Abstract
In this paper, a new comprehensive learning gravitational search algorithm (CLGSA) is proposed to enhance the performance of basic GSA. The proposed algorithm is a new kind of intelligent optimization algorithm which has better ability to choose good elements. An intensive comprehensive learning methodology is proposed to enrich the optimization ability of the GSA. The efficiency of the proposed algorithm was evaluated by 28 benchmark functions which have been proposed in IEEE-CEC 2013 sessions. The results are compared with eight state-of-the-art algorithms IPOP, BIPOP, NIPOP, NBIPOP, DE/rand, SPSRDEMMS, SPSO-2011 and GSA. A variety of ways are considered to examine the ability of the proposed technique in terms of convergence ability, success rate and statistical behavior of algorithm over dimensions 10, 30 and 50. Apart from experimental studies, theoretical stability of the proposed CLGSA is also proved. It was concluded that the proposed algorithm performed efficiently with good results.
Similar content being viewed by others
References
Rashedi E, Nezamabadi HP, Saryadi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Formato RA (2008) Central force optimization: a new nature inspired computational framework of multidimensional search and optimization. Stud Comput Intell 129:221–238
Formato RA (2007) Central force optimization: a new metaheuristic with application in applied electromagnetic. Prog Electromagn Res 77:425–491
Mirajalili S, Hashim SZ (2010) A new hybrid psogsa algorithm for function optimization. In: Proceeding of international conference of computer and information applications 2010, pp 374–377
Newton I (xxxx) Philosophiae naturalis principia mathematica, sumptibus. Soc 1714
Qin AK, Li X (2013) Differential evolution on CEC 2013 single objective continuous optimization testbed. In: IEEE congress on evolutionary computation, pp 1096–1106
Auger A, Hansen N, Restart A (2005) CMA evolution strategy with increasing population size. In: IEEE congress on evolutionary computation, IEEE Press, pp 1769–1776
Hansen N (2009) Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed. In: GECCO companion, pp 2389–2396
Loshchilov I, Schoenauer M, Sebag M (2012) Black-box optimization benchmarking of NIPOP-aCMA-ES and NBIPOP-aCMA-ES on the BBOB-2012 Noiseless Testbed. In: Genetic and evolutionary computation conference (GECCO Companion), ACM Press, pp 269–276
Loshchilov I, Schoenauer M, Sebag M (2012) Alternative restart strategies for CMA-ES. Parallel problem solving from nature (PPSN XII), LNCS. Springer, Berlin, pp 296–305
Zamuda A, Brest J, Mezura-Montes E (2013) Structured population size reduction differential evolution with multiple mutation strategies on CEC 2013 real parameter optimization. In: 2013 IEEE congress on evolutionary computation, pp 1925–1931
Liang JJ, QBY, SPN (2013) Problem definitions and evaluation criteria for the CEC 2013 special session and competition on real-parameter optimization. In: Computational intelligence Laboratory, Zhengzhou University, Zhengzhou China And Nanyang Technological University, Singapore, Technical Report 2012
Astrom KJ, Wittenmark B (1997) Computer-controlled systems-theory and design, 3rd edn. Englewood Cliffs, Prentice Hall
Črepinšek M, Liu S-H, Mernik L, Mernik M (2016) Is a comparison of results meaningful from the inexact replications of computational experiments? Soft Comput 20(1):223–235
Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of non parametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18
Črepinšek M, Liu S-H, Mernik M (2014) Replication and comparison of computational experiments in applied evolutionary computing: common pitfall sand guidelines to avoid them. Appl Soft Comput 19:161–170
Črepinšek M, Liu S-H, Mernik L (2012) A note on teaching-learning-based optimi- zation algorithm. Inf Sci 212:79–93
Jianga S, Wanga Y, Ji Z (2014) Convergence analysis and performance of an improved gravitational search algorithm. Appl Soft Comput 24:363–384
Clerc M (2011) Standard particle swarm optimisation. http://clerc.maurice.free.fr/PSO/PSOmathstuff/PSOmathstuff.htm
van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971
Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696
Qin A, Huang V, Suganthan P (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evolut Comput 10(3):281–294
Chen W, Zhang J, Chung H, Zhong W, Wu W, Shi Y (2010) A novel set based particle swarm optimization method for discrete optimization problems. IEEE Trans Evol Comput 14(2):278–300
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1(1):33–57
Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self -adaptive control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657
Cheng J, Zhang G, Neri F (2013) Enhencing distributed differential evolution with multicultural migration for global numerical optimization. Inf Sci 247:72–93
Sarafrazi S, Nezamabadi-Pour H, Saryazdi S (2011) Disruption: a new operator in gravitational search algorithm. Sci Iranica 18(3):539–548
Gao S, Virappan C, Wang Y, Cao Q, Tang Z (2014) Gravitational search algorithm combined with Chaos for unconstrained numerical optimization. Appl Math Comput 231:48–62
Khajehzadeh M, Taha MR, El-Shafie A, Eslami M (2012) ‘A modified gravitational search algorithm for slope stability analysis’. Eng Appl Artif Intell 25(8):1589–1597
Yazdani S, Nezamabadi-Pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evol Comput 14:1–14
David R-C, Precup R-E, Petriu E, Rdac M-B, Purcaru C, Dragos C-A, Preitl S (2012) Adaptive gravitational search algorithm for PI-fuzzy controller tuning. In: Proceedings of the 9th international conference on informatics in control, automation and robotics, pp 136–141
Rashedi E, Nezamabadi H-P, Saryazdi S (2009) BGSA: binary gravitational search algorithm. Nat Comput 9(3):727–745
Mirjalili S, Hashim SZ, Sardroudi HM (2012) Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218(22):11125–11137
Sun G, Zhang A (2013) A hybrid genetic algorithm and gravitational using multilevel thresholding. Pattern Recognit Image Anal 7887:707–714
Guo Z (2012) A hybrid optimization algorithm based on artificial bee colony and gravitational search algorithm. Int J Digit Content Technol Appl 6(17):620–626
Xiangtao L, Yin M, Ma Z (2011) Hybrid differential evolution and gravitation search algorithm for unconstrained optimization. Int J Phys Sci 6(25):5961–5981
Yin M, Hu Y, Yang F, Li X, Gu W (2011) A novel hybrid K-harmonic means and gravitational search algorithm approach for clustering. Expert Syst Appl 38(8):9319–9324
Mirjalili S, Gandomi AH (2017) Chaotic gravitational constants for the gravitational search algorithm. Appl Soft Comput 53:407–419
Ghalambaz M, Noghrehabadi AR, Behrang MA, Assareh E, Ghanbarzadeh A, Hedayat N (2011) A hybrid neural network and gravitational search algorithm (HNNGSA) method to solve well known Wessinger’s Equation. In: World academy of science, engineering and technology, pp 803–807
Palanikkumar D, Anbuselvan P, Rithu B (2012) A gravitational search algorithm for effective Web service selection for composition with enhanced QoS in SOA. Int J Comput Appl 42(8):12–15
Kumar JV, Kumar DV, Edukondalu K (2013) Strategic bidding using fuzzy adaptive gravitational search algorithm in a pool based electricity market. Appl Soft Comput 13(5):2445–2455
Qasem RA, Eldos T (2013) An efficient cell placement using gravitational search algorithms. J Comput Sci 9(8):943–948
Li C, Zhou J (2011) ‘Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm’. Energy Convers Manage 52(1):374–381
Mallick S, Ghoshal S, Acharjee P, Thakur S (2013) Optimal static state estimation using improved particle swarm optimization and gravitational search algorithm. Int J Electr Power Energy Syst 52:254–265
Bahrololoum A, Nezamabadi-Pour H, Bahrololoum H, Saeed M (2012) A prototype classifier based on gravitational search algorithm. Appl Soft Comput 12(2):819–825
González-Álvarez D, Vega-Rodríguez M, Gómez-Pulido J, Sánchez-Pérez J (2011) Applying a multiobjective gravitational search algorithm (MO-GSA) to discover motifs. In: Advances in computational intelligence. Springer: Berlin, pp 372–379
Acknowledgement
This work was supported by the National Institute of Technology Jalandhar, India. We would like to express our gratitude toward the unknown potential reviewers who have agreed to review this article and who have provided valuable suggestions to improve the quality of the article.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bala, I., Yadav, A. Comprehensive learning gravitational search algorithm for global optimization of multimodal functions. Neural Comput & Applic 32, 7347–7382 (2020). https://doi.org/10.1007/s00521-019-04250-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-019-04250-5