Skip to main content
Log in

A multi-strategy enhanced salp swarm algorithm for global optimization

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

Abstract

As a typical nature-inspired swarm intelligence algorithm, because of the simple framework and good optimization performance, salp swarm algorithm (SSA) has been extensively applied to a lot of practical problems. Nevertheless, when facing a number of complicated optimization problems, particularly the high dimensionality and multi-dimensional problems, SSA will come to stagnation and decrease the optimal performance. To tackle this problem, this paper presents an enhanced SSA (ESSA) in which several strategies, including orthogonal learning, quadratic interpolation, and generalized oppositional learning are embedded to boost the global exploration and local exploitation performance of SSA. Orthogonal learning can help the worse salp break away from local optima, while quadratic interpolation is utilized to improve the accuracy of the global optimal through local search near the globally optimal solution. Also, generalized oppositional learning is used to improve the population quality through the initialization step and generation jumping. These strategies work together to assist SSA in promoting convergence performance. At the last CEC2017 benchmark suite and CEC2011, a real-world optimization benchmark is employed to estimate the property of ESSA in dealing with the high dimensionality and multi-dimensional problems. Three constrained engineering optimization problems are also used to assess the capability of ESSA in tackling practical engineering application problems. The experimental results and responding analysis make clear that the presented algorithm significantly outperforms the original SSA and other state-of-the-art methods.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Chen H et al (2020) Efficient multi-population outpost fruit fly-driven optimizers: framework and advances in support vector machines. Expert Syst Appl 142:112999

    Google Scholar 

  2. Chen H et al (2019) An efficient double adaptive random spare reinforced whale optimization algorithm. Expert systems with applications. Elsevier, Amsterdam

    Google Scholar 

  3. Chen H et al (2019) An enhanced bacterial foraging optimization and its application for training kernel extreme learning machine. Appl Soft Comput 86:105884

    Google Scholar 

  4. Heidari AA et al (2019) Harris Hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872

    Google Scholar 

  5. Yu H et al (2020) Chaos-enhanced synchronized bat optimizer. Appl Math Model 77:1201–1215

    Google Scholar 

  6. Li S et al (2020) Slime mould algorithm: a new method for stochastic optimization. Future Gener Comput Syst 111:300–323

    Google Scholar 

  7. Chen H et al (2020) Multi-population differential evolution-assisted Harris Hawks optimization: framework and case studies. Future Gener Comput Syst 111:175–198

    Google Scholar 

  8. Zhang Y et al (2020) Boosted binary Harris Hawks optimizer and feature selection. Eng Comput. https://doi.org/10.1007/s00366-020-01028-5

    Article  Google Scholar 

  9. Wang M et al (2020) Exploratory differential ant lion-based optimization. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2020.113548

    Article  Google Scholar 

  10. Ba AF et al (2020) Levy-based ant lion-inspired optimizers with orthogonal learning scheme. Eng Comput. https://doi.org/10.1007/s00366-020-01042-7

    Article  Google Scholar 

  11. Luo J et al (2018) An improved grasshopper optimization algorithm with application to financial stress prediction. Appl Math Model 64:654–668

    MathSciNet  MATH  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. Luo J et al (2019) Multi-strategy boosted mutative whale-inspired optimization approaches. Appl Math Model 73:109–123

    MathSciNet  MATH  Google Scholar 

  14. Chen H, Wang M, Zhao X (2020) A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems. Appl Math Comput. https://doi.org/10.1016/j.amc.2019.124872

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  16. Mirjalili S et al (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Google Scholar 

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

    Google Scholar 

  18. Faris H et al (2020) Time-varying hierarchical chains of salps with random weight networks for feature selection. Expert Syst Appl 140:112898

    Google Scholar 

  19. Gupta S et al (2019) Harmonized salp chain-built optimization. Engineering with computers. Springer, New York, pp 1–31

    Google Scholar 

  20. Faris H et al (2020) Salp swarm algorithm: theory, literature review, and application in extreme learning machines. In: Mirjalili S, Song Dong J, Lewis A (eds) Nature-inspired optimizers: theories, literature reviews and applications. Springer International Publishing, Cham, pp 185–199

    Google Scholar 

  21. Mafarja M et al (2020) Efficient hybrid nature-inspired binary optimizers for feature selection. Cogn Comput 12(1):150–175

    Google Scholar 

  22. Taradeh M et al (2019) An evolutionary gravitational search-based feature selection. Inf Sci 497:219–239

    Google Scholar 

  23. Namous F et al (2020) Evolutionary and swarm-based feature selection for imbalanced data classification. Evolutionary machine learning techniques. Springer, Singapore, pp 231–250

    Google Scholar 

  24. 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

    Google Scholar 

  25. 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

    Google Scholar 

  26. 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

    Google Scholar 

  27. 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

    Google Scholar 

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

    Google Scholar 

  29. 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 

  30. Khamees M, Albakry A, Shaker K (2018) A new approach for features selection based on binary slap swarm algorithm. J Theor Appl Inf Technol 96:1896–1906

    Google Scholar 

  31. Aljarah I et al (2018) Asynchronous accelerating multi-leader salp chains for feature selection. Appl Soft Comput 71:964–979

    Google Scholar 

  32. El-Fergany AA (2018) Extracting optimal parameters of PEM fuel cells using salp swarm optimizer. Renew Energy 119:641–648

    Google Scholar 

  33. Hussien AG, Hassanien AE, Houssein EH (2018) Swarming behaviour of salps algorithm for predicting chemical compound activities. In: 2017 IEEE 8th International conference on intelligent computing and information systems, ICICIS 2017. 2018

  34. Zhang J, Wang Z, Luo X (2018) Parameter estimation for soil water retention curve using the salp swarm algorithm. Water (Switzerland) 10(6):815–825

    Google Scholar 

  35. Zhao H, Huang G, Yan N (2018) Forecasting energy-related CO2 emissions employing a novel SSA-LSSVM model: considering structural factors in China. Energies 11(4):781–801

    Google Scholar 

  36. Asaithambi S, Rajappa M (2018) Swarm intelligence-based approach for optimal design of CMOS differential amplifier and comparator circuit using a hybrid salp swarm algorithm. Rev Sci Instrum 89(5):54702–54710

    Google Scholar 

  37. El-Fergany AA, Hasanien HM (2019) Salp swarm optimizer to solve optimal power flow comprising voltage stability analysis. Neural Comput Appl 1–17

  38. Ateya AA et al (2019) Chaotic salp swarm algorithm for SDN multi-controller networks. Eng Sci Technol Int J 22(4):1001–1012

    Google Scholar 

  39. Ismael SM et al (2018) Practical considerations for optimal conductor reinforcement and hosting capacity enhancement in radial distribution systems. IEEE Access 6:27268–27277

    Google Scholar 

  40. Tolba M et al (2018) A novel robust methodology based salp swarm algorithm for allocation and capacity of renewable distributed generators on distribution grids. Energies 11(10):2556–2589

    MathSciNet  Google Scholar 

  41. Wang M et al (2018) Voice conversion based on quantum particle swarm optimization of generalized regression neural network. Chin J Liq Cryst Disp 33(2):165–173

    Google Scholar 

  42. Yang B et al (2019) Novel bio-inspired memetic salp swarm algorithm and application to MPPT for PV systems considering partial shading condition. J Clean Prod 215:1203–1222

    Google Scholar 

  43. Abbassi R et al (2019) An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers Manag 179:362–372

    Google Scholar 

  44. Abbassi A et al (2020) Parameters identification of photovoltaic cell models using enhanced exploratory salp chains-based approach. Energy 198:117333

    Google Scholar 

  45. Gupta S et al (2019) Harmonized salp chain-built optimization. Eng Comput. https://doi.org/10.1007/s00366-019-00871-5

    Article  Google Scholar 

  46. Ibrahim RA et al (2018) Improved salp swarm algorithm based on particle swarm optimization for feature selection. J Ambient Intell Humaniz Comput 10:3155–3169

    Google Scholar 

  47. Rizk-Allah RM et al (2018) A new binary salp swarm algorithm: development and application for optimization tasks. Neural Comput Appl 31:1–23

    Google Scholar 

  48. Andersen V, Nival P (1986) A model of the population dynamics of salps in coastal waters of the Ligurian Sea. J Plankton Res 8:1091–1110

    Google Scholar 

  49. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: Proceedings—International conference on computational intelligence for modelling, control and automation, CIMCA 2005 and international conference on intelligent agents, web technologies and internet. 2005. Vienna, Austria: IEEE

  50. Rahnamayan RS, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79

    Google Scholar 

  51. Zhangjun W et al (2008) Opposition based comprehensive learning particle swarm optimization. In: 2008 3rd International conference on intelligent system and knowledge engineering. 2008

  52. El-Abd M (2012) Generalized opposition-based artificial bee colony algorithm. In: 2012 IEEE congress on evolutionary computation. 2012

  53. Zhan ZH et al (2011) Orthogonal learning particle swarm optimization. IEEE Trans Evol Comput 15(6):832–847

    Google Scholar 

  54. Bai W, Eke I, Lee KY (2015) Improved artificial bee colony based on orthogonal learning for optimal power flow. In: 2015 18th international conference on intelligent system application to power systems (ISAP). 2015

  55. Lei YX et al (2017) Improved differential evolution with a modified orthogonal learning strategy. IEEE Access 5:9699–9716

    Google Scholar 

  56. Xiong G, Shi D (2018) Orthogonal learning competitive swarm optimizer for economic dispatch problems. Appl Soft Comput J 66:134–148

    Google Scholar 

  57. Zhang H et al (2020) Orthogonal Nelder–Mead moth flame method for parameters identification of photovoltaic modules. Energy Convers Manag 211:112764

    Google Scholar 

  58. Zhang H et al (2020) Advanced orthogonal moth flame optimization with Broyden–Fletcher–Goldfarb–Shanno algorithm: framework and real-world problems. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2020.113617

    Article  Google Scholar 

  59. Yang Y et al (2020) Orthogonal learning harmonizing mutation-based fruit fly-inspired optimizers. Appl Math Model 86:368–383

    MathSciNet  MATH  Google Scholar 

  60. Zhu W et al (2020) Evaluation of sino foreign cooperative education project using orthogonal sine cosine optimized kernel extreme learning machine. IEEE Access 8:61107–61123

    Google Scholar 

  61. Chen H et al (2020) Advanced orthogonal learning-driven multi-swarm sine cosine optimization: framework and case studies. Expert Syst Appl 144:113113

    Google Scholar 

  62. Jiao S et al (2020) Orthogonally adapted Harris Hawks optimization for parameter estimation of photovoltaic models. Energy. https://doi.org/10.1016/j.energy.2020.117804

    Article  Google Scholar 

  63. Xu Z et al (2020) Orthogonally-designed adapted grasshopper optimization: a comprehensive analysis. Expert Syst Appl 150:113282

    Google Scholar 

  64. Li X, Wang J, Yin M (2014) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247

    Google Scholar 

  65. Zeng SY, Kang LS, Ding LX (2004) An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints. Evol Comput 12(1):77–98

    Google Scholar 

  66. Tao H, Jian H, Jun Z (2008) An orthogonal local search genetic algorithm for the design and optimization of power electronic circuits. In: 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence). 2008

  67. Deep K, Das KN (2008) Quadratic approximation based hybrid genetic algorithm for function optimization. Appl Math Comput 203(1):86–98

    MATH  Google Scholar 

  68. Li H, Jiao Y-C, Zhang L (2011) Hybrid differential evolution with a simplified quadratic approximation for constrained optimization problems. Eng Optim 43(2):115–134

    MathSciNet  Google Scholar 

  69. Derrac J et al (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(1):3–18

    Google Scholar 

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

    Google Scholar 

  71. Xu C et al (2016) Biogeography-based learning particle swarm optimization. Soft Comput 21(24):1–23

    Google Scholar 

  72. Liang JJ et al (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Google Scholar 

  73. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Google Scholar 

  74. Brest J et al (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657

    Google Scholar 

  75. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Google Scholar 

  76. Chen X et al (2016) Parameters identification of solar cell models using generalized oppositional teaching learning based optimization. Energy 99:170–180

    Google Scholar 

  77. Sathish Kumar K et al (2015) An efficient invasive weed optimization algorithm for distribution feeder reconfiguration and loss minimization. Springer, New Delhi

    Google Scholar 

  78. Sun Y et al (2018) A modified whale optimization algorithm for large-scale global optimization problems. Expert Syst Appl 114:563–577

    Google Scholar 

  79. Yousri D, Allam D, Eteiba MB (2019) Chaotic whale optimizer variants for parameters estimation of the chaotic behavior in Permanent Magnet Synchronous Motor. Appl Soft Comput 74:479–503

    Google Scholar 

  80. Niu J et al (2015) Fruit fly optimization algorithm based on differential evolution and its application on gasification process operation optimization. Knowl Based Syst 88:253–263

    Google Scholar 

  81. Jiang J et al (2018) Self-organized resource allocation based on traffic prediction for load imbalance in HetNets with NOMA. Lecture notes of the institute for computer sciences, social-informatics and telecommunications engineering. Springer, Cham, pp 55–65

    Google Scholar 

  82. Hu R et al (2017) A short-term power load forecasting model based on the generalized regression neural network with decreasing step fruit fly optimization algorithm. Neurocomputing 221:24–31

    Google Scholar 

  83. García-Martínez C, Lozano M, Herrera F et al (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Oper Res 185(3):1088–1113

    MATH  Google Scholar 

  84. Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  89. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: IEEE international conference on neural networks, 1995, p 7

  90. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  91. Yang X-S (2010) A new meta-heuristic bat-inspired algorithm. In: González JR, et al. (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74

    Google Scholar 

  92. Suganthan PN, Das S (2010) Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Jadavpur University, Kolkata

    Google Scholar 

  93. Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Methods Eng 21(9):1583–1599

    MATH  Google Scholar 

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

    Google Scholar 

  95. Arora JS (2017) Introduction to optimum design, 4th edn. Academic Press, Boston

    Google Scholar 

  96. Krohling RA, dos Coelho Santos L (2006) Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems. IEEE Trans Syst Man Cybern Part B (Cybernetics) 36(6):1407–1416

    Google Scholar 

  97. Zahara E, Kao Y-T (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36(2, Part 2):3880–3886

    Google Scholar 

  98. 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

    Google Scholar 

  99. Li LJ et al (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7):340–349

    Google Scholar 

  100. Wang G-G et al (2014) Chaotic Krill Herd algorithm. Inf Sci 274:17–34

    MathSciNet  Google Scholar 

  101. Coello Coello CA, Becerra RL (2004) Efficient evolutionary optimization through the use of a cultural algorithm. Eng Optim 36(2):219–236

    Google Scholar 

  102. Yuan Q, Qian F (2010) A hybrid genetic algorithm for twice continuously differentiable NLP problems. Comput Chem Eng 34(1):36–41

    Google Scholar 

  103. Eskandar H et al (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110–111:151–166

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  107. He Q, Wang L (2007) A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl Math Comput 186(2):1407–1422

    MathSciNet  MATH  Google Scholar 

  108. dos Coelho Santos L (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683

    Google Scholar 

  109. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. J Mech Des 112(2):223–229

    Google Scholar 

Download references

Acknowledgements

This research is supported by National Natural Science Foundation of China (U1809209), Medical and Health Technology Projects of Zhejiang province (2019RC207), The Ministry of Education of Humanities and Social Science Project of Wenzhou Business College (20YJA790090).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Fangjun Kuang, Huiling Chen or Yuping Li.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, H., Cai, Z., Ye, X. et al. A multi-strategy enhanced salp swarm algorithm for global optimization. Engineering with Computers 38, 1177–1203 (2022). https://doi.org/10.1007/s00366-020-01099-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01099-4

Keywords

Navigation