl Soft Comput 61:765–791

    Google Scholar 

  73. Wu S-C et al (2016) Quantum evolutionary algorithm and tabu search in pressurized water reactor loading pattern design. Ann Nucl Energy 94:773–782

    Google Scholar 

  74. Patvardhan C, Bansal S, Srivastav A (2015) Solving the 0–1 Quadratic Knapsack Problem with a competitive Quantum Inspired Evolutionary Algorithm. J Comput Appl Math 285:86–99

    MathSciNet  MATH  Google Scholar 

  75. Zhijian Q et al (2015) Hamming-distance-based adaptive quantum-inspired evolutionary algorithm for network coding resources optimization. J China Universities Posts Telecommunications 22(3):92–99

    Google Scholar 

  76. Dey S, Bhattacharyya S, Maulik U (2014) Quantum inspired genetic algorithm and particle swarm optimization using chaotic map model based interference for gray level image thresholding. Swarm Evol Comput 15:38–57

    Google Scholar 

  77. Tirumala SS, Chen G, Pang S (2014) Quantum Inspired Evolutionary Algorithm by Representing Candidate Solution as Normal Distribution. in Neural Information Processing. Springer International Publishing, Cham

    Google Scholar 

  78. Li P (2014) A quantum-behaved evolutionary algorithm based on the Bloch spherical search. Commun Nonlinear Sci Numer Simul 19(4):763–771

    MathSciNet  MATH  Google Scholar 

  79. Ma T et al (2013) Replica creation strategy based on quantum evolutionary algorithm in data gird. Knowl Based Syst 42:85–96

    Google Scholar 

  80. Lu T-C, Juang J-C (2013) A region-based quantum evolutionary algorithm (RQEA) for global numerical optimization. J Comput Appl Math 239:1–11

    MathSciNet  MATH  Google Scholar 

  81. Wang Y et al (2012) Short-term hydrothermal generation scheduling using differential real-coded quantum-inspired evolutionary algorithm. Energy 44(1):657–671

    Google Scholar 

  82. Li Y et al (2012) Quantum evolutionary clustering algorithm based on watershed applied to SAR image segmentation. Neurocomputing 87:90–98

    Google Scholar 

  83. Qu Z-g, Zhang X-y (2012) A Multi-objective Optimization based on Hybrid Quantum Evolutionary Algorithm in Networked Control System. Physics Procedia 25:1561–1568

    Google Scholar 

  84. Wang Y et al (2012) A clonal real-coded quantum-inspired evolutionary algorithm with Cauchy mutation for short-term hydrothermal generation scheduling. Int J Electr Power Energy Syst 43(1):1228–1240

    Google Scholar 

  85. Fiasché M (2012) A Quantum-Inspired Evolutionary Algorithm for Optimization Numerical Problems. in Neural Information Processing. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  86. Nicolau AdS, Schirru R (2011) Alvarenga de Moura Meneses, Quantum evolutionary algorithm applied to transient identification of a nuclear power plant. Prog Nucl Energy 53(1):86–91

    Google Scholar 

  87. Neto JXV, Bernert DLdA, Coelho LdS (2011) Improved quantum-inspired evolutionary algorithm with diversity information applied to economic dispatch problem with prohibited operating zones. Energy Conv Manag 52(1):8–14

    Google Scholar 

  88. Arpaia P, Maisto D, Manna C (2011) A Quantum-inspired Evolutionary Algorithm with a competitive variation operator for Multiple-Fault Diagnosis. Appl Soft Comput 11(8):4655–4666

    Google Scholar 

  89. Xing H et al (2010) An improved quantum-inspired evolutionary algorithm for coding resource optimization based network coding multicast scheme. AEU - International Journal of Electronics and Communications 64(12):1105–1113

    Google Scholar 

  90. Wang L, Li L-p (2010) An effective hybrid quantum-inspired evolutionary algorithm for parameter estimation of chaotic systems. Expert Syst Appl 37(2):1279–1285

    MathSciNet  Google Scholar 

  91. Xing Z, Duan H, Xu C (2009) An Improved Quantum Evolutionary Algorithm with 2-Crossovers. in Advances in Neural Networks – ISNN 2009. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  92. Xing H et al (2009) An adaptive-evolution-based quantum-inspired evolutionary algorithm for QoS multicasting in IP/DWDM networks. Comput Commun 32(6):1086–1094

    Google Scholar 

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

    Google Scholar 

  94. Li P, Song K, Yang E(2010) Quantum ant colony optimization with application. in 2010 Sixth International Conference on Natural Computation.

  95. Oh E, Lee H (2022) Effective route generation framework using quantum mechanism-based multi-directional and parallel ant colony optimization. Comput Ind Eng 169(1):108308

    Google Scholar 

  96. Ding Y, Li J(2017) The application of Quantum-inspired ant colony algorithm in automatic segmentation of tomato image. in 2nd International Conference on Image, Vision and Computing (ICIVC). 2017

  97. Yong Q, Cheng B, Xing Y(2017) A Novel Quantum Ant Colony Algorithm Used for Campus Path. in IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC). 2017

  98. Yang Y et al(2016) IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC). 2016

  99. Dey S, Bhattacharyya S, Maulik U (2016) New quantum inspired meta-heuristic techniques for multi-level colour image thresholding. Appl Soft Comput 46:677–702

    Google Scholar 

  100. Ma Y, Tian W, Fan Y(2014) Improved quantum ant colony algorithm for solving TSP problem. in 2014 IEEE Workshop on Electronics, Computer and Applications.

  101. Zhang J, Wang Y (2012) Defection Recognition of Cold Rolling Strip Steel Based on ACO Algorithm with Quantum Action. in Transactions on Edutainment VII. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  102. Tian Y et al(2010) Quantum Ant Colony Optimization Algorithm and Its Application on Collision Detection. in 2010 International Conference on Computational and Information Sciences.

  103. Weili L, Qiaoyu Y, Xiaochen Z(2010) Continuous quantum ant colony optimization and its application to optimization and analysis of induction motor structure. in IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA). 2010

  104. Weili L, Yin Q, Xiaochen Z(2010) Calculation and analysis of electromagnetic in an induction motor based on continuous quantum ant colony optimization. in Digests of the 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation.

  105. Zhang Y et al(2009) A Quantum-Inspired Ant Colony Optimization for robot coalition formation. in 2009 Chinese Control and Decision Conference.

  106. You X, Xingwai M, Liu S(2009) Quantum computing-based Ant Colony Optimization algorithm for TSP. in 2nd International Conference on Power Electronics and Intelligent Transportation System (PEITS). 2009

  107. Yumin D, Li Z(2014) Quantum Behaved Particle Swarm Optimization Algorithm Based on Artificial Fish Swarm. Hindawi Publishing Corporation, Mathematical Problems in Engineering, 2014: p. 1–10

  108. Kongcun Z, Mingyan J(2010) Quantum Artificial Fish Swarm Algorithm. in 2010 8th World Congress on Intelligent Control and Automation.

  109. Dey A et al (2019) Quantum-Inspired Bat Optimization Algorithm for Automatic Clustering of Grayscale Images. in Recent Trends in Signal and Image Processing. Springer Singapore, Singapore

    Google Scholar 

  110. Zhu B et al(2016) A Novel Quantum-Behaved Bat Algorithm with Mean Best Position Directed for Numerical Optimization. Hindawi Publishing Corporation, Computational Intelligence and Neuroscience, : p. 1–17

  111. Huo F et al(2017) Bloch quantum artificial bee colony algorithm and its application in image threshold segmentation. Signal, Image and Video Processing, 11(8): p. 1585–1592

  112. Can E, Sayan H(2016) PID and fuzzy controlling three phase asynchronous machine by low level DC source three phase inverter.Tehnicki Vjesnik-Technical Gazette, 23(3)

  113. Can E(2019) Mathematical algorithm of fuzzy logic controller for multilevel inverter creating vertical divided voltage.

  114. Can E (2020) Application of adaptive neuro-fuzzy logic method of noised electrical signals for correction. Tecciencia 15(28):1–13

    Google Scholar 

  115. Can E(2021) A flexible closed-loop (fcl) pid and dynamic fuzzy logic + pid controllers for optimization of dc motor.Journal of Engineering Research,

  116. Feng Y et al (2018) An Improved Fuzzy C-Means Clustering Algorithm Based on Multi-chain Quantum Bee Colony Optimization. Wireless Pers Commun 102(2):1421–1441

    Google Scholar 

  117. Gao H-y, Li C-w (2014) Membrane-inspired quantum bee colony optimization and its applications for decision engine. J Cent South Univ 21(5):1887–1897

    MathSciNet  Google Scholar 

  118. Li F et al (2015) Quantum Bacterial Foraging Optimization for Cognitive Radio Spectrum Allocation, vol 9. KSII TRANSACTIONS ON INTERNET AND INFORMATION SYSTEMS, pp 564–582. 2

  119. Li F et al(2014) Quantum bacterial foraging optimization algorithm. in 2014 IEEE Congress on Evolutionary Computation (CEC).

  120. Li L, Mai XF (2013) Bacterial Foraging Algorithm Based on Quantum-Behaved Particle Swarm Optimization for Global Optimization. Adv Mater Res 655:948–954

    Google Scholar 

  121. Cao J, Gao H (2012) A Quantum-inspired Bacterial Swarming Optimization Algorithm for Discrete Optimization Problems. in Advances in Swarm Intelligence. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  122. Zhu H et al (2019) Quantum-inspired cuckoo co-search algorithm for no-wait flow shop scheduling. Appl Intell 49(2):791–803

    Google Scholar 

  123. Das P, Naskar SK, Patra SN (2018) Hardware efficient FIR filter design using Global Best Steered Quantum Inspired Cuckoo Search Algorithm. Appl Soft Comput 71:1–19

    Google Scholar 

  124. Boussalia SR, Chaoui A (2014) Optimizing QoS-Based Web Services Composition by Using Quantum Inspired Cuckoo Search Algorithm. Mobile Web Information Systems. Springer International Publishing, Cham

    Google Scholar 

  125. Wang C et al (2016) Fault reconfiguration of shipboard power system based on triple quantum differential evolution algorithm. J Shanghai Jiaotong Univ (Science) 21(4):433–442

    Google Scholar 

  126. Yin J, Wang Y, Hu J (2012) Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration. J Netw Comput Appl 35(3):1035–1051

    Google Scholar 

  127. Zheng T, Yamashiro M (2010) Solving flow shop scheduling problems by quantum differential evolutionary algorithm. Int J Adv Manuf Technol 49(5):643–662

    Google Scholar 

  128. Layeb A, Saidouni D-E (2009) Quantum Differential Evolution Algorithm for Variable Ordering Problem of Binary Decision Diagram. in Advances in Computer Science and Engineering. Springer Berlin Heidelberg, Berlin, Heidelberg

    MATH  Google Scholar 

  129. Ozsoydan FB, Baykasoğlu A (2019) Quantum firefly swarms for multimodal dynamic optimization problems. Expert Syst Appl 115:189–199

    Google Scholar 

  130. Tao SB, D.Z.Liu, and Tang AP(2019) Bridge Critical State Search by Using Quantum Genetic Firefly Algorithm. Hindawi, : p. 1–10

  131. Shareef H et al (2014) Power quality and reliability enhancement in distribution systems via optimum network reconfiguration by using quantum firefly algorithm. Int J Electr Power Energy Syst 58:160–169

    Google Scholar 

  132. Hongyuan G, Yanan D, Chenwan L (2018) Quantum fireworks algorithm for optimal cooperation mechanism of energy harvesting cognitive radio. J Syst Eng Electron 29(1):18–30

    Google Scholar 

  133. Gao H, Li C (2015) Opposition-based quantum firework algorithm for continuous optimisation problems. Int J Comput Sci Math 6(3):256–265

    MathSciNet  MATH  Google Scholar 

  134. Gao H, Du Y, Zhang S (2017) Quantum flower pollination algorithm for optimal multiple relay selection scheme. Int J Wire Mob Comput 13(4):299–305

    Google Scholar 

  135. Gao H et al(2017) IEEE 17th International Conference on Communication Technology (ICCT). 2017

  136. Lu K, Li H(2015) Quantum-Behaved Flower Pollination Algorithm. in 2015 14th International Symposium on Distributed Computing and Applications for Business Engineering and Science (DCABES).

  137. Narayanan A, Moore M(1996) Quantum-inspired genetic algorithms. in Proceedings of IEEE International Conference on Evolutionary Computation.

  138. Das S et al (2019) Color MRI Image Segmentation Using Quantum-Inspired Modified Genetic Algorithm-Based FCM. Recent Trends in Signal and Image Processing. Springer Singapore, Singapore

    Google Scholar 

  139. Mousavi S et al (2019) Use of a quantum genetic algorithm for coalition formation in large-scale UAV networks. Ad Hoc Netw 87(1):26–36

    Google Scholar 

  140. Gandhi T, Nitin, Alam T(2017) Quantum genetic algorithm with rotation angle refinement for dependent task scheduling on distributed systems. in Tenth International Conference on Contemporary Computing (IC3). 2017

  141. Alam T, Raza Z (2018) Quantum genetic algorithm based scheduler for batch of precedence constrained jobs on heterogeneous computing systems. J Syst Softw 135(1):126–142

    Google Scholar 

  142. Chen Z, Zhou W(2017) Path Planning for a Space-Based Manipulator System Based on Quantum Genetic Algorithm. Hindawi, Journal of Robotics, : p. 1–10

  143. Konar D et al (2017) An improved Hybrid Quantum-Inspired Genetic Algorithm (HQIGA) for scheduling of real-time task in multiprocessor system. Appl Soft Comput 53(1):296–307

    MathSciNet  Google Scholar 

  144. Zheng D et al(2016) Chinese Control and Decision Conference (CCDC). 2016

  145. Liu Z et al(2016) IEEE International Conference on Information and Automation (ICIA). 2016

  146. Pitchai A, Reddy AV, Savarimuthu N(2015) Quantum Walk based genetic algorithm for 0–1 quadratic knapsack problem. in International Conference on Computing and Network Communications (CoCoNet). 2015

  147. Wang H et al(2014) Improved Quantum Genetic Algorithm in Application of Scheduling Engineering. Hindawi Publishing Corporation, Abstract and Applied Analysis, : p. 1–10

  148. Bukhori I, Silitonga A(2014) A new approach of quantum-inspired genetic algorithm for self-generation of fuzzy logic controller. in 2014 International Conference on Intelligent Autonomous Agents, Networks and Systems.

  149. Wang H et al(2013) The Improvement of Quantum Genetic Algorithm and Its Application on Function. Hindawi Publishing Corporation, Mathematical Problems in Engineering, : p. 1–10

  150. Li D(2012) To Solve the Job Shop Scheduling Problem with the Improve Quantum Genetic Algorithm. in 2012 Third Global Congress on Intelligent Systems.

  151. Sun Y, Ding M(2010) Quantum Genetic Algorithm for Mobile Robot Path Planning. in Fourth International Conference on Genetic and Evolutionary Computing. 2010

  152. Xiao J et al (2010) A quantum-inspired genetic algorithm for k-means clustering. Expert Syst Appl 37(7):4966–4973

    Google Scholar 

  153. Gu J et al (2010) A novel competitive co-evolutionary quantum genetic algorithm for stochastic job shop scheduling problem. Comput Oper Res 37(5):927–937

    MathSciNet  MATH  Google Scholar 

  154. Vlachogiannis JG, Østergaard J(2009) Reactive power and voltage control based on general quantum genetic algorithms. Expert Systems with Applications, 36(3, Part 2): p. 6118–6126

  155. Guo J et al(2009) An Improved Quantum Genetic Algorithm. in 2009 Third International Conference on Genetic and Evolutionary Computing.

  156. Gu J, Gu X, Gu M (2009) A novel parallel quantum genetic algorithm for stochastic job shop scheduling. J Math Anal Appl 355(1):63–81

    MathSciNet  MATH  Google Scholar 

  157. Wang L, Li B-b (2008) Quantum-inspired genetic algorithms for flow shop scheduling. In: Nedjah N, Coelho LdS, Mourelle LdM (eds) Quantum Inspired Intelligent Systems. Springer, Berlin Heidelberg: Berlin, Heidelberg, pp 17–56

    Google Scholar 

  158. Peng W(2008) Quantum Model of Genetic Algorithm. in 2008 International Symposium on Knowledge Acquisition and Modeling.

  159. Wang L, Tang F, Wu H(2005) Hybrid genetic algorithm based on quantum computing for numerical optimization and parameter estimation. Applied Mathematics and Computation, 171(2): p. 1141–1156

  160. da Cruz AVA et al (2005) Cultural Operators for a Quantum-Inspired Evolutionary Algorithm Applied to Numerical Optimization Problems. in Artificial Intelligence and Knowledge Engineering Applications: A Bioinspired Approach. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  161. Li Y et al (2005) A Novel Immune Quantum-Inspired Genetic Algorithm. in Advances in Natural Computation. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  162. Kuk-Hyun H et al(2001) Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. in Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

  163. Kuk-Hyun H, Jong-Hwan K(2000) Genetic quantum algorithm and its application to combinatorial optimization problem. in Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

  164. Barani F, Mirhosseini M, Nezamabadi-pour H (2017) Application of binary quantum-inspired gravitational search algorithm in feature subset selection. Appl Intell 47(2):304–318

    Google Scholar 

  165. Lou J et al (2018) Failure prediction by relevance vector regression with improved quantum-inspired gravitational search. J Netw Comput Appl 103:171–177

    Google Scholar 

  166. Mirhosseini M, Barani F, Nezamabadi-pour H(2017) QQIGSA: A quadrivalent quantum-inspired GSA and its application in optimal adaptive design of wireless sensor networks. Journal of Network and Computer Applications, 78: p. 231–241

  167. Soleimanpour-moghadam M, Nezamabadi-pour H, Farsangi MM (2014) A quantum inspired gravitational search algorithm for numerical function optimization. Inf Sci 267:83–100

    MathSciNet  MATH  Google Scholar 

  168. Gao H, Du Y, Diao M (2017) Quantum-inspired glowworm swarm optimisation and its application. Int J Comput Sci Math 8(1):91–100

    MathSciNet  MATH  Google Scholar 

  169. Gao H, Li J, Diao M (2018) Direction finding of bistatic MIMO radar based on quantum-inspired grey wolf optimization in the impulse noise. EURASIP J Adv Signal Process 2018(1):75

    Google Scholar 

  170. Wang P et al (2018) Multi-scale quantum harmonic oscillator algorithm for global numerical optimization. Appl Soft Comput 69:655–670

    Google Scholar 

  171. Layeb A (2013) A hybrid quantum inspired harmony search algorithm for 0–1 optimization problems. J Comput Appl Math 253:14–25

    MathSciNet  MATH  Google Scholar 

  172. Razmjooy N, Ramezani M (2014) An Improved Quantum Evolutionary Algorithm Based on Invasive Weed Optimization. Indian J Sci Res 4(2):413–422

    Google Scholar 

  173. Sayed GI, Darwish A, Hassanien AE(2019) Quantum multiverse optimization algorithm for optimization problems. Neural Computing and Applications, 31(7): p. 2763–2780

  174. Jun S, Bin F, Wenbo X(2004) Particle swarm optimization with particles having quantum behavior. in Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

  175. Ma B et al (2022) Parameter estimation of the COVID-19 transmission model using an improved quantum-behaved particle swarm optimization algorithm. Digit Signal Proc 127(5):103577

    Google Scholar 

  176. Zhang Q et al (2021) A new quantum particle swarm optimization algorithm for controller placement problem in software-defined networking. Comput Electr Eng 95(3):107456

    Google Scholar 

  177. Lai X et al (2020) Diversity-preserving quantum particle swarm optimization for the multidimensional knapsack problem. Expert Syst Appl 149(1):113310

    Google Scholar 

  178. Agrawal RK, Kaur B, Agarwal P (2021) Quantum inspired Particle Swarm Optimization with guided exploration for function optimization. Appl Soft Comput 102(2):107122

    Google Scholar 

  179. Liu T et al (2021) Fracture performance prediction of polyvinyl alcohol fiber-reinforced cementitious composites containing nano-SiO2 using least-squares support vector machine optimized with quantum-behaved particle swarm optimization algorithm. Theoret Appl Fract Mech 115:103074

    Google Scholar 

  180. Kanchan P (2019) Pushparaj Shetty. Quantum PSO Algorithm for Clustering in Wireless Sensor Networks to Improve Network Lifetime. Emerging Technologies in Data Mining and Information Security. Springer Singapore, Singapore

    Google Scholar 

  181. Pesaran Hajiabbas M et al(2018) The Utilization of Quantum Inspired Computational Intelligent in Power Systems Optimization, in Quantum Computing:An Environment for Intelligent Large Scale Real Application, A.E. Hassanien, M. Elhoseny, and J. Kacprzyk, Editors. Springer International Publishing: Cham. p. 489–505

  182. Nazari-Heris M et al(2018) Optimal Distributed Generation Allocation Using Quantum Inspired Particle Swarm Optimization, in Quantum Computing:An Environment for Intelligent Large Scale Real Application, A.E. Hassanien, M. Elhoseny, and J. Kacprzyk, Editors. Springer International Publishing: Cham. p. 419–432

  183. Guo Y, Wei L, Xu X (2018) A sonar image segmentation algorithm based on quantum-inspired particle swarm optimization and fuzzy clustering. Neural Computing and Applications

  184. Li B, Chen G, Tao N (2018) A Quantum Particle Swarm-Inspired Algorithm for Dynamic Vehicle Routing Problem. Recent Developments in Mechatronics and Intelligent Robotics. Springer International Publishing, Cham

    Google Scholar 

  185. Sharma R et al (2018) A Model for Resource Constraint Project Scheduling Problem Using Quantum Inspired PSO. in Smart and Innovative Trends in Next Generation Computing Technologies. Springer Singapore, Singapore

    Google Scholar 

  186. Zouache D, Ben Abdelaziz F (2018) A cooperative swarm intelligence algorithm based on quantum-inspired and rough sets for feature selection. Comput Ind Eng 115:26–36

    Google Scholar 

  187. Agarwal S, Ranjan P (2018) MR-TP-QFPSO: map reduce two phases quantum fuzzy PSO for feature selection. Int J Syst Assur Eng Manage 9(4):888–900

    Google Scholar 

  188. Logesh R et al (2018) A hybrid quantum-induced swarm intelligence clustering for the urban trip recommendation in smart city. Future Generation Computer Systems 83:653–673

    Google Scholar 

  189. Hassani K, Lee W-S (2016) Multi-objective design of state feedback controllers using reinforced quantum-behaved particle swarm optimization. Appl Soft Comput 41(5):66–76

    Google Scholar 

  190. Wang F et al(2015) Kinematics Parameters Identification for IRB 1400 Using Improved Quantum Behaved Particle Swarm Optimization. in Proceedings of the International Conference on Communications, Signal Processing, and Systems. 2016. Berlin, Heidelberg: Springer Berlin Heidelberg

  191. Dey S, Bhattacharyya S, Maulik U (2017) Efficient quantum inspired meta-heuristics for multi-level true colour image thresholding. Appl Soft Comput 56:472–513

    Google Scholar 

  192. Fang W et al (2016) A decentralized quantum-inspired particle swarm optimization algorithm with cellular structured population. Inf Sci 330:19–48

    Google Scholar 

  193. Xi M et al (2015) Calibrating RZWQM2 model using quantum-behaved particle swarm optimization algorithm. Comput Electron Agric 113:72–80

    Google Scholar 

  194. Wang G-G et al (2016) A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput Appl 27(4):989–1006

    Google Scholar 

  195. Dey S et al (2014) Multi-level thresholding using quantum inspired meta-heuristics. Knowl Based Syst 67:373–400

    Google Scholar 

  196. Tang D et al (2014) A quantum-behaved particle swarm optimization with memetic algorithm and memory for continuous non-linear large scale problems. Inf Sci 289:162–189

    Google Scholar 

  197. Al-Baity H, Meshoul S, Kaban A (2012) Constrained Multi-objective Optimization Using a Quantum Behaved Particle Swarm. Neural Information Processing. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  198. Niu Q, Zhou Z, Zeng T (2012) A Hybrid Quantum-Inspired Particle Swarm Evolution Algorithm and SQP Method for Large-Scale Economic Dispatch Problems. in Bio-Inspired Computing and Applications. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  199. Bachlaus M, Tiwari MK, Chan FTS (2009) Multi-objective resource assignment problem in a product-driven supply chain using a Taguchi-based DNA algorithm. Int J Prod Res 47(9):2345–2371

    MATH  Google Scholar 

  200. Yu G, Huang Y, Huang L(2010) T-S fuzzy control for magnetic levitation systems using quantum particle swarm optimization. in Proceedings of SICE Annual Conference 2010.

  201. Zhisheng Z (2010) Quantum-behaved particle swarm optimization algorithm for economic load dispatch of power system. Expert Syst Appl 37(2):1800–1803

    Google Scholar 

  202. Gou S et al (2013) Multi-elitist immune clonal quantum clustering algorithm. Neurocomputing 101:275–289

    Google Scholar 

  203. Niu Q et al (2012) An efficient quantum immune algorithm to minimize mean flow time for hybrid flow shop problems. Math Comput Simul 84:1–25

    MathSciNet  Google Scholar 

  204. Gao J, Wang J (2011) A hybrid quantum-inspired immune algorithm for multiobjective optimization. Appl Math Comput 217(9):4754–4770

    MathSciNet  MATH  Google Scholar 

  205. Shang R et al (2018) Quantum-Inspired Immune Clonal Algorithm for solving large-scale capacitated arc routing problems. Memetic Comput 10(1):81–102

    Google Scholar 

  206. Yang S, Wang M, Jiao L (2010) Quantum-inspired immune clone algorithm and multiscale Bandelet based image representation. Pattern Recogn Lett 31(13):1894–1902

    Google Scholar 

  207. Wu Q et al (2009) A novel quantum-inspired immune clonal algorithm with the evolutionary game approach. Prog Nat Sci 19(10):1341–1347

    MathSciNet  Google Scholar 

  208. Jiao L et al(2008) Quantum-Inspired Immune Clonal Algorithm for Global Optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38(5): p. 1234–1253

  209. Li Y, Jiao L (2005) Quantum-Inspired Immune Clonal Algorithm. in Artificial Immune Systems. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  210. Pavithr RS, Gursaran (2016) Quantum Inspired Social Evolution (QSE) algorithm for 0–1 knapsack problem. Swarm Evol Comput 29:33–46

    Google Scholar 

  211. Li W et al (2018) A collaborative filtering recommendation method based on discrete quantum-inspired shuffled frog leaping algorithms in social networks. Future Generation Computer Systems 88:262–270

    Google Scholar 

  212. Cheng C et al (2015) Quantum-Inspired Shuffled Frog Leaping Algorithm for Spectrum Sensing in Cooperative Cognitive Radio Network. Human Centered Computing. Springer International Publishing, Cham

    Google Scholar 

  213. Lu T-C, Juang J-C (2011) Quantum-inspired space search algorithm (QSSA) for global numerical optimization. Appl Math Comput 218(6):2516–2532

    MathSciNet  MATH  Google Scholar 

  214. Waidyasooriya HM et al (2019) OpenCL-based design of an FPGA accelerator for quantum annealing simulation. J Supercomputing 75(8):5019–5039

    Google Scholar 

  215. Dey A et al(2018) Simulated Annealing Based Quantum Inspired Automatic Clustering Technique. in The International Conference on Advanced Machine Learning Technologies and Applications (AMLTA 2018. Cham: Springer International Publishing

  216. Silva C, Dutra I, Dahlem MS(2018) Driven tabu search: a quantum inherent optimisation.Emerging Technologies, : p.1–6

  217. Kuo S, Chou Y (2017) Entanglement-Enhanced Quantum-Inspired Tabu Search Algorithm for Function Optimization. IEEE Access 5:13236–13252

    Google Scholar 

  218. Kuo S-Y, Chou Y-H, Chen C-Y (2017) Quantum-inspired algorithm for cyber-physical visual surveillance deployment systems. Comput Netw 117:5–18

    Google Scholar 

  219. Chou Y, Yang Y, Chiu C(2011) Classical and quantum-inspired Tabu search for solving 0/1 knapsack problem. in IEEE International Conference on Systems, Man, and Cybernetics. 2011

  220. Kaveh A et al (2021) Quantum Teaching-Learning-Based Optimization algorithm for sizing optimization of skeletal structures with discrete variables. Structures 32(3):1798–1819

    Google Scholar 

  221. Gao HY et al (2019) Quantum-Inspired Teaching-Learning-Based Optimization for Linear Array Pattern Synthesis. in Communications, Signal Processing, and Systems. Springer Singapore, Singapore

    Google Scholar 

  222. Li P, Zhao Y (2019) A quantum-inspired vortex search algorithm with application to function optimization. Nat Comput 18(3):647–674

    MathSciNet  Google Scholar 

  223. Barani F et al (2017) Unit commitment by an improved binary quantum GSA. Appl Soft Comput 60:180–189

    Google Scholar 

  224. Srikanth K et al (2018) Meta-heuristic framework: Quantum inspired binary grey wolf optimizer for unit commitment problem. Comput Electr Eng 70(1):243–260

    MathSciNet  Google Scholar 

  225. Meraihi Y et al (2017) A quantum-inspired binary firefly algorithm for QoS multicast routing. Int J Metaheuristics 6(4):309–333

    Google Scholar 

  226. Nezamabadi-pour H (2015) A quantum-inspired gravitational search algorithm for binary encoded optimization problems. Eng Appl Artif Intell 40(5):62–75

    Google Scholar 

  227. Ibrahim AA, Mohamed A, Shareef H (2014) Optimal power quality monitor placement in power systems using an adaptive quantum-inspired binary gravitational search algorithm. Int J Electr Power Energy Syst 57:404–413

    Google Scholar 

  228. Ji B et al (2014) Application of quantum-inspired binary gravitational search algorithm for thermal unit commitment with wind power integration. Energy Conv Manag 87:589–598

    Google Scholar 

  229. Han X et al (2013) Facing the classification of binary problems with a hybrid system based on quantum-inspired binary gravitational search algorithm and K-NN method. Eng Appl Artif Intell 26(10):2424–2430

    Google Scholar 

  230. Mahseur M, Boukra A, Meraihi Y (2019) QoS Multicast Routing Based on a Quantum Chaotic Dragonfly Algorithm. in Modelling and Implementation of Complex Systems. Springer International Publishing, Cham

    Google Scholar 

  231. Xu B et al(2019) Fault Diagnosis of Variable Load Bearing Based on Quantum Chaotic Fruit Fly VMD and Variational RVM. Hindawi, Shock and Vibration, : p. 1–20

  232. Mahseur M, Boukra A, Meraihi Y (2018) Improved Quantum Chaotic Animal Migration Optimization Algorithm for QoS Multicast Routing Problem. in Computational Intelligence and Its Applications. Springer International Publishing, Cham

    Google Scholar 

  233. Nie X, Wang W, Nie H (2017) Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT. Comput Intell Neurosci 2017:1583847

    Google Scholar 

  234. Wu Z et al (2017) A New Quantum-Behaved Particle Swarm Optimization with a Chaotic Operator. Intelligent Computing, Networked Control, and Their Engineering Applications. Springer Singapore, Singapore

    Google Scholar 

  235. Ishak Boushaki S, Kamel N, Bendjeghaba O (2018) A new quantum chaotic cuckoo search algorithm for data clustering. Expert Syst Appl 96:358–372

    MATH  Google Scholar 

  236. Turgut OE (2016) Hybrid Chaotic Quantum behaved Particle Swarm Optimization algorithm for thermal design of plate fin heat exchangers. Appl Math Model 40(1):50–69

    MathSciNet  MATH  Google Scholar 

  237. Yuan X et al (2015) A new quantum inspired chaotic artificial bee colony algorithm for optimal power flow problem. Energy Conv Manag 100:1–9

    Google Scholar 

  238. Zhu H, Zhao C, Liu W (2014) Sub-pixel mapping of remote-sensing imagery based on chaotic quantum bee colony algorithm. Int J Comput Sci Math 5(1):61–71

    MathSciNet  Google Scholar 

  239. Turgut OE, Turgut MS, Coban MT (2014) Chaotic quantum behaved particle swarm optimization algorithm for solving nonlinear system of equations. Comput Math Appl 68(4):508–530

    MathSciNet  MATH  Google Scholar 

  240. Liu W et al(2014) An Environmental-Economic Dispatch Method for Smart Microgrids Using VSS_QGA. Hindawi Publishing Corporation, Journal of Applied Mathematics, : p. 1–11

  241. Liu A-j, Li H, Dong M(2013) Chaotic Simulated Annealing Quantum-Behaved Particle Swarm Optimization Research. in Proceedings of 20th International Conference on Industrial Engineering and Engineering Management. Berlin, Heidelberg: Springer Berlin Heidelberg

  242. Zhang H, Hu Y (2011) A hybrid chaotic quantum evolutionary algorithm for resource combinatorial optimization in manufacturing grid system. Int J Adv Manuf Technol 52(5):821–831

    Google Scholar 

  243. Liao G(2010) Using chaotic quantum genetic algorithm solving environmental economic dispatch of Smart Microgrid containing distributed generation system problems. in 2010 International Conference on Power System Technology.

  244. Xiao J et al (2009) A hybrid quantum chaotic swarm evolutionary algorithm for DNA encoding. Comput Math Appl 57(11):1949–1958

    Google Scholar 

  245. Teng H, Zhao B, Yang B(2008) An Improved Mutative Scale Chaos Optimization Quantum Genetic Algorithm. in Fourth International Conference on Natural Computation. 2008

  246. Sarvaghad-Moghaddam M, Niemann P, Drechsler R (2018) Multi-objective Synthesis of Quantum Circuits Using Genetic Programming. in Reversible Computation. Springer International Publishing, Cham

    MATH  Google Scholar 

  247. Guo Y-n et al (2018) Interval multi-objective quantum-inspired cultural algorithms. Neural Comput Appl 30(3):709–722

    Google Scholar 

  248. Konar D et al (2018) A Multi-Objective Quantum-Inspired Genetic Algorithm (Mo-QIGA) for Real-Time Tasks Scheduling in Multiprocessor Environment. Procedia Comput Sci 131:591–599

    Google Scholar 

  249. Dey S, Bhattacharyya S, Maulik U(2017) Chap. 6 - Quantum-inspired multi-objective simulated annealing for bilevel image thresholding**Fully documented templates are available in the elsarticle package oni>http://www.ctan.org/tex-archive/macros/latex/contrib/elsarticleCTAN, in Quantum Inspired Computational Intelligence, S. Bhattacharyya, U. Maulik, and P. Dutta, Editors. Morgan Kaufmann: Boston. p. 207–232.

  250. Feng Z-k, Niu W-j, Cheng C-t (2017) Multi-objective quantum-behaved particle swarm optimization for economic environmental hydrothermal energy system scheduling. Energy 131:165–178

    Google Scholar 

  251. Zhang G, Sun H (2017) Multi-objective machining parameter optimisation for residual stress based on quantum cat swarm. Int J Service Comput Oriented Manuf 3(1):54–70

    Google Scholar 

  252. Dwivedi AK, Patel RN(2017) Chap. 10 Digital filter design using quantum-inspired multiobjective cat swarm optimization algorithm, inQuantum Inspired Computational Intelligence. p.327–359

  253. Li L et al (2017) Quantum-behaved discrete multi-objective particle swarm optimization for complex network clustering. Pattern Recogn 63:1–14

    Google Scholar 

  254. Xu S-h et al (2016) Multi-objective quantum-behaved particle swarm optimization algorithm with double-potential well and share-learning. Optik 127(12):4921–4927

    Google Scholar 

  255. Wang Y, Li Y, Jiao L (2016) Quantum-inspired multi-objective optimization evolutionary algorithm based on decomposition. Soft Comput 20(8):3257–3272

    Google Scholar 

  256. Li Y et al (2015) Overlapping community detection through an improved multi-objective quantum-behaved particle swarm optimization. J Heuristics 21(4):549–575

    Google Scholar 

  257. Li Y et al (2014) SAR image segmentation based on quantum-inspired multiobjective evolutionary clustering algorithm. Inform Process Lett 114(6):287–293

    MATH  Google Scholar 

  258. Charan Kumari A, Srinivas K, Gupta MP (2013) Software Requirements Optimization Using Multi-Objective Quantum-Inspired Hybrid Differential Evolution. in EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  259. Guo Y, Chen, Wang C (2013) Multi-objective Quantum Cultural Algorithm and Its Application in the Wireless Sensor Networks’ Energy-Efficient Coverage Optimization. in Intelligent Data Engineering and Automated Learning – IDEAL 2013. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  260. Guo Y et al (2013) An Energy-Efficient Coverage Optimization Method for the Wireless Sensor Networks Based on Multi-objective Quantum-Inspired Cultural Algorithm. in Advances in Neural Networks – ISNN 2013. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  261. Lu TC, Yu GR (2013) An adaptive population multi-objective quantum-inspired evolutionary algorithm for multi-objective 0/1 knapsack problems. Inf Sci 243:39–56

    MathSciNet  MATH  Google Scholar 

  262. Li Z, Rudolph G, Li K (2009) Convergence performance comparison of quantum-inspired multi-objective evolutionary algorithms. Comput Math Appl 57(11):1843–1854

    MathSciNet  MATH  Google Scholar 

  263. Li Z, Li Z, Rudolph G (2007) On the Convergence Properties of Quantum-Inspired Multi-Objective Evolutionary Algorithms. Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. Springer Berlin Heidelberg, Berlin, Heidelberg

    Google Scholar 

  264. Wittek P(2014) Quantum Machine Learning: What Quantum Computing Means to Data Mining. Elsevier, 1st Edition, Academic Press,

  265. Schuld M, Sinayskiy I, Petruccione F (2014) An introduction to quantum machine learning. Contemporary P hysics, Taylor & Francis

  266. Yahyaoui’s A, Yahyaoui I, Yumuşak N (2018) 13 - Machine Learning Techniques for Data Classification, in Advances in Renewable Energies and Power Technologies. Elsevier, pp 441–450. I. Yahyaoui, Editor

  267. Liu J et al (2020) An echo state network architecture based on quantum logic gate and its optimization. Neurocomputing 371(1):100–107

    Google Scholar 

  268. Kamruzzaman A et al (2020) Quantum Deep Learning Neural Networks. in Advances in Information and Communication. Springer International Publishing, Cham

    Google Scholar 

  269. Patel OP et al (2019) Enhanced quantum-based neural network learning and its application to signature verification. Soft Comput 23(9):3067–3080

    Google Scholar 

  270. Jeswal SK, Chakraverty S (2019) Recent Developments and Applications in Quantum Neural Network: A Review. Arch Comput Methods Eng 26(4):793–807

    MathSciNet  Google Scholar 

  271. Xiang W et al (2018) Quantum weighted gated recurrent unit neural network and its application in performance degradation trend prediction of rotating machinery. Neurocomputing 313:85–95

    Google Scholar 

  272. Das G, Panda S, Padhy SK (2018) Quantum Particle Swarm Optimization Tuned Artificial Neural Network Equalizer. Soft Computing: Theories and Applications. Springer Singapore, Singapore

    Google Scholar 

  273. Gao Z et al (2018) IMA health state evaluation using deep feature learning with quantum neural network. Eng Appl Artif Intell 76:119–129

    Google Scholar 

  274. Gupta S et al(2017) 8th Annual Industrial Automation and Electromechanical Engineering Conference (IEMECON). 2017

  275. Altaisky MV et al (2017) Entanglement in a quantum neural network based on quantum dots. Photonics Nanostruct Fundam Appl 24:24–28

    Google Scholar 

  276. Pi J, Huang J, Ma L(2017) Aeroengine Fault Diagnosis Using Optimized Elman Neural Network. Hindawi, Mathematical Problems in Engineering, : p. 1–8

  277. Zhang Z, Gong W(2016) Short-Term Load Forecasting Model Based on Quantum Elman Neural Networks. Hindawi Publishing Corporation, Mathematical Problems in Engineering, : p. 1–8

  278. da Silva AJ, de Oliveira WR (2016) Comments on “quantum artificial neural networks with applications”. Inf Sci 370–371:120–122

    MATH  Google Scholar 

  279. Zhang K et al(2016) A Network Traffic Prediction Model Based on Quantum-Behaved Particle Swarm Optimization Algorithm and Fuzzy Wavelet Neural Network. Hindawi Publishing Corporation, Discrete Dynamics in Nature and Society, : p. 1–11

  280. Cao H, Cao F, Wang D (2015) Quantum artificial neural networks with applications. Inf Sci 290:1–6

    MathSciNet  MATH  Google Scholar 

  281. Wiśniewska J, Sawerwain M (2015) Detecting Entanglement in Quantum Systems with Artificial Neural Network. in Intelligent Information and Database Systems. Springer International Publishing, Cham

    Google Scholar 

  282. Lv F et al (2014) The Research on Controlling the Iteration of Quantum-Inspired Evolutionary Algorithms for Artificial Neural Networks. Algorithmic Aspects in Information and Management. Springer International Publishing, Cham

    Google Scholar 

  283. Altaisky MV, Kaputkina NE, Krylov VA (2014) Quantum neural networks: Current status and prospects for development. Phys Part Nucl 45(6):1013–1032

    Google Scholar 

  284. Narayan R, Singh VP, Chakraverty S(2014) Quantum Neural Network Based Machine Translator for Hindi to English. Hindawi Publishing Corporation, Scientific World Journal, : p. 1–8

  285. Cui Q, Kuang HB, Li Y(2013) The Evaluation of Dynamic Airport Competitiveness Based on IDCQGA-BP Algorithm. Hindawi Publishing Corporation, Mathematical Problems in Engineering, : p. 1–8

  286. Hou X(2011) Research of model of Quantum Learning Vector Quantization Neural Network. in Proceedings of International Conference on Electronic & Mechanical Engineering and Information Technology. 2011

  287. Sagheer A, Metwally N(2010) Communication via quantum neural networks. in 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC).

  288. Fei L, Guobiao X(2009) Quantum BP Neural Network for speech enhancement. in 2009 Asia-Pacific Conference on Computational Intelligence and Industrial Applications (PACIIA).

  289. Lian GY et al (2010) Training algorithm for radial basis function neural network based on quantum-behaved particle swarm optimization. Int J Comput Math 87(3):629–641

    MathSciNet  MATH  Google Scholar 

  290. Yu S, Ma N(2008) Quantum Neural Network and Its Application in Vehicle Classification. in Fourth International Conference on Natural Computation. 2008

  291. Rigui Z et al(2006) Self-Organizing Quantum Neural Network. in The IEEE International Joint Conference on Neural Network Proceedings. 2006

  292. Ezhov AA, Ventura D(2000) Quantum Neural Networks, in Future Directions for Intelligent Systems and Information Sciences: The Future of Speech and Image Technologies, Brain Computers, WWW, and Bioinformatics, N. Kasabov, Editor. Physica-Verlag HD: Heidelberg. p. 213–235

  293. Cherukuri AK (2021) Quantum-inspired ensemble approach to multi-attributed and multi-agent decision-making. Appl Soft Comput 106:107283

    Google Scholar 

  294. Lu S, Braunstein SL (2014) Quantum decision tree classifier. Quantum Inf Process 13(3):757–770

    MathSciNet  MATH  Google Scholar 

  295. García J, Maureira C (2021) A KNN quantum cuckoo search algorithm applied to the multidimensional knapsack problem. Appl Soft Comput 102(1):107077

    Google Scholar 

  296. Dang Y et al (2018) Image classification based on quantum K-Nearest-Neighbor algorithm. Quantum Inf Process 17(9):239

    MATH  Google Scholar 

  297. Ruan Y et al (2017) Quantum Algorithm for K-Nearest Neighbors Classification Based on the Metric of Hamming Distance. Int J Theor Phys 56(11):3496–3507

    MathSciNet  MATH  Google Scholar 

  298. Ding S et al (2022) Multiple birth support vector machine based on dynamic quantum particle swarm optimization algorithm. Neurocomputing 480(10):146–156

    Google Scholar 

  299. Willsch D et al(2020) Support vector machines on the D-Wave quantum annealer. ArXiv, abs/1906.06283(5)

  300. Tharwat A, Hassanien AE (2019) Quantum-Behaved Particle Swarm Optimization for Parameter Optimization of Support Vector Machine. J Classif 36(3):576–598

    MathSciNet  MATH  Google Scholar 

  301. Xi M et al (2016) Cancer Feature Selection and Classification Using a Binary Quantum-Behaved Particle Swarm Optimization and Support Vector Machine. Computational and Mathematical Methods in Medicine. Hindawi Publishing Corporation, pp 1–9

  302. Yan S, Xiao-Min L, Xiao-Hui Q(2010) Parameter Optimization of Support Vector Machine Based on Combined Algorithm of QPSO and SA. in First International Conference on Pervasive Computing, Signal Processing and Applications. 2010

  303. Wang J, Liu Z, Lu P(2008) Electricity Load Forecasting Based on Adaptive Quantum-Behaved Particle Swarm Optimization and Support Vector Machines on Global Level. in 2008 International Symposium on Computational Intelligence and Design.

  304. Liu Y et al (2022) HPCP-QCWOA: High Performance Clustering Protocol based on Quantum Clone Whale Optimization Algorithm in Integrated Energy System. Future Generation Computer Systems 135(5):315–332

    MathSciNet  Google Scholar 

  305. Zhang Y et al (2022) Adaptive mutation quantum-inspired squirrel search algorithm for global optimization problems. Alexandria Eng J 61(9):7441–7476

    Google Scholar 

  306. Dohare S, Rajput RS (2022) Adaptive Gaussian Quantum based PSO and TSA optimization for parametric Optimizaiton of Toughned glass on Toughening machine. Ceramics International

  307. Zou P et al (2022) Quantum entanglement inspired hard constraint handling for operations engineering optimization with an application to airport shift planning. Expert Syst Appl 205(1):117684

    Google Scholar 

  308. Si Y et al (2022) Configuration optimization and energy management of hybrid energy system for marine using quantum computing. Energy 253(1):124131

    Google Scholar 

  309. Zhou T et al (2022) Multi-objective stochastic project scheduling with alternative execution methods: An improved quantum-behaved particle swarm optimization approach. Expert Syst Appl 203(1):117029

    Google Scholar 

  310. Gölcük İ, Ozsoydan FB (2021) Quantum particles-enhanced multiple Harris Hawks swarms for dynamic optimization problems. Expert Syst Appl 167(1):114202

    Google Scholar 

  311. Wang D et al (2020) A novel quantum grasshopper optimization algorithm for feature selection. Int J Approximate Reasoning 127(1):33–53

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Farhad Soleimanian Gharehchopogh.

Additional information

Publisher’s Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gharehchopogh, F.S. Quantum-inspired metaheuristic algorithms: comprehensive survey and classification. Artif Intell Rev 56, 5479–5543 (2023). https://doi.org/10.1007/s10462-022-10280-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10462-022-10280-8

Keywords

Navigation