Neural Computing and Applications

, Volume 25, Issue 6, pp 1423–1435 | Cite as

Binary optimization using hybrid particle swarm optimization and gravitational search algorithm

  • Seyedali Mirjalili
  • Gai-Ge Wang
  • Leandro dos S. Coelho
Original Article


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.


Binary optimization Binary algorithms PSOGSA Particle swarm optimization Gravitational search algorithm 


  1. 1.
    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82CrossRefGoogle Scholar
  2. 2.
    Kennedy J, Eberhart R (1995) Particle swarm optimization, vol 4, pp 1942–1948Google Scholar
  3. 3.
    Holland JH (1992) Genetic algorithms. Sci Am 267:66–72CrossRefGoogle Scholar
  4. 4.
    Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Aarts EHL, Laarhoven PJM (1989) Simulated annealing: an introduction. Stat Neerl 43:31–52CrossRefzbMATHGoogle Scholar
  6. 6.
    Geem ZW, Kim JH (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68CrossRefGoogle Scholar
  7. 7.
    Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1:28–39CrossRefGoogle Scholar
  8. 8.
    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248CrossRefzbMATHGoogle Scholar
  9. 9.
    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713CrossRefGoogle 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 2:655–658CrossRefGoogle 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 CrossRefGoogle Scholar
  14. 14.
    Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17:4831–4845MathSciNetCrossRefzbMATHGoogle 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 138:392–402Google Scholar
  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):2454–2462Google Scholar
  17. 17.
    Wang G-G, Gandomi AH, Alavi AH (2014) Stud krill herd algorithm. Neurocomputing 128:363–370CrossRefGoogle Scholar
  18. 18.
    Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H (2014) Chaotic Krill Herd algorithm. Inf Sci 274:17–34Google Scholar
  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 57–57Google Scholar
  22. 22.
    Holden N, Freitas AA (2008) A hybrid PSO/ACO algorithm for discovering classification rules in data mining. J Artif Evol Appl 2008:2Google 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 2745–2750Google Scholar
  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 651–655Google Scholar
  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 156–163Google Scholar
  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 3816–3821Google Scholar
  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):6962–6978MathSciNetCrossRefGoogle 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 190–193Google Scholar
  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 35:21–33CrossRefGoogle 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 178–185Google Scholar
  33. 33.
    Li C, Zhou J (2011) Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm. Energy Convers Manag 52:374–381CrossRefGoogle Scholar
  34. 34.
    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2010) BGSA: binary gravitational search algorithm. Nat Comput 9:727–745MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Rashedi E, Nezamabadi S, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248CrossRefzbMATHGoogle Scholar
  36. 36.
    Wang L, Xu Y, Mao Y, Fei M (2010) A discrete harmony search algorithm. Life Syst Model Intell Comput 37–43Google Scholar
  37. 37.
    Wang L, Fu X, Menhas M, Fei M (2010) A modified binary differential evolution algorithm. Life Syst Model Intell Comput 6329:49–57Google Scholar
  38. 38.
    Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm, vol 5, pp 4104–4108Google Scholar
  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 thesisGoogle Scholar
  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 CrossRefGoogle 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 3:82–102CrossRefGoogle Scholar
  44. 44.
    Yang XS (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, LondonCrossRefGoogle Scholar
  45. 45.
    Molga M, Smutnicki C (2005) Test functions for optimization needs.
  46. 46.
    Digalakis J, Margaritis K (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77:481–506MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Liang J, Suganthan P, Deb K (2005) Novel composition test functions for numerical global optimization, pp 68–75Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Seyedali Mirjalili
    • 1
  • Gai-Ge Wang
    • 2
  • Leandro dos S. Coelho
    • 3
    • 4
  1. 1.School of Information and Communication TechnologyGriffith UniversityNathan, BrisbaneAustralia
  2. 2.School of Computer Science and TechnologyJiangsu Normal UniversityXuzhouChina
  3. 3.Industrial and Systems Engineering Graduate Program (PPGEPS)Pontifical Catholic University of Parana (PUCPR)CuritibaBrazil
  4. 4.Electrical Engineering Graduate Program (PPGEE), Department of Electrical Engineering, Polytechnic CenterFederal University of Parana (UFPR)CuritibaBrazil

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