Skip to main content
Log in

Selection scheme sensitivity for a hybrid Salp Swarm Algorithm: analysis and applications

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

Abstract

This paper proposes a hybrid version of the Salp Swarm Algorithm (SSA) and the hill climbing (HC) technique using various selection schemes to solve engineering design problems. The proposed algorithm consists of two stages. In the first stage, the basic SSA is hybridized with HC local search to improve its exploitation capabilities; we refer to the hybridized algorithm as HSSA. In the second stage, a selection scheme is applied to enhance the exploration capabilities of the hybrid SSA. Six popular selection schemes were investigated, and the proportional selection scheme was selected as it yielded the best performance. We refer to the hybridized SSA along with the proportional selection scheme as PHSSA. To validate the performance of the proposed algorithms, a series of experiments were conducted using thirty benchmark functions and four engineering design problems. The investigations using benchmark functions revealed that HSSA overcame the weaknesses of the local search in the basic SSA. Moreover, PHSSA enhanced performance by providing an appropriate balance between exploration and exploitation as well as maintaining the diversity of the solutions and avoiding premature convergence. Finally, PHSSA produced results on engineering design problems that were at least comparable and in many cases superior to SSA and similar algorithms in the literature.

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

Similar content being viewed by others

References

  1. Ewees AA, Elaziz MA, Houssein EH (2018) Improved grasshopper optimization algorithm using opposition-based learning. Expert Syst Appl 112:156–172

    Google Scholar 

  2. Abualigah L (2020) Multi-verse optimizer algorithm: a comprehensive survey of its results, variants, and applications. Neural Comput Appl. https://doi.org/10.1007/s00521-020-04839-1

    Article  Google Scholar 

  3. Xu Y, Chen H, Heidari AA, Luo J, Zhang Q, Zhao X, Li C (2019) An efficient chaotic mutative moth-flame-inspired optimizer for global optimization tasks. Expert Syst Appl 129:135–155

    Google Scholar 

  4. Osman IH, Laporte G (1996) Metaheuristics: a bibliography. Springer, Berlin

    MATH  Google Scholar 

  5. Sörensen K (2015) Metaheuristics—the metaphor exposed. Int Trans Oper Res 22:3–18

    MathSciNet  MATH  Google Scholar 

  6. Abualigah LM, Khader AT, Hanandeh ES (2019) Modified krill herd algorithm for global numerical optimization problems. In: Shandilya S, Shandilya S, Nagar A (eds) Advances in nature-inspired computing and applications. Springer, Berlin, pp 205–221

    Google Scholar 

  7. 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

    Google Scholar 

  8. Abualigah L, Diabat A (2020) A novel hybrid antlion optimization algorithm for multi-objective task scheduling problems in cloud computing environments. Cluster Comput. https://doi.org/10.1007/s10586-020-03075-5

    Article  Google Scholar 

  9. Shehab M, Alshawabkah H, Abualigah L, Nagham A-M (2020) Enhanced a hybrid moth-flame optimization algorithm using new selection schemes. Eng Comput. https://doi.org/10.1007/s00366-020-00971-7

    Article  Google Scholar 

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

    Google Scholar 

  11. Yıldız BS, Yıldız AR (2019) The Harris Hawks optimization algorithm, salp swarm algorithm, grasshopper optimization algorithm and dragonfly algorithm for structural design optimization of vehicle components. Mater Test 61:744–748

    Google Scholar 

  12. Abbassi R, Abbassi A, Heidari AA, Mirjalili S (2019) An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers Manage 179:362–372

    Google Scholar 

  13. Qais MH, Hasanien HM, Alghuwainem S (2019) Enhanced salp swarm algorithm: application to variable speed wind generators. Eng Appl Artif Intell 80:82–96

    Google Scholar 

  14. Singh N, Chiclana F, Magnot J-P et al (2020) A new fusion of salp swarm with sine cosine for optimization of non-linear functions. Eng Comput 36:185–212

    Google Scholar 

  15. Rizk-Allah RM, Hassanien AE, Elhoseny M, Gunasekaran M (2019) A new binary salp swarm algorithm: development and application for optimization tasks. Neural Comput Appl 31:1641–1663

    Google Scholar 

  16. Kaur S, Awasthi LK, Sangal A (2020) HMOSHSSA: a hybrid meta-heuristic approach for solving constrained optimization problems. Eng Comput. https://doi.org/10.1007/s00366-020-00989-x

    Article  Google Scholar 

  17. Mirjalili S, Hashim SZM, Sardroudi HM (2012) Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218:11125–11137

    MathSciNet  MATH  Google Scholar 

  18. Kao Y-T, Zahara E, Kao I-W (2008) A hybridized approach to data clustering. Expert Syst Appl 34:1754–1762

    Google Scholar 

  19. Abualigah LM, Khader AT, Hanandeh ES (2018) A combination of objective functions and hybrid krill herd algorithm for text document clustering analysis. Eng Appl Artif Intell 73:111–125

    Google Scholar 

  20. Abualigah LMQ (2019) Feature selection and enhanced krill herd algorithm for text document clustering. Springer, Berlin

    Google Scholar 

  21. Abualigah LM, Khader AT, Hanandeh ES (2018) Hybrid clustering analysis using improved krill herd algorithm. Appl Intell 48:4047–4071

    Google Scholar 

  22. Bairathi D, Gopalani D (2018) Opposition based salp swarm algorithm for numerical optimization. In: International conference on intelligent systems design and applications. Springer, pp 821–831

  23. Moghdani R, Abd Elaziz M, Mohammadi D, Neggaz N (2020) An improved volleyball premier league algorithm based on sine cosine algorithm for global optimization problem. Eng Comput. https://doi.org/10.1007/s00366-020-00962-8

    Article  Google Scholar 

  24. Long W, Cai S, Jiao J, Tang M (2020) An efficient and robust grey wolf optimizer algorithm for large-scale numerical optimization. Soft Comput 24:997–1026

    Google Scholar 

  25. Chen D, Zou F, Li Z, Wang J, Li S (2015) An improved teaching–learning-based optimization algorithm for solving global optimization problem. Inf Sci 297:171–190

    Google Scholar 

  26. Yang X-S (2010) Nature-inspired metaheuristic algorithms. Luniver Press, Bristol

    Google Scholar 

  27. Abualigah L, Shehab M, Alshinwan M, Mirjalili S, Abd Elaziz M (2020) Ant lion optimizer: a comprehensive survey of its variants and applications. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-020-09420-6

    Article  Google Scholar 

  28. McCauley DJ, Pinsky ML, Palumbi SR, Estes JA, Joyce FH, Warner RR (2015) Marine defaunation: animal loss in the global ocean. Science 347:1255641

    Google Scholar 

  29. Shehab M, Khader AT, Al-Betar M (2016) New selection schemes for particle swarm optimization. IEEJ Trans Electron Inf Syst 136:1706–1711

    Google Scholar 

  30. Abualigah L, Shehab M, Alshinwan M, Alabool H (2019) Salp swarm algorithm: a comprehensive survey. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04629-4

    Article  Google Scholar 

  31. Shehab M, Khader AT, Laouchedi M (2017) Modified cuckoo search algorithm for solving global optimization problems. In: International conference of reliable information and communication technology. Springer, pp 561–570

  32. Shehab M, Khader AT, Laouchedi M, Alomari OA (2019) Hybridizing cuckoo search algorithm with bat algorithm for global numerical optimization. J Supercomput 75:2395–2422

    Google Scholar 

  33. Ibrahim RA, Ewees AA, Oliva D, Elaziz MA, Lu S (2019) Improved salp swarm algorithm based on particle swarm optimization for feature selection. J Ambient Intell Human Comput 10:3155–3169

    Google Scholar 

  34. Abusnaina AA, Ahmad S, Jarrar R, Mafarja M (2018) Training neural networks using salp swarm algorithm for pattern classification. In: Proceedings of the 2nd international conference on future networks and distributed systems. ACM, p 17

  35. Grefenstette JJ (1989) How genetic algorithms work: a critical look at implicit parallelism. In: Genetic algorithm and their applications: proceedings of third international conference of genetic algorithm

  36. Blickle T, Thiele L (1995) A mathematical analysis of tournament selection. In: ICGA, vol 95. Citeseer, pp 9–15

  37. Mitchell M (1998) An introduction to genetic algorithms. MIT Press, Cambridge

    MATH  Google Scholar 

  38. Oladele R, Sadiku J (2013) Genetic algorithm performance with different selection methods in solving multi-objective network design problem. Int J Comput Appl 70:5–9

    Google Scholar 

  39. Sharma P, Wadhwa A (2014) Analysis of selection schemes for solving an optimization problem in genetic algorithm. Int J Comput Appl 93:1–3

    Google Scholar 

  40. Holland JH et al (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press, Cambridge

    Google Scholar 

  41. Razali NM, Geraghty J et al (2011) Genetic algorithm performance with different selection strategies in solving TSP. In: Proceedings of the world congress on engineering, vol 2. International Association of Engineers Hong Kong, pp 1–6

  42. Hancock PJ (1994) An empirical comparison of selection methods in evolutionary algorithms. In: AISB workshop on evolutionary computing. Springer, pp 80–94

  43. Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1(1):33–57

    Google Scholar 

  44. Schlierkamp-Voosen D, Mühlenbein H (1993) Predictive models for the breeder genetic algorithm. Evol Comput 1:25–49

    Google Scholar 

  45. Bäck T (1995) Generalized convergence models for tournament-and (\(\mu\), \(\lambda\))-selection. In: Proceedings of the sixth international conference on genetic algorithms, pp 2–8

  46. Volkovs M, Chiang F, Szlichta J, Miller RJ (2014) Continuous data cleaning. In: 2014 IEEE 30th international conference on data engineering. IEEE, pp 244–255

  47. Karaboga D, Basturk B (2007) Artificial bee colony (abc) optimization algorithm for solving constrained optimization problems. In: International fuzzy systems association world congress. Springer, pp 789–798

  48. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74

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

    Google Scholar 

  50. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073

    Google Scholar 

  51. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3:95–99

    Google Scholar 

  52. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

    Google Scholar 

  53. Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17:4831–4845

    MathSciNet  MATH  Google Scholar 

  54. Singh N (2018) A modified variant of grey wolf optimizer. Int J Sci Technol Sci Iran. https://doi.org/10.24200/sci.2018.50122.1523

  55. Ragsdell K, Phillips D (1976) Optimal design of a class of welded structures using geometric programming. J Eng Ind 98:1021–1025

    Google Scholar 

  56. Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29:2013–2015

    Google Scholar 

  57. Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  62. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27:495–513

    Google Scholar 

  63. Elaziz MA, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500

    Google Scholar 

  64. Arora JS (2004) Introduction to optimum design. Elsevier, Amsterdam

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  67. Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37:443–473

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  69. Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10:629–640

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  73. Millán-Páramo C (2018) Modified simulated annealing algorithm for discrete sizing optimization of truss structure. Jordan J Civ Eng 12:683

    Google Scholar 

  74. Sabour M, Eskandar H, Salehi P (2011) Imperialist competitive ant colony algorithm for truss structures. World Appl Sci J 12:105–2011

    Google Scholar 

  75. Dede T (2014) Application of teaching-learning-based-optimization algorithm for the discrete optimization of truss structures. KSCE J Civ Eng 18:1759–1767

    Google Scholar 

  76. Zhang Y-N, Liu P, Liu B, Zhu C-Y, Li Y (2005) Application of improved hybrid genetic algorithm to optimized design of architecture structures. Huanan Ligong Daxue Xuebai (Ziran Kexue Ban)/J South China Univ Technol (Natural Science Edition)(China) 33:69–72

    Google Scholar 

  77. Cheng M-Y, Prayogo D, Wu Y-W, Lukito MM (2016) A hybrid harmony search algorithm for discrete sizing optimization of truss structure. Autom Constr 69:21–33

    Google Scholar 

  78. Li L, Huang Z, Liu F (2009) A heuristic particle swarm optimization method for truss structures with discrete variables. Comput Struct 87:435–443

    Google Scholar 

  79. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2012) Mine blast algorithm for optimization of truss structures with discrete variables. Comput Struct 102:49–63

    Google Scholar 

  80. Cheng M-Y, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112

    Google Scholar 

  81. Oftadeh R, Mahjoob M, Shariatpanahi M (2010) A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search. Comput Math Appl 60:2087–2098

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Laith Abualigah.

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

Abualigah, L., Shehab, M., Diabat, A. et al. Selection scheme sensitivity for a hybrid Salp Swarm Algorithm: analysis and applications. Engineering with Computers 38, 1149–1175 (2022). https://doi.org/10.1007/s00366-020-01067-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01067-y

Keywords

Navigation