Levy-based antlion-inspired optimizers with orthogonal learning scheme


Antlion optimization (ALO) is an efficient metaheuristic paradigm that imitates antlion’s foraging behavior when they search for the ants. However, the conventional variant appears to encounter difficulties in avoiding local optima stagnation and slow convergence speed in dealing with complex problems. Hence, there are problems in the performance that need to be mitigated. To alleviate these shortcomings, an improved variant called Lévy orthogonal learning ALO is developed, which enhances the efficacy of the core method with orthogonal learning strategy, Levy flight, and primary core mechanisms. To measure the effectiveness of the new method, it is compared with the basic version, variant called Levy flight ALO, and variant called orthogonal learning ALO using thirty benchmark functions from IEEE CEC 2017. Also, it is compared with 15 well-known metaheuristic algorithms. Empirical results have shown the superiority of the proposed algorithm in solving the majority of test functions in terms of solution quality and convergence speed. To further validate the efficacy of the enhanced algorithm, it is applied to common practical engineering problems with constrained and unknown search spaces. The obtained results vividly demonstrate that the proposed algorithm provides satisfactory results for solving these problems.

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  1. 1.

    Qiao W, Moayedi H, Foong LK (2020) Nature-inspired hybrid techniques of IWO, DA, ES, GA, and ICA, validated through a k-fold validation process predicting monthly natural gas consumption. Energy Build 217:110023

    Article  Google Scholar 

  2. 2.

    Moayedi H, Hayati S (2018) Applicability of a CPT-based neural network solution in predicting load-settlement responses of bored pile. Int J Geomech 18(6):06018009

    Article  Google Scholar 

  3. 3.

    Moayedi H, Rezaei A (2019) An artificial neural network approach for under-reamed piles subjected to uplift forces in dry sand. Neural Comput Appl 31(2):327–336

    Article  Google Scholar 

  4. 4.

    Moayedi H, Hayati S (2018) Modelling and optimization of ultimate bearing capacity of strip footing near a slope by soft computing methods. Appl Soft Comput 66:208–219

    Article  Google Scholar 

  5. 5.

    Heidari AA, Faris H, Aljarah I, Mirjalili S (2019) An efficient hybrid multilayer perceptron neural network with grasshopper optimization. Soft Comput 23:7941–7958

    Article  Google Scholar 

  6. 6.

    Tang H et al (2020) Predicting green consumption behaviors of students using efficient firefly grey wolf-assisted K-nearest neighbor classifiers. IEEE Access 8:35546–35562

    Article  Google Scholar 

  7. 7.

    Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with Lévy flight for optimization tasks. Appl Soft Comput 60:115–134

    Article  Google Scholar 

  8. 8.

    Aljarah I, Mafarja M, Heidari AA, Faris H, Mirjalili S (2019) Clustering analysis using a novel locality-informed grey wolf-inspired clustering approach. Knowl Inf Syst J 62:507–539

    Article  Google Scholar 

  9. 9.

    Faris H et al (2019) Time-varying hierarchical chains of salps with random weight networks for feature selection. Expert Syst Appl 140:112898

    Article  Google Scholar 

  10. 10.

    Faris H et al (2019) An intelligent system for spam detection and identification of the most relevant features based on evolutionary random weight networks. Inf Fusion 48:67–83

    Article  Google Scholar 

  11. 11.

    Mafarja M et al (2018) Binary dragonfly optimization for feature selection using time-varying transfer functions. Knowl Based Syst 161:185–204

    Article  Google Scholar 

  12. 12.

    Faris H et al (2018) An efficient binary salp swarm algorithm with crossover scheme for feature selection problems. Knowl Based Syst 154:43–67

    Article  Google Scholar 

  13. 13.

    Mafarja M et al (2018) Evolutionary population dynamics and grasshopper optimization approaches for feature selection problems. Knowl Based Syst 145:25–45

    Article  Google Scholar 

  14. 14.

    Aljarah I, Mafarja M, Heidari AA, Faris H, Zhang Y, Mirjalili S (2018) Asynchronous accelerating multi-leader salp chains for feature selection. Appl Soft Comput 71:964–979

    Article  Google Scholar 

  15. 15.

    Rodríguez-Esparza E et al (2020) An efficient Harris Hawks-inspired image segmentation method. Expert Syst Appl 155:113428

    Article  Google Scholar 

  16. 16.

    Elaziz MA, Heidari AA, Fujita H, Moayedi H (2020) A competitive chain-based Harris Hawks optimizer for global optimization and multi-level image thresholding problems. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2020.106347

    Article  Google Scholar 

  17. 17.

    Zhang X, Wang D, Zhou Z, Ma Y (2019) Robust low-rank tensor recovery with rectification and alignment. IEEE Trans Pattern Anal Mach Intell. https://doi.org/10.1109/tpami.2019.2929043

    Article  Google Scholar 

  18. 18.

    Bianchi L, Dorigo M, Gambardella LM, Gutjahr WJ (2009) A survey on metaheuristics for stochastic combinatorial optimization. Nat Comput 8(2):239–287

    MathSciNet  MATH  Article  Google Scholar 

  19. 19.

    Eiben A, Schippers C (1998) On evolutionary exploration and exploitation. Fundam Inform 35:35–50

    MATH  Article  Google Scholar 

  20. 20.

    Yang X-S, Deb S, Fong S (2013) Metaheuristic algorithms: optimal balance of intensification and diversification. Appl Math Inf Sci 8:977–983

    Article  Google Scholar 

  21. 21.

    Colorni A, Dorigo M, Maniezzo V (1991) Distributed optimization by ant colonies. In: Proceedings of the first European conference on artificial life

  22. 22.

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

    Article  Google Scholar 

  23. 23.

    Cai Z et al (2019) Evolving an optimal kernel extreme learning machine by using an enhanced grey wolf optimization strategy. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2019.07.031

    Article  Google Scholar 

  24. 24.

    Zhao X et al (2019) Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients. Comput Biol Chem 78:481–490

    Article  Google Scholar 

  25. 25.

    Wang M et al (2017) Grey wolf optimization evolving kernel extreme learning machine: application to bankruptcy prediction. Eng Appl Artif Intell 63:54–68

    Article  Google Scholar 

  26. 26.

    Heidari AA, Ali Abbaspour R, Chen H (2019) Efficient boosted grey wolf optimizers for global search and kernel extreme learning machine training. Appl Soft Comput 81:105521

    Article  Google Scholar 

  27. 27.

    Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Fut Gener Comput Syst 97:849–872

    Article  Google Scholar 

  28. 28.

    Chen H, Jiao S, Wang M, Heidari AA, Zhao X (2019) Parameters identification of photovoltaic cells and modules using diversification-enriched Harris hawks optimization with chaotic drifts. J Clean Prod 244:118778

    Article  Google Scholar 

  29. 29.

    Wang G-G (2018) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memet Comput 10(2):151–164

    Article  Google Scholar 

  30. 30.

    Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Fut Gener Comput Syst. https://doi.org/10.1016/j.future.2020.03.055

    Article  Google Scholar 

  31. 31.

    Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  32. 32.

    Wang M, Chen H (2019) Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2019.105946

    Article  Google Scholar 

  33. 33.

    Luo J, Chen H, Heidari AA, Xu Y, Zhang Q, Li C (2019) Multi-strategy boosted mutative whale-inspired optimization approaches. Appl Math Model 73:109–123

    MathSciNet  MATH  Article  Google Scholar 

  34. 34.

    Chen H, Yang C, Heidari AA, Zhao X (2019) An efficient double adaptive random spare reinforced whale optimization algorithm. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2019.113018

    Article  Google Scholar 

  35. 35.

    Chen H, Xu Y, Wang M, Zhao X (2019) A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model 71:45–59

    MathSciNet  MATH  Article  Google Scholar 

  36. 36.

    Zhang X et al (2020) Gaussian mutational chaotic fruit fly-built optimization and feature selection. Expert Syst Appl 141:112976

    Article  Google Scholar 

  37. 37.

    Zhang Q et al (2019) Chaos-induced and mutation-driven schemes boosting salp chains-inspired optimizers. IEEE Access 7:31243–31261

    Article  Google Scholar 

  38. 38.

    Yu H, Zhao N, Wang P, Chen H, Li C (2020) Chaos-enhanced synchronized bat optimizer. Appl Math Model 77:1201–1215

    MATH  Article  Google Scholar 

  39. 39.

    Xu Y, Chen H, Luo J, Zhang Q, Jiao S, Zhang X (2019) Enhanced Moth-flame optimizer with mutation strategy for global optimization. Inf Sci 492:181–203

    MathSciNet  Article  Google Scholar 

  40. 40.

    Xu Y et al (2019) An efficient chaotic mutative moth-flame-inspired optimizer for global optimization tasks. Expert Syst Appl 129:135–155

    Article  Google Scholar 

  41. 41.

    Deng W, Xu J, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292

    Article  Google Scholar 

  42. 42.

    Deng W, Xu J, Song Y, Zhao H (2019) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292

    Article  Google Scholar 

  43. 43.

    Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21(15):4387–4398

    Article  Google Scholar 

  44. 44.

    Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302

    Article  Google Scholar 

  45. 45.

    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82

    Article  Google Scholar 

  46. 46.

    Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98

    Article  Google Scholar 

  47. 47.

    Ali ES, Abd Elazim SM, Abdelaziz AY (2017) Ant lion optimization algorithm for optimal location and sizing of renewable distributed generations. Renew Energy 101:1311–1324

    Article  Google Scholar 

  48. 48.

    Dubey HM, Pandit M, Panigrahi BK (2016) Ant lion optimization for short-term wind integrated hydrothermal power generation scheduling. Int J Electr Power Energy Syst 83:158–174

    Article  Google Scholar 

  49. 49.

    Pradhan R, Majhi SK, Pradhan JK, Pati BB (2017) Performance evaluation of PID controller for an automobile cruise control system using ant lion optimizer. Eng J Thail 21(5):347–361

    Article  Google Scholar 

  50. 50.

    Pradhan R, Majhi SK, Pati BB (2018) Design of PID controller for automatic voltage regulator system using ant lion optimizer. World J Eng 15(3):373–387

    Article  Google Scholar 

  51. 51.

    Yogarajan G, Revathi T (2018) Improved cluster based data gathering using ant lion optimization in wireless sensor networks. Wirel Pers Commun 98(3):2711–2731

    Article  Google Scholar 

  52. 52.

    Nair SS, Rana KPS, Kumar V, Chawla A (2017) Efficient modeling of linear discrete filters using ant lion optimizer. Circuits Syst Signal Process 36(4):1535–1568

    Article  Google Scholar 

  53. 53.

    Van TP, Snášel V, Nguyen TT (2020) Antlion optimization algorithm for optimal non-smooth economic load dispatch. Int J Electr Comput Eng 10(2):1187–1199

    Google Scholar 

  54. 54.

    Mishra M, Barman SK, Maity D, Maiti DK (2019) Ant lion optimisation algorithm for structural damage detection using vibration data. J Civ Struct Health Monit 9(1):117–136

    Article  Google Scholar 

  55. 55.

    Emary E, Zawbaa HM, Hassanien AE (2016) Binary ant lion approaches for feature selection. Neurocomputing 213:54–65

    Article  Google Scholar 

  56. 56.

    Dinkar SK, Deep K (2019) Accelerated opposition-based antlion optimizer with application to order reduction of linear time-invariant systems. Arab J Sci Eng 44(3):2213–2241

    Article  Google Scholar 

  57. 57.

    Wu Z, Yu D, Kang X (2017) Parameter identification of photovoltaic cell model based on improved ant lion optimizer. Energy Convers Manag 151:107–115

    Article  Google Scholar 

  58. 58.

    Majhi SK, Biswal S (2018) Optimal cluster analysis using hybrid K-means and ant lion optimizer. Karbala Int J Mod Sci 4(4):347–360

    Article  Google Scholar 

  59. 59.

    Roy K, Mandal KK, Mandal AC (2019) Ant-lion optimizer algorithm and recurrent neural network for energy management of micro grid connected system. Energy 167:402–416

    Article  Google Scholar 

  60. 60.

    Wang M, Gao L, Huang X, Jiang Y, Gao X (2019) A texture classification approach based on the integrated optimization for parameters and features of gabor filter via hybrid ant lion optimizer. Appl Sci Basel 9(11), Art. no. Unsp 2173

  61. 61.

    Toz M (2019) An improved form of the ant lion optimization algorithm for image clustering problems. Turk J Electr Eng Comput Sci 27(2):1445–1460

    Article  Google Scholar 

  62. 62.

    Zhang Z, Jiang F, Li B, Zhang B (2018) A novel time difference of arrival localization algorithm using a neural network ensemble model. Int J Distrib Sens Netw 14(11), Art. no. 1550147718815798

  63. 63.

    Bai W, Eke I, Lee KY (2017) An improved artificial bee colony optimization algorithm based on orthogonal learning for optimal power flow problem. Control Eng Pract 61:163–172

    Article  Google Scholar 

  64. 64.

    Wang Z, Zhan Z, Du K, Yu Z, Zhang J (2016) Orthogonal learning particle swarm optimization with variable relocation for dynamic optimization. In: 2016 IEEE congress on evolutionary computation (CEC), pp 594–600

  65. 65.

    Chechkin A, Metzler R, Klafter J, Gonchar V (2008) Introduction to the theory of Lévy flights. In Anomalous transport: Foundations and Applications, Wiley-VCH

  66. 66.

    Coelho LDS, Bora TC, Klein CE (2014) A genetic programming approach based on Lévy flight applied to nonlinear identification of a poppet valve. Appl Math Model 38(5):1729–1736

    MathSciNet  MATH  Article  Google Scholar 

  67. 67.

    Jensi R, Jiji GW (2016) An enhanced particle swarm optimization with levy flight for global optimization. Appl Soft Comput 43:248–261

    Article  Google Scholar 

  68. 68.

    Dinkar SK, Deep K (2018) An efficient opposition based Lévy flight antlion optimizer for optimization problems. J Comput Sci 29:119–141

    Article  Google Scholar 

  69. 69.

    Wang M, Wu C, Wang L, Xiang D, Huang X (2019) A feature selection approach for hyperspectral image based on modified ant lion optimizer. Knowl Based Syst 168:39–48

    Article  Google Scholar 

  70. 70.

    Qin Q, Cheng S, Zhang Q, Wei Y, Shi Y (2015) Multiple strategies based orthogonal design particle swarm optimizer for numerical optimization. Comput Oper Res 60:91–110

    MathSciNet  MATH  Article  Google Scholar 

  71. 71.

    Chen H, Heidari AA, Zhao X, Zhang L, Chen H (2020) Advanced orthogonal learning-driven multi-swarm sine cosine optimization: framework and case studies. Expert Syst Appl 144:113113

    Article  Google Scholar 

  72. 72.

    LaTorre A, Pena JM (2017) A comparison of three large-scale global optimizers on the CEC 2017 single objective real parameter numerical optimization benchmark. In: Proceedings of the 2017 IEEE congress on evolutionary computation (CEC 2017), pp 1063–1070

  73. 73.

    García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064

    Article  Google Scholar 

  74. 74.

    Chen W et al (2013) Particle swarm optimization with an aging leader and challengers. IEEE Trans Evol Comput 17(2):241–258

    Article  Google Scholar 

  75. 75.

    Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Article  Google Scholar 

  76. 76.

    Chen X, Tianfield H, Mei C, Du W, Liu G (2017) Biogeography-based learning particle swarm optimization. Soft Comput 21(24):7519–7541

    Article  Google Scholar 

  77. 77.

    Lyu S, Li Z, Huang Y, Wang J, Hu J (2019) Improved self-adaptive bat algorithm with step-control and mutation mechanisms. J Comput Sci 30:65–78

    MathSciNet  Article  Google Scholar 

  78. 78.

    Yong J, He F, Li H, Zhou W (2018) A novel bat algorithm based on collaborative and dynamic learning of opposite population. In: 2018 IEEE 22nd international conference on computer supported cooperative work in design (CSCWD), pp 541–546

  79. 79.

    Adarsh BR, Raghunathan T, Jayabarathi T, Yang X-S (2016) Economic dispatch using chaotic bat algorithm. Energy 96:666–675

    Article  Google Scholar 

  80. 80.

    Liang H, Liu Y, Shen Y, Li F, Man Y (2018) A hybrid bat algorithm for economic dispatch with random wind power. IEEE Trans Power Syst 33(5):5052–5061

    Article  Google Scholar 

  81. 81.

    Tubishat M, Abushariah MAM, Idris N, Aljarah I (2019) Improved whale optimization algorithm for feature selection in Arabic sentiment analysis. Appl Intell 49(5):1688–1707

    Article  Google Scholar 

  82. 82.

    Ling Y, Zhou Y, Luo Q (2017) Lévy flight trajectory-based whale optimization algorithm for global optimization. IEEE Access 5:6168–6186

    Article  Google Scholar 

  83. 83.

    Price K, Storn R, Lampinen J (2005) Differential evolution—a practical approach to global optimization. Springer, Berlin, Heidelberg

    Google Scholar 

  84. 84.

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

    Article  Google Scholar 

  85. 85.

    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the ICNN’95—international conference on neural networks, vol 4, pp 1942–1948

  86. 86.

    Yang X-S, Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29:464-483

    Article  Google Scholar 

  87. 87.

    Weibiao Q, Bingfan L, Zhangyang K (2019) Differential scanning calorimetry and electrochemical tests for the analysis of delamination of 3PE coatings. Int J Electrochem Sci 14:7389–7400

    Article  Google Scholar 

  88. 88.

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

    MATH  Article  Google Scholar 

  89. 89.

    Coello Coello CA (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civ Eng Environ Syst 17(4):319–346

    Article  Google Scholar 

  90. 90.

    Coello Coello CA (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11):1245–1287

    MathSciNet  MATH  Article  Google Scholar 

  91. 91.

    Coello Coello CA, Mezura Montes E (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Article  Google Scholar 

  92. 92.

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

    MATH  Article  Google Scholar 

  93. 93.

    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 

  94. 94.

    Ragsdell KM, Phillips DT (1976) Optimal design of a class of welded structures using geometric programming. Trans ASME J Manuf Sci Eng 98(3):1021–1025

    Article  Google Scholar 

  95. 95.

    Siddall JN (1972) Analytical decision-making in engineering design. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  96. 96.

    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 

  97. 97.

    Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Article  Google Scholar 

  98. 98.

    Arora JS (2004) 8—Numerical methods for unconstrained optimum design. In: Arora JS (ed) Introduction to optimum design, 2nd edn. Academic Press, San Diego, pp 277–304

    Google Scholar 

  99. 99.

    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

    MathSciNet  MATH  Article  Google Scholar 

  100. 100.

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

    Article  Google Scholar 

  101. 101.

    Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    MathSciNet  MATH  Google Scholar 

  102. 102.

    Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7):340–349

    Article  Google Scholar 

  103. 103.

    Huang F, Wang L, Qie HE (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356

    MathSciNet  MATH  Google Scholar 

  104. 104.

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

    MATH  Article  Google Scholar 

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This research was financially supported by the Natural Science Foundation of China (61702376), the Zhejiang Provincial Natural Science Foundation of China (LSZ19F020001), and was partially supported by Science and Technology Plan Project of Wenzhou (2018ZG012), Wenzhou Major Scientific and Technological Innovation Project (ZY2019019).

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Ba, A.F., Huang, H., Wang, M. et al. Levy-based antlion-inspired optimizers with orthogonal learning scheme. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-01042-7

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  • Antlion optimization algorithm
  • Levy flight
  • Global optimization
  • Engineering design