Skip to main content
SpringerLink
Log in

A novel chaotic salp swarm algorithm for global optimization and feature selection

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Salp Swarm Algorithm (SSA) is one of the most recently proposed algorithms driven by the simulation behavior of salps. However, similar to most of the meta-heuristic algorithms, it suffered from stagnation in local optima and low convergence rate. Recently, chaos theory has been successfully applied to solve these problems. In this paper, a novel hybrid solution based on SSA and chaos theory is proposed. The proposed Chaotic Salp Swarm Algorithm (CSSA) is applied on 14 unimodal and multimodal benchmark optimization problems and 20 benchmark datasets. Ten different chaotic maps are employed to enhance the convergence rate and resulting precision. Simulation results showed that the proposed CSSA is a promising algorithm. Also, the results reveal the capability of CSSA in finding an optimal feature subset, which maximizes the classification accuracy, while minimizing the number of selected features. Moreover, the results showed that logistic chaotic map is the optimal map of the used ten, which can significantly boost the performance of original SSA.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Similar content being viewed by others

References

  1. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, vol 4, pp 1942–1948

  2. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J Glob Optim 39:459–530

    Article  MathSciNet  MATH  Google Scholar 

  3. Colorni A, Dorigo M, Maniezzo V (1991) Distributed optimization by ant colonies. In: Proceedings of the first european conference on artificial life, pp 134–176

  4. Hong Y, Angelo A, Beltran J, Paglinawan A (2016) A chaos-enhanced particle swarm optimization with adaptive parameters and its application in maximum power point tracking. Math Probl Eng 2016:19

    Google Scholar 

  5. Li B, Jiang W (1998) Optimizing complex functions by chaos search. Journal of Cybernetics and Systems 29:409–419

    Article  MATH  Google Scholar 

  6. Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimization with chaos. Neural Comput & Applic 25(5):1077–1097

    Article  Google Scholar 

  7. Sayed G, Hassanien A, Azar A (2017) Feature selection via a novel chaotic crow search algorithm. Neural Comput & Applic:1–18. https://doi.org/10.1007/s00521-017-2988-6

  8. Coelho L, Mariani V (2008) Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization. Expert System with Application 34(3):1905–1918

    Article  Google Scholar 

  9. Zhang L, Zhang CJ (2008) Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers. Kybernetika 44(1):35–42

    MathSciNet  MATH  Google Scholar 

  10. Zhu ZL, Li SP, Yu H (2008) A new approach to generalized chaos synchronization based on the stability of the error system. Kybernetika 44(4):492–500

    MathSciNet  MATH  Google Scholar 

  11. Yang DX, Li G, Cheng GD (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34:1366–1375

    Article  MathSciNet  Google Scholar 

  12. Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187:1076–1085

    MathSciNet  MATH  Google Scholar 

  13. Lassoued A, Boubaker O (2016) On new chaotic and hyperchaotic systems: a literature survey. Nonlinear Analysis: Modelling and Control 21(6):770–789

    Article  MathSciNet  Google Scholar 

  14. Mahmoud E, Abood F (2017) A new nonlinear chaotic complex model and its complex antilag synchronization. Complexity 2017:1–13

    MathSciNet  MATH  Google Scholar 

  15. Lassoued A, Boubaker O (2017) Dynamic analysis and circuit design of a novel hyperchaotic system with fractional-order terms. Complexity 2017:1–10

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang X, Akgul A, Kacar S, Pham V (2017) Multimedia security application of a ten-term chaotic system without equilibrium. Complexity 2017:1–10

    MathSciNet  MATH  Google Scholar 

  17. Abdullah A, Enayatifa R, Lee M (2012) A hybrid genetic algorithm and chaotic function model for image encryption. Journal of Electronics and Communication 66(1):806–816

    Google Scholar 

  18. Pan Q, Wang L, Gao L (2011) A chaotic harmony search algorithm for the flow shop scheduling problem with limited buffers. Appl Soft Comput 11:5270–5280

    Article  Google Scholar 

  19. Zawbaa H, Emary E, Grosan C (2016) Feature selection via chaotic antlion optimization. PloS ONE 11(3):1–21. e0150652. https://doi.org/10.1371/journal.pone.0150652

    Article  Google Scholar 

  20. Chen CH (2014) A hybrid intelligent model of analyzing clinical breast cancer data using clustering techniques with feature selection. Appl Soft Comput 20:4–14

    Article  Google Scholar 

  21. Rui Y, Huang TS, Chang S (1999) Image retrieval: current techniques, promising directions and open issues. J Vis Commun Image Represent 10:39–62

    Article  Google Scholar 

  22. Yang Y, Pederson JO (1997) A comparative study on feature selection in text categorization. In: Proceedings of the fourteenth international conference on machine learning, pp 412–420

  23. Ng K, Liu H (2000) Customer retention via data mining. AI Review 14:569–590

    MATH  Google Scholar 

  24. Ben-Dor A (2000) Tissue classiffication with gene expression profiles. J Comput Biol 7:559–583

    Article  Google Scholar 

  25. Golub TR (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286:531–537

    Article  Google Scholar 

  26. Yu Z (2014) Hybrid clustering solution selection strategy. Pattern Recogn 47:3362–3375

    Article  Google Scholar 

  27. Guyon I, Elisseeff A (2003) An introduction to variable and attribute selection. Machine Learning Researc 3:1157–1182

    MATH  Google Scholar 

  28. Sayed G, Hassanien A (2017) Moth-flame swarm optimization with neutrosophic sets for automatic mitosis detection in breast cancer histology images. Appl Intell 47(2):397–408

    Article  Google Scholar 

  29. Emary E, Zawbaa H, Hassanien A (2016) Binary gray wolf optimization approaches for feature selection. Neurocomputing 172:371–381

    Article  Google Scholar 

  30. Lin S, Shih-Chieh Ying K, Lee Z (2008) Particle swarm optimization for parameter determination and feature selection of support vector machines. Expert Systems with Applications 35(4):1817–1824

    Article  Google Scholar 

  31. Schiezaro M, Pedrini H (2013) Data feature selection based on artificial bee colony algorithm. EURASIP Journal on Image and Video Processing 2013(1):1–8

    Article  Google Scholar 

  32. Seyedali M, Gandomi A, Mirjalili S, Saremi S, Faris H, Mirjalili S (2017) Salp swarm a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  33. Gandomia AH, Yangb XH (2014) Chaotic bat algorithm. Journal of Computational Science 5:224–232

    Article  MathSciNet  Google Scholar 

  34. Tavazoei MS, Haeri M (2007) An optimization algorithm based on chaotic behavior and fractal nature. J Comput Appl Math 2016(2):1070–1081

    Article  MathSciNet  MATH  Google Scholar 

  35. Wanga GG, Guo L, Gandomi AH, Hao GH, Wangb H (2014) Chaotic krill herd algorithm. Inf Sci 274:17–34

    Article  MathSciNet  Google Scholar 

  36. Zhang Q, Li Z, Zhou CJ, Wei XP (2013) Bayesian network structure learning based on the chaotic particle swarm optimization algorithm. Genet Mol Res 12(4):4468–4479

    Article  Google Scholar 

  37. Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimization with chaos. Neural Comput & Applic 25(5):1077–1097

    Article  Google Scholar 

  38. Emary E, Zawbaa H, Hassanien A (2016) Binary gray wolf optimization approaches for feature selection. Neurocomputing 172:371–381

    Article  Google Scholar 

  39. Sayed G, Darwish A, Hassanien A (2017) Quantum multiverse optimization algorithm for optimization problems. Neural Comput & Applic:1–18. https://doi.org/10.1007/s00521-017-3228-9

  40. Digalakis J, Margaritis K (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77:481–506

    Article  MathSciNet  MATH  Google Scholar 

  41. Yang XS (2010) Test problems in optimization. Wiley, UK

    Google Scholar 

  42. Molga M, Smutnicki aC (2005) Test functions for optimization needs. Unpublished paper

  43. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse imizer: a nature-inspired algorithm for global optimization. Neural Comput & Applic 27(2):1–19

    Article  Google Scholar 

  44. Bache K, Lichman M Uci machine learning repository. http://archive.ics.uci.edu/ml. Retrieved November 12, 2017

  45. Subanya B, Rajalaxmi RR (2014) Feature selection using artificial bee colony for cardiovascular disease classification. In: International conference on electronics and communication systems (ICECS), pp 1–6

  46. Wang X, Yang J, Teng X, Xia W, Jensen R (2007) Feature selection based on rough sets and particle swarm optimization. Pattern Recogn Lett 28(4):459–471

    Article  Google Scholar 

  47. Hafez AI, Zawbaa HM, Emary E, Mahmoud HA, Hassanien AE (2015) An innovative approach for feature selection based on chicken swarm optimization. In: The 7th international conference of soft computing and pattern recognition (soCPaR). Fukuoka, Japan, pp 19–24

  48. Emary E, Zawbaa HM, Grosan C, Hassenian A (2015) Feature subset selection approach by gray-wolf optimization. Springer International Publishing, Cham, pp 1–13

    Google Scholar 

  49. Meng X, Gao X, Lu L, Liu Y, Zhang H (2016) A new bio-inspired optimisation algorithm: bird swarm algorithm. Journal of Experimental & Theoretical Artificial Intelligence 28(4):673–687

    Article  Google Scholar 

  50. Canayaz M, Demir M (2017) Feature selection with the whale optimization algorithm and artificial neural network. In: International artificial intelligence and data processing symposium (IDAP), pp 1–5

  51. Hafez A, Zawbaa H, Emary E, Hassanien A (2016) Sine cosine optimization algorithm for feature selection. In: International symposium on INnovations in intelligent systems and applications (INISTA), pp 1–5

  52. Mahanipour A, Nezamabadi-pour H (2017) Improved pso-based feature construction algorithm using feature selection methods. In: The 2nd conference on swarm intelligence and evolutionary computation (CSIEC), pp 1–5

  53. Peng A, new bio-inspired optimisation algorithm A (2017) Bird swarm algorithm. J Nanoelectron Optoelectron 12(4):404–408

    Article  Google Scholar 

  54. Yao B, Yan Q, Zhang M, Yang Y (2017) Improved artificial bee colony algorithm for vehicle routing problem with time windows. PLoS ONE 12(9):1–18

    Google Scholar 

  55. Xue B, Zhang M, Browne WN (2014) Particle swarm optimisation for feature selection in classification novel initialisation and updating mechanisms. Applied Soft Computing 18:261–276, 05

    Article  Google Scholar 

  56. Mehdi H, Boubaker O (2017) The inverted pendulum in control theory and robotics: from theory to new innovations. Chapter Stabilization and tracking control of the inverted pendulum on a cart via a modified PSO fractional order PID controller. Tunisia, pp 93–115

  57. Zhao X, Turk M, Li W, Lien K, Wang G (2016) A multilevel image thresholding segmentation algorithm based on two-dimensional k–l divergence and modified particle swarm optimization. Appl Soft Comput 48:151–159

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computers and Information, Cairo University, Giza, Egypt

    Gehad Ismail Sayed

  2. Scientific Research Group in Egypt, Giza, Egypt

    Gehad Ismail Sayed

  3. Faculty of Computers and Information, Helwan University, Helwan, Egypt

    Ghada Khoriba & Mohamed H. Haggag

Authors
  1. Gehad Ismail Sayed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghada Khoriba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamed H. Haggag
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gehad Ismail Sayed.

Appendix A: List of benchmark functions

Appendix A: List of benchmark functions

Table 12 Definition of unimodal benchmark functions
Full size table
Table 13 Definition of multimodal benchmark functions
Full size table
Table 14 Properties of unimodal benchmark functions, lb denotes lower bound, ub denotes upper bound, dim denotes dimensions, opt denotes optimum point
Full size table
Table 15 Properties of multimodal benchmark functions, lb denotes lower bound, ub denotes upper bound, dim denotes dimensions, opt denotes optimum point
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sayed, G.I., Khoriba, G. & Haggag, M.H. A novel chaotic salp swarm algorithm for global optimization and feature selection. Appl Intell 48, 3462–3481 (2018). https://doi.org/10.1007/s10489-018-1158-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-018-1158-6

Keywords

Search

Navigation