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Adaptive gbest-guided gravitational search algorithm

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Abstract

One heuristic evolutionary algorithm recently proposed is the gravitational search algorithm (GSA), inspired by the gravitational forces between masses in nature. This algorithm has demonstrated superior performance among other well-known heuristic algorithms such as particle swarm optimisation and genetic algorithm. However, slow exploitation is a major weakness that might result in degraded performance when dealing with real engineering problems. Due to the cumulative effect of the fitness function on mass in GSA, masses get heavier and heavier over the course of iteration. This causes masses to remain in close proximity and neutralise the gravitational forces of each other in later iterations, preventing them from rapidly exploiting the optimum. In this study, the best mass is archived and utilised to accelerate the exploitation phase, ameliorating this weakness. The proposed method is tested on 25 unconstrained benchmark functions with six different scales provided by CEC 2005. In addition, two classical, constrained, engineering design problems, namely welded beam and tension spring, are also employed to investigate the efficiency of the proposed method in real constrained problems. The results of benchmark and classical engineering problems demonstrate the performance of the proposed method.

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References

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

  2. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: IEEE international conference on evolutionary computation. Anchorage, Alaska, pp 69–73

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

    Article  Google Scholar 

  4. Price K, Storn R (1997) Differential evolution. Dr. Dobb’s J 22:18–20

    Google Scholar 

  5. Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, New York

    Google Scholar 

  6. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. Comput Intell Mag, IEEE 1(4):28–39. doi:10.1109/MCI.2006.329691

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

    Article  Google Scholar 

  8. 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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Guo L, Wang G-G, Gandomi AH, Alavi AH, Duan H (2014) A new improved krill herd algorithm for global numerical optimization. Neurocomputing. doi:10.1016/j.neucom.2014.01.023

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

    Article  MATH  Google Scholar 

  13. Mirjalili S, Mirjalili SM, Yang X-S (2013) Binary bat algorithm. Neural Comput Appl 1–19. doi:10.1007/s00521-013-1525-5

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

    Article  Google Scholar 

  15. 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, 2009. ICCSIT 2009. pp 651–655

  16. Esmin AAA, Lambert-Torres G, Alvarenga GB (2006) Hybrid evolutionary algorithm based on PSO and GA mutation. In: International conference on hybrid intelligent systems. IEEE Computer Society, Los Alamitos, CA, USA, p 57. http://doi.ieeecomputersociety.org/10.1109/HIS.2006.33

  17. Zhang WJ, Xie XF (2003) DEPSO: hybrid particle swarm with differential evolution operator, vol. 4, pp. 3816–3821

  18. 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

  19. Holden NP, Freitas AA (2007) A hybrid PSO/ACO algorithm for classification, pp 2745–2750

  20. 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 

  21. 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

  22. Wang G-G, Gandomi AH, Alavi AH (2013) An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl Math Model. doi:10.1016/j.apm.2013.10.052

  23. Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12:107–125

    Article  Google Scholar 

  24. Chen J, Qin Z, Liu Y, Lu J (2005) Particle swarm optimization with local search, pp 481–484

  25. Chen S, Mei T, Luo M, Yang X (2007) Identification of nonlinear system based on a new hybrid gradient-based PSO algorithm, pp 265–268

  26. Meuleau N, Dorigo M (2002) Ant colony optimization and stochastic gradient descent. Artif Life 8:103–121

    Article  Google Scholar 

  27. Wang G–G, Gandomi AH, Alavi AH (2013) A chaotic particle-swarm krill herd algorithm for global numerical optimization. Kybernetes 42:9

    MathSciNet  Google Scholar 

  28. Wang G-G, Guo L, Gandomi AH, Hao G-S, Wang H (2014) Chaotic Krill Herd algorithm. Inf Sci. doi:10.1016/j.ins.2014.02.123

  29. Saremi S, Mirjalili SM, Mirjalili S (2014) Chaotic Krill Herd optimization algorithm. Procedia Technol 12:180–185

    Article  Google Scholar 

  30. Wang G-G, Gandomi AH, Alavi AH (2014) Stud Krill Herd algorithm. Neurocomputing 128:363–370

    Article  Google Scholar 

  31. Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2014) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 24(3–4):853–871. doi:10.1007/s00521-012-1304-8

  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). Springer, Berlin/Heidelberg, pp. 178–185

  33. Sinaie S (2010) Solving shortest path problem using gravitational search algorithm and neural networks. Master, Faculty of Computer Science and Information Systems, Universiti Teknologi Malaysia (UTM), Johor Bahru, Malaysia

  34. 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 Electric Power Energy Syst 35:21–33

    Article  Google Scholar 

  35. Chen H, Li S, Tang Z (2011) Hybrid gravitational search algorithm with random-key encoding scheme combined with simulated annealing. IJCSNS 11:208

    MATH  Google Scholar 

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

  37. 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 

  38. Mirjalili S, Mohd Hashim SZ, Moradian Sardroudi H (2012) Training feed forward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218:11125–11137

    Article  MATH  MathSciNet  Google Scholar 

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

  40. Gauci M, Dodd TJ, Groß R (2012) Why ‘GSA: a gravitational search algorithm’ is not genuinely based on the law of gravity. Nat Comput 11(4):719–720. doi:10.1007/s11047-012-9322-0

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  42. Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Nanyang Technological University, Singapore, Tech. Rep, vol 2005005

  43. Derrac J, García S, Molina D, Herrera F (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. doi:10.1016/j.swevo.2011.02.002

    Article  Google Scholar 

  44. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics Bull 1:80–83

    Article  Google Scholar 

  45. Arora JS (2004) Introduction to optimum design. Academic Press, London

    Google Scholar 

  46. Belegundu AD (1983) Study of mathematical programming methods for structural optimization. Dissertation abstracts international part B: science and engineering [DISS. ABST. INT. PT. B- SCI. & ENG.], vol 43, p 1983

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  53. Yang XS (2011) Nature-inspired metaheuristic algorithms. Luniver Press, UK

    Google Scholar 

  54. Carlos A, Coello C (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civil Eng Syst 17:319–346

    Article  Google Scholar 

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

    Article  Google Scholar 

  56. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338

    Article  MATH  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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Information and Communication Technology, Griffith University, Brisbane, QLD, 4111, Australia

    Seyedali Mirjalili & Andrew Lewis

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  1. Seyedali Mirjalili
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  2. Andrew Lewis
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Correspondence to Seyedali Mirjalili.

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Mirjalili, S., Lewis, A. Adaptive gbest-guided gravitational search algorithm. Neural Comput & Applic 25, 1569–1584 (2014). https://doi.org/10.1007/s00521-014-1640-y

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