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EDOA: An Elastic Deformation Optimization Algorithm

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Abstract

In recent years, a large number of meta-heuristic algorithms have been proposed to efficiently solve various complex optimization problems in reality. Most of these algorithms are based on the intelligent behavior of swarms in the natural world. In this article, we take Hooke's law of elasticity and Newton's second law of motion as the information interaction tools and innovatively propose a new meta-heuristic algorithm that is based on the laws of physics, called the elastic deformation optimization algorithm (EDOA). A new parameter adaptive adjustment mechanism is designed in the EDOA to better explore and exploit the search space. At the same time, we compare the proposed EDOA with six well-known search algorithms and conduct simulation experiments on 23 classical benchmark functions and IEEE CEC 2020 benchmark functions respectively. We have further analyzed the experimental results, used two nonparametric statistical test methods, and drawn iterative curves of the algorithms to prove the powerful comprehensive performance of the proposed EDOA.

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References

  1. Uymaz SA, Tezel G, Yel E (2015) Artificial algae algorithm (AAA) for nonlinear global optimization. Appl Soft Comput 31:153–171. https://doi.org/10.1016/j.asoc.2015.03.003

    Article  Google Scholar 

  2. Mirjalili S (2016) SCA: A Sine Cosine Algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  3. Gogna A, Tayal A (2013) Metaheuristics: review and application. J Exp Theor Artif Intell 25:503–526. https://doi.org/10.1080/0952813X.2013.782347

    Article  Google Scholar 

  4. Minhas F u AA, Arif M (2011) MOX: A novel global optimization algorithm inspired from Oviposition site selection and egg hatching inhibition in mosquitoes. Appl Soft Comput 11:4614–4625. https://doi.org/10.1016/j.asoc.2011.07.020

    Article  Google Scholar 

  5. Parouha RP, Verma P (2021) Design and applications of an advanced hybrid meta-heuristic algorithm for optimization problems. Artif Intell Rev. https://doi.org/10.1007/s10462-021-09962-6

  6. Dai Q, Yao C (2017) A hierarchical and parallel branch-and-bound ensemble selection algorithm. Appl Intell 46:45–61. https://doi.org/10.1007/s10489-016-0817-8

    Article  Google Scholar 

  7. Yu Q, Küçükyavuz S (2021) An exact cutting plane method for k -submodular function maximization. Discret Optim 42:100670. https://doi.org/10.1016/j.disopt.2021.100670

    Article  MathSciNet  MATH  Google Scholar 

  8. Lu J, Wei Q, Wang F-Y (2020) Parallel control for optimal tracking via adaptive dynamic programming. IEEE/CAA J Autom Sinica 7:1662–1674. https://doi.org/10.1109/JAS.2020.1003426

    Article  MathSciNet  Google Scholar 

  9. Simpson AR, Dandy GC, Murphy LJ (1994) Genetic Algorithms Compared to Other Techniques for Pipe Optimization. J Water Resour Plan Manag 120:423–443. https://doi.org/10.1061/(ASCE)0733-9496(1994)120:4(423)

    Article  Google Scholar 

  10. Spall JC (2003) Introduction to stochastic search and optimization: estimation, simulation, and control. Wiley-Interscience, Hoboken

    Book  MATH  Google Scholar 

  11. Boussaïd I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117. https://doi.org/10.1016/j.ins.2013.02.041

    Article  MathSciNet  MATH  Google Scholar 

  12. Parejo JA, Ruiz-Cortés A, Lozano S, Fernandez P (2012) Metaheuristic optimization frameworks: a survey and benchmarking. Soft Comput 16:527–561. https://doi.org/10.1007/s00500-011-0754-8

    Article  Google Scholar 

  13. Zhou A, Qu B-Y, Li H et al (2011) Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm Evol Comput 1:32–49. https://doi.org/10.1016/j.swevo.2011.03.001

    Article  Google Scholar 

  14. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13:533–549. https://doi.org/10.1016/0305-0548(86)90048-1

    Article  MathSciNet  MATH  Google Scholar 

  15. Osman IH, Laporte G (1996) Metaheuristics: A bibliography. Ann Oper Res 63:511–623. https://doi.org/10.1007/BF02125421

    Article  MATH  Google Scholar 

  16. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: Ray Optimization. Comput Struct 112–113:283–294. https://doi.org/10.1016/j.compstruc.2012.09.003

    Article  Google Scholar 

  17. Dokeroglu T, Sevinc E, Kucukyilmaz T, Cosar A (2019) A survey on new generation metaheuristic algorithms. Comput Ind Eng 137:106040. https://doi.org/10.1016/j.cie.2019.106040

    Article  Google Scholar 

  18. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf Optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  19. Mirjalili S, Lewis A (2016) The Whale Optimization Algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  20. Tang J, Liu G, Pan Q (2021) A Review on Representative Swarm Intelligence Algorithms for Solving Optimization Problems: Applications and Trends. IEEE/CAA J Autom Sin 8:1627–1643

    Article  MathSciNet  Google Scholar 

  21. Holland JH (1975) Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press, Oxford

    MATH  Google Scholar 

  22. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by Simulated Annealing. Science 220:671–680. https://doi.org/10.1126/science.220.4598.671

    Article  MathSciNet  MATH  Google Scholar 

  23. Farmer JD, Packard NH, Perelson AS (1986) The immune system, adaptation, and machine learning. Phys D: Nonlinear Phenom 22:187–204. https://doi.org/10.1016/0167-2789(86)90240-X

    Article  MathSciNet  Google Scholar 

  24. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks. pp 1942–1948

  25. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B Cybern 26:29–41. https://doi.org/10.1109/3477.484436

    Article  Google Scholar 

  26. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Computat 1:67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  27. Yi H, Duan Q, Liao TW (2013) Three improved hybrid metaheuristic algorithms for engineering design optimization. Appl Soft Comput 13:2433–2444. https://doi.org/10.1016/j.asoc.2012.12.004

    Article  Google Scholar 

  28. Phan HD, Ellis K, Barca JC, Dorin A (2020) A survey of dynamic parameter setting methods for nature-inspired swarm intelligence algorithms. Neural Comput Appl 32:567–588. https://doi.org/10.1007/s00521-019-04229-2

    Article  Google Scholar 

  29. Cruz DPF, Maia RD, de Castro LN (2021) A framework for the analysis and synthesis of Swarm Intelligence algorithms. J Exp Theor Artif Intell 33:659–681. https://doi.org/10.1080/0952813X.2020.1764635

    Article  Google Scholar 

  30. Khan TA, Ling SH (2020) A survey of the state-of-the-art swarm intelligence techniques and their application to an inverse design problem. J Comput Electron 19:1606–1628. https://doi.org/10.1007/s10825-020-01567-6

    Article  Google Scholar 

  31. Zhao X, Zhou Y, Xiang Y (2019) A grouping particle swarm optimizer. Appl Intell 49:2862–2873. https://doi.org/10.1007/s10489-019-01409-4

    Article  Google Scholar 

  32. Tang C, Zhou Y, Tang Z, Luo Q (2021) Teaching-learning-based pathfinder algorithm for function and engineering optimization problems. Appl Intell 51:5040–5066. https://doi.org/10.1007/s10489-020-02071-x

    Article  Google Scholar 

  33. Shadravan S, Naji HR, Bardsiri VK (2019) The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Eng Appl Artif Intell 80:20–34. https://doi.org/10.1016/j.engappai.2019.01.001

    Article  Google Scholar 

  34. Sotoudeh-Anvari A, Hafezalkotob A (2018) A bibliography of metaheuristics-review from 2009 to 2015. KES 22:83–95. https://doi.org/10.3233/KES-180376

    Article  Google Scholar 

  35. Beyer H-G, Schwefel H-P (2002) Evolution strategies-a comprehensive introduction. Nat Comput 1:3–52. https://doi.org/10.1023/A:1015059928466

    Article  MathSciNet  MATH  Google Scholar 

  36. Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial Intelligence through Simulated Evolution. Wiley-IEEE Press. https://library.isical.ac.in/cgi-bin/koha/opac-detail.pl?biblionumber=59545&shelfbrowse_itemnumber=74568

  37. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  38. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Computat 12:702–713. https://doi.org/10.1109/TEVC.2008.919004

    Article  Google Scholar 

  39. Sulaiman MH, Mustaffa Z, Saari MM, Daniyal H (2020) Barnacles Mating Optimizer: A new bio-inspired algorithm for solving engineering optimization problems. Eng Appl Artif Intell 87:103330. https://doi.org/10.1016/j.engappai.2019.103330

    Article  Google Scholar 

  40. Li X (2003) A new intelligent optimization-artificial fish swarm algorithm. Zhejiang University. https://xueshu.baidu.com/usercenter/paper/show?paperid=693ef4d66e12c6b8cb0c38492892710c&site=xueshu_se

  41. Basturk B, Karaboga D (2006) An artificial bee colony (ABC) algorithm for numeric function optimization. USA, pp 12–14

  42. Yang X (2010) A New Metaheuristic Bat-Inspired Algorithm. In: González JR, Pelta DA, Cruz C et al (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). Springer Berlin Heidelberg, Berlin, Heidelberg, pp 65–74

    Chapter  Google Scholar 

  43. Xue J, Shen B (2020) A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci Control Eng 8:22–34. https://doi.org/10.1080/21642583.2019.1708830

    Article  Google Scholar 

  44. Erol OK, Eksin I (2006) A new optimization method: Big Bang–Big Crunch. Adv Eng Softw 37:106–111. https://doi.org/10.1016/j.advengsoft.2005.04.005

    Article  Google Scholar 

  45. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: A Gravitational Search Algorithm. Inf Sci 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  46. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289. https://doi.org/10.1007/s00707-009-0270-4

    Article  MATH  Google Scholar 

  47. Anita YA (2019) AEFA: Artificial electric field algorithm for global optimization. Swarm Evol Comput 48:93–108. https://doi.org/10.1016/j.swevo.2019.03.013

    Article  Google Scholar 

  48. Geem ZW, Kim JH, Loganathan GV (2001) A New Heuristic Optimization Algorithm: Harmony Search. Simulation 76:60–68. https://doi.org/10.1177/003754970107600201

    Article  Google Scholar 

  49. He S, Wu QH, Saunders JR (2006) A Novel Group Search Optimizer Inspired by Animal Behavioural Ecology. In: 2006 IEEE International Conference on Evolutionary Computation. IEEE, Vancouver, BC, Canada, pp 1272–1278

  50. Kashan A (2009) League Championship Algorithm: A New Algorithm for Numerical Function Optimization. 2009 International Conference of Soft Computing and Pattern Recognition 43–48

  51. Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315. https://doi.org/10.1016/j.cad.2010.12.015

    Article  Google Scholar 

  52. Ghorbani N, Babaei E (2014) Exchange market algorithm. Appl Soft Comput 19:177–187

    Article  Google Scholar 

  53. Askari Q, Younas I, Saeed M (2020) Political Optimizer: A novel socio-inspired meta-heuristic for global optimization. Knowl-Based Syst 195:105709. https://doi.org/10.1016/j.knosys.2020.105709

    Article  Google Scholar 

  54. Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm Evol Comput 44:148–175. https://doi.org/10.1016/j.swevo.2018.02.013

    Article  Google Scholar 

  55. Hooke R (1678) Lectures de potentia restitutiva, or of spring explaining the power of springing bodies. https://xueshu.baidu.com/usercenter/paper/show?paperid=bf661185b2e671f08821a17dd0b824d6&site=xueshu_se&hitarticle=1

  56. Putranta H, Wiyatmo Y, Supahar XX, Dwandaru WSB (2020) A simple liquid density measuring instrument based on Hooke’s law and hydrostatic pressure. Phys Educ 55:025010. https://doi.org/10.1088/1361-6552/ab5ebd

    Article  Google Scholar 

  57. Halliday D (1993) Fundamentals of physics. John Wiley and Sons. https://xueshu.baidu.com/usercenter/paper/show?paperid=df615b86875256ffdd735a452d6891f1&site=xueshu_se

  58. Choi TJ, Ahn CW (2021) An improved LSHADE-RSP algorithm with the Cauchy perturbation: iLSHADE-RSP. Knowl-Based Syst 215:106628. https://doi.org/10.1016/j.knosys.2020.106628

    Article  Google Scholar 

  59. Leon M, Xiong N (2020) Adaptive differential evolution with a new joint parameter adaptation method. Soft Comput 24:12801–12819. https://doi.org/10.1007/s00500-020-05182-2

    Article  Google Scholar 

  60. Guanghui L, Zaiwen W, Ya-xiang Y, Qichao W (2020) Complexity analysis for optimization methods. Sci Sin-Math 50:1271. https://doi.org/10.1360/N012018-00251

    Article  MATH  Google Scholar 

  61. Mirsadeghi E, Khodayifar S (2021) Hybridizing particle swarm optimization with simulated annealing and differential evolution. Clust Comput 24:1135–1163. https://doi.org/10.1007/s10586-020-03179-y

    Article  Google Scholar 

  62. Yue C, Price K, Suganthan P, et al (2020) Problem Definitions and Evaluation Criteria for the CEC 2020 Special Session and Competition on Single Objective Bound Constrained Numerical Optimization. Nanyang Technological University

  63. Xiaobing Y, Xianrui Y, Hong C (2019) An improved gravitational search algorithm for global optimization. IFS 37:5039–5047. https://doi.org/10.3233/JIFS-182779

    Article  Google Scholar 

  64. Gao H, Fu Z, Pun C-M et al (2020) An Efficient Artificial Bee Colony Algorithm With an Improved Linkage Identification Method. IEEE Trans Cybern PP:1–15. https://doi.org/10.1109/TCYB.2020.3026716

    Article  Google Scholar 

  65. Hsu H-P, Yang S-W (2020) Optimization of Component Sequencing and Feeder Assignment for a Chip Shooter Machine Using Shuffled Frog-Leaping Algorithm. IEEE Trans Automat Sci Eng 17:56–71. https://doi.org/10.1109/TASE.2019.2916925

    Article  Google Scholar 

  66. Duan M, Yang H, Liu H, Chen J (2019) A differential evolution algorithm with dual preferred learning mutation. Appl Intell 49:605–627. https://doi.org/10.1007/s10489-018-1267-2

    Article  Google Scholar 

  67. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1:3–18. https://doi.org/10.1016/j.swevo.2011.02.002

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank many developers of the algorithms in this paper for their valuable discussions on intelligent optimization algorithms, and thank the Editor-In-Chief, Associate Editor, and reviewers for their contributions to the improvement of this paper.

Funding

This work was supported by the National Natural Science Foundation Project of China [grant number 62073330] and the Natural Science Foundation Project of Hunan Province of China [grant number 2019JJ20021].

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Correspondence to Jun Tang.

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Pan, Q., Tang, J. & Lao, S. EDOA: An Elastic Deformation Optimization Algorithm. Appl Intell 52, 17580–17599 (2022). https://doi.org/10.1007/s10489-022-03471-x

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