Skip to main content

Binary optimization using hybrid particle swarm optimization and gravitational search algorithm

Abstract

The PSOGSA is a novel hybrid optimization algorithm, combining strengths of both particle swarm optimization (PSO) and gravitational search algorithm (GSA). It has been proven that this algorithm outperforms both PSO and GSA in terms of improved exploration and exploitation. The original version of this algorithm is well suited for problems with continuous search space. Some problems, however, have binary parameters. This paper proposes a binary version of hybrid PSOGSA called BPSOGSA to solve these kinds of optimization problems. The paper also considers integration of adaptive values to further balance exploration and exploitation of BPSOGSA. In order to evaluate the efficiencies of the proposed binary algorithm, 22 benchmark functions are employed and divided into three groups: unimodal, multimodal, and composite. The experimental results confirm better performance of BPSOGSA compared with binary gravitational search algorithm (BGSA), binary particle swarm optimization (BPSO), and genetic algorithm in terms of avoiding local minima and convergence rate.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

References

  1. 1.

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

    Article  Google Scholar 

  2. 2.

    Kennedy J, Eberhart R (1995) Particle swarm optimization, vol 4, pp 1942–1948

  3. 3.

    Holland JH (1992) Genetic algorithms. Sci Am 267:66–72

    Article  Google Scholar 

  4. 4.

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

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Aarts EHL, Laarhoven PJM (1989) Simulated annealing: an introduction. Stat Neerl 43:31–52

    Article  MATH  Google Scholar 

  6. 6.

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

    Article  Google Scholar 

  7. 7.

    Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1:28–39

    Article  Google Scholar 

  8. 8.

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

    Article  MATH  Google Scholar 

  9. 9.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713

    Article  Google Scholar 

  10. 10.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209. doi:10.1016/j.ins.2014.01.038

  11. 11.

    Saremi S, Mirjalili S, Lewis A (2014) Biogeography-based optimisation with chaos. Neural Comput Appl 1–21. doi:10.1007/s00521-014-1597-x

  12. 12.

    Saremi S, Mirjalili S (2013) Integrating chaos to biogeography-based optimization algorithm. Int J Comput Commun Eng 2:655–658

    Article  Google Scholar 

  13. 13.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. doi:10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  14. 14.

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

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Guo L, Wang G-G, Gandomi AH, Alavi AH, Duan H (2014) A new improved krill herd algorithm for global numerical optimization. Neurocomputing 138:392–402

  16. 16.

    Wang G-G, Gandomi AH, Alavi AH (2013) An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl Math Model 38(9–10):2454–2462

  17. 17.

    Wang G-G, Gandomi AH, Alavi AH (2014) Stud krill herd algorithm. Neurocomputing 128:363–370

    Article  Google Scholar 

  18. 18.

    Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H (2014) Chaotic Krill Herd algorithm. Inf Sci 274:17–34

  19. 19.

    Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2012) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 1–19. doi:10.1007/s00521-012-1304-8

  20. 20.

    Saremi S, Mirjalili SM, Mirjalili S (2014) Chaotic Krill Herd optimization algorithm. Procedia Technol 12:180–185. doi:10.1016/j.protcy.2013.12.473

  21. 21.

    Esmin A, Lambert-Torres G, Alvarenga GB (2006) Hybrid evolutionary algorithm based on PSO and GA mutation. In: Sixth international conference on hybrid intelligent systems, pp 57–57

  22. 22.

    Holden N, Freitas AA (2008) A hybrid PSO/ACO algorithm for discovering classification rules in data mining. J Artif Evol Appl 2008:2

    Google Scholar 

  23. 23.

    Holden NP, Freitas AA (2007) A hybrid PSO/ACO algorithm for classification. In: GECCO '07 proceedings of the 9th annual conference companion on genetic and evolutionary computation, pp 2745–2750

  24. 24.

    Lai X, Zhang M (2009) An efficient ensemble of GA and PSO for real function optimization. In: 2nd IEEE international conference on computer science and information technology, pp 651–655

  25. 25.

    Niu B, Li L (2008) A novel PSO-DE-based hybrid algorithm for global optimization. In: Advanced intelligent computing theories and applications. With aspects of artificial intelligence, pp 156–163

  26. 26.

    Zhang WJ, Xie XF (2003) DEPSO: hybrid particle swarm with differential evolution operator. In: IEEE international conference on systems, man and cybernetics, vol 4, pp 3816–3821

  27. 27.

    Wang G-G, Gandomi AH, Alavi AH, Hao G-S (2013) Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput Appl 1–12. doi:10.1007/s00521-013-1485-9

  28. 28.

    Wang G-G, Gandomi AH, Alavi AH (2013) A chaotic particle-swarm krill herd algorithm for global numerical optimization. Kybernetes 42(6):6962–6978

    MathSciNet  Article  Google Scholar 

  29. 29.

    Mirjalili S, Hashim SZM (2010) A new hybrid PSOGSA algorithm for function optimization. In: 2010 international conference on computer and information application (ICCIA), pp 374–377. doi:10.1109/ICCIA.2010.6141614

  30. 30.

    Hatamlou A, Abdullah S, Othman Z (2011) Gravitational search algorithm with heuristic search for clustering problems. In: 3rd conference on data mining and optimization (DMO), pp 190–193

  31. 31.

    Shaw B, Mukherjee V, Ghoshal SP (2012) A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. Int J Electr Power Energy Syst 35:21–33

    Article  Google Scholar 

  32. 32.

    Zhang Y, Wu L, Zhang Y, Wang J (2012) Immune gravitation inspired optimization algorithm advanced intelligent computing, vol 6838. In: Huang D-S, Gan Y, Bevilacqua V, Figueroa J (eds) Advanced intelligent computing. Springer, Berlin, pp 178–185

  33. 33.

    Li C, Zhou J (2011) Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm. Energy Convers Manag 52:374–381

    Article  Google Scholar 

  34. 34.

    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2010) BGSA: binary gravitational search algorithm. Nat Comput 9:727–745

    MathSciNet  Article  MATH  Google Scholar 

  35. 35.

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

    Article  MATH  Google Scholar 

  36. 36.

    Wang L, Xu Y, Mao Y, Fei M (2010) A discrete harmony search algorithm. Life Syst Model Intell Comput 37–43

  37. 37.

    Wang L, Fu X, Menhas M, Fei M (2010) A modified binary differential evolution algorithm. Life Syst Model Intell Comput 6329:49–57

  38. 38.

    Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm, vol 5, pp 4104–4108

  39. 39.

    Mirjalili S, Mohd Hashim SZ, Moradian Sardroudi H (2012) Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218(22):11125–11137. doi:10.1016/j.amc.2012.04.069

  40. 40.

    Mirjalili S (2011) Hybrid particle swarm optimization and gravitational search algorithm for multilayer perceptron learning. Universiti Teknologi Malaysia, Faculty of Computer Science and Information System, Master thesis

  41. 41.

    Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput 9:1–14. doi:10.1016/j.swevo.2012.09.002

    Article  Google Scholar 

  42. 42.

    Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Comput Appl. doi:10.1007/s00521-014-1640-y

  43. 43.

    Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102

    Article  Google Scholar 

  44. 44.

    Yang XS (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, London

    Book  Google Scholar 

  45. 45.

    Molga M, Smutnicki C (2005) Test functions for optimization needs. http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf

  46. 46.

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

    MathSciNet  Article  MATH  Google Scholar 

  47. 47.

    Liang J, Suganthan P, Deb K (2005) Novel composition test functions for numerical global optimization, pp 68–75

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Seyedali Mirjalili.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mirjalili, S., Wang, GG. & Coelho, L.S. Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput & Applic 25, 1423–1435 (2014). https://doi.org/10.1007/s00521-014-1629-6

Download citation

Keywords

  • Binary optimization
  • Binary algorithms
  • PSOGSA
  • Particle swarm optimization
  • Gravitational search algorithm