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An information entropy-based grey wolf optimizer

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Abstract

In this study, an entropy-based grey wolf optimizer (IEGWO) algorithm is proposed for solving global optimization problems. This improvement is proposed to alleviate the lack of population diversity, the imbalance between exploitation and exploration, and the premature convergence of grey wolf optimizer algorithm and consists of three aspects: Firstly, we proposed an information entropy-based population generation strategy to optimize the distribution of initial grey wolf pack. Secondly, a modified dynamic position update equation based on information entropy is introduced to maintain the population diversity in the process of iteration, thus avoiding premature convergence. Thirdly, a nonlinear convergence strategy is proposed to balance the exploration and exploitation. The performance of the proposed IEGWO algorithm is assessed on the CEC2014 and CEC2017 test suites and compared with other meta-heuristic algorithms. Furthermore, two engineering design problems and one real-world problem are also solved using the IEGWO algorithm. The experimental and statistical results indicate that the IEGWO algorithm has better solution accuracy and robustness than the compared algorithms in solving global optimization problems.

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Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

References

  • Adhikary J, Acharyya S (2022) Randomized balanced grey wolf optimizer (RBGWO) for solving real life optimization problems. Appl Soft Comput 117:108429

    Google Scholar 

  • Arjenaki HG, Nadimi-Shahraki MH, Nourafza N (2015) A low cost model for diagnosing coronary artery disease based on effective features. Int J Electron Commun Comput Eng 6(1):93–97

    Google Scholar 

  • Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23(3):715–734

    Google Scholar 

  • Awad NH, Ali MZ, Liang JJ, Qu BY, Suganthan PN (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. Technical Report

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

    Google Scholar 

  • Das SC, Manna AK, Rahman MS, Shaikh AA, Bhunia AK (2021) An inventory model for non-instantaneous deteriorating items with preservation technology and multiple credit periods-based trade credit financing via particle swarm optimization. Soft Comput 25(7):5365–5384

    MATH  Google Scholar 

  • Duarte D, de Moura Oliveira PB et al (2020) Entropy based grey wolf optimizer. Springer International Publishing, Cham

    Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science

  • Feng H, Grifoll M, Yang Z, Zheng P (2022) Collision risk assessment for ships’routeing waters: an information entropy approach with automatic identification system (AIS) data. Ocean Coast Manag 224:106184

    Google Scholar 

  • Gupta S, Deep K (2019) An opposition-based chaotic grey wolf optimizer for global optimisation tasks. J Exp Theor Artif Intell 31(5):751–779

    Google Scholar 

  • Gupta S, Deep K (2020) A memory-based grey wolf optimizer for global optimization tasks. Appl Soft Comput 93:106367

    Google Scholar 

  • Hadavandi E, Mostafay S, Soltani P (2018) A grey wolf optimizer-based neural network coupled with response surface method for modeling the strength of siro-spun yarn in spinning mills. Appl Soft Comput 72:1–13

    Google Scholar 

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

    Google Scholar 

  • Hu X, Zhang S, Li M, Deng JD (2021) Multimodal particle swarm optimization for feature selection. Appl Soft Comput 113:107887

    Google Scholar 

  • Kalemci EN, Kizler SB, Dede T, Angn Z (2020) Design of reinforced concrete cantilever retaining wall using grey wolf optimization algorithm. Structures 23:245–253

    Google Scholar 

  • Karasu S, Saraç Z (2020) Classification of power quality disturbances by 2D-Riesz Transform, multi-objective grey wolf optimizer and machine learning methods. Digit. Signal Process 101:102711

    Google Scholar 

  • Kumar N, Manna AK, Shaikh AA, Bhunia AK (2021) Application of hybrid binary tournament-based quantum-behaved particle swarm optimization on an imperfect production inventory problem. Soft Comput 25(16):11245–11267

    MATH  Google Scholar 

  • Li S, Chen H, Wang M, Heidari AA, Mirjalili S (2020) Slime mould algorithm: a new method for stochastic optimization. Future Gener Comput Syst 111:300–323

    Google Scholar 

  • Liang J, Qu B, Suganthan, P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. In: Computational intelligence laboratory, Zhengzhou

  • Long W, Liang X, Cai S, Jiao J, Zhang W (2017) A modified augmented lagrangian with improved grey wolf optimization to constrained optimization problems. Neural Comput Appl 28(1):421–438

    Google Scholar 

  • Long W, Jiao J, Liang X, Tang M (2018a) Inspired grey wolf optimizer for solving large-scale function optimization problems. Appl Math Model 60:112–126

    MathSciNet  MATH  Google Scholar 

  • Long W, Jiao J, Liang X, Tang M (2018b) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Eng Appl Artif Intell 68:63–80

    Google Scholar 

  • Luo K, Zhao Q (2019) A binary grey wolf optimizer for the multidimensional knapsack problem. Appl Soft Comput 83:105645

    Google Scholar 

  • Manna AK, Bhunia AK (2022) Investigation of green production inventory problem with selling price and green level sensitive interval-valued demand via different metaheuristic algorithms. Soft Comput. https://doi.org/10.1007/s00500-022-06856-9

    Article  Google Scholar 

  • Manna AK, Akhtar M, Shaikh AA, Bhunia AK (2021) Optimization of a deteriorated two-warehouse inventory problem with all-unit discount and shortages via tournament differential evolution. Appl Soft Comput 107:107388

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Mohakud R, Dash R (2022) Skin cancer image segmentation utilizing a novel EN-GWO based hyper-parameter optimized FCEDN. J King Saud Univ Comput Inf Sci. https://doi.org/10.1016/j.jksuci.2021.12.018

    Article  Google Scholar 

  • Naserbegi A, Aghaie M (2021) Exergy optimization of nuclear-solar dual proposed power plant based on GWO algorithm. Prog Nucl Energy 140:103925

    Google Scholar 

  • Qu C, Gai W, Zhong M, Zhang J (2020) A novel reinforcement learning based grey wolf optimizer algorithm for unmanned aerial vehicles (UAVs) path planning. Appl Soft Comput 89:106099

    Google Scholar 

  • Rodríguez L, Castillo O, Soria J, Melin P, Valdez F, Gonzalez CI, Martinez GE, Soto J (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328

    Google Scholar 

  • Samuel OD, Okwu MO, Oyejide OJ, Taghinezhad E, Afzal A, Kaveh M (2020) Optimizing biodiesel production from abundant waste oils through empirical method and grey wolf optimizer. Fuel 281:118701

    Google Scholar 

  • Saxena A, Kumar R, Mirjalili S (2020) A harmonic estimator design with evolutionary operators equipped grey wolf optimizer. Expert Syst Appl 145:113125

    Google Scholar 

  • Shannon CE (1948) The mathematical theory of communication. Bell Syst Tech J 27(3):373–423

    MathSciNet  Google Scholar 

  • Suktanarak S, Teerachaichayut S (2017) Non-destructive quality assessment of hens’ eggs using hyperspectral images. J Food Eng 215:97–103

    Google Scholar 

  • Sundaramurthy S, Jayavel P (2020) A hybrid grey wolf optimization and particle swarm optimization with C4.5 approach for prediction of rheumatoid arthritis. Appl Soft Comput 94:106500

    Google Scholar 

  • Tawhid MA, Ali AF (2017) A hybrid grey wolf optimizer and genetic algorithm for minimizing potential energy function. Memet Comput 9(4):347–359

    Google Scholar 

  • Venkataraman NL, Kumar R, Shakeel PM (2020) Ant lion optimized bufferless routing in the design of low power application specific network on chip. Circuits Syst Signal Process 39(2):961–976

    Google Scholar 

  • Wang L, Zheng X, Wang S (2013) A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl-Based Syst 48:17–23

    Google Scholar 

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

    Google Scholar 

  • Xu J, Riccioli C, Sun D (2016) Development of an alternative technique for rapid and accurate determination of fish caloric density based on hyperspectral imaging. J Food Eng 190:185–194

    Google Scholar 

  • Xue J, Shen B (2020) A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci Control Eng 8(1):22–34

    Google Scholar 

  • Yao K, Sun J, Chen C, Xu M, Zhou X, Cao Y, Tian Y (2022) Non-destructive detection of egg qualities based on hyperspectral imaging. J Food Eng 325:111024

    Google Scholar 

  • 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 

  • Zareie A, Sheikhahmadi A, Jalili M (2020) Identification of influential users in social network using gray wolf optimization algorithm. Expert Syst Appl 142:112971

    Google Scholar 

  • Zhang S, Zhou Y, Li Z, Pan W (2016) Grey wolf optimizer for unmanned combat aerial vehicle path planning. Adv Eng Softw 99:121–136

    Google Scholar 

Download references

Acknowledgements

This work is partially supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX20_3033). Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD-2018-87). Six Talent Peaks Project in Jiangsu Province (ZBZZ-019).

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Authors and Affiliations

  1. School of Electrical and Information Engineering of Jiangsu University, Zhenjiang, 212000, China

    Kunshan Yao, Jun Sun, Yan Cao, Min Xu, Xin Zhou, Ningqiu Tang & Yan Tian

  2. School of Economics and Management of Jiangsu University of Science and Technology, Zhenjiang, 212000, China

    Chen Chen

Authors
  1. Kunshan Yao
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  2. Jun Sun
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  3. Chen Chen
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  4. Yan Cao
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  5. Min Xu
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  6. Xin Zhou
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  7. Ningqiu Tang
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  8. Yan Tian
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Correspondence to Jun Sun.

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Yao, K., Sun, J., Chen, C. et al. An information entropy-based grey wolf optimizer. Soft Comput 27, 4669–4684 (2023). https://doi.org/10.1007/s00500-022-07593-9

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