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Gravitational search algorithm: a comprehensive analysis of recent variants

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Abstract

Gravitational search algorithm is a nature-inspired algorithm based on the mathematical modelling of the Newton’s law of gravity and motion. In a decade, researchers have presented many variants of gravitational search algorithm by modifying its parameters to efficiently solve complex optimization problems. This paper conducts a comparative analysis among ten variants of gravitational search algorithm which modify three parameters, namely Kbest, velocity, and position. Experiments are conducted on two sets of benchmark categories, namely standard functions and CEC2015 functions, including problems belonging to different categories such as unimodal, multimodal, and unconstrained optimization functions. The performance comparison is evaluated and statistically validated in terms of mean fitness value and convergence graph. In experiments, IGSA has achieved better precision with balanced trade-off between exploration and exploitation. Moreover, triple negative breast cancer dataset has been considered to analysis the performance of GSA variants for the nuclei segmentation. The variants performance has been analysed in terms of both qualitative and quantitive with aggregated Jaccard index as performance measure. Experiments affirm that IGSA-based method has outperformed other methods.

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References

  1. Bansal JC, Joshi SK, Nagar AK (2018) Fitness varying gravitational constant in gsa. Appl Intell 48(10):3446–3461

    Article  Google Scholar 

  2. Brest J, Bošković B, Zamuda A, Fister I, Mezura-Montes E (2013) Real parameter single objective optimization using self-adaptive differential evolution algorithm with more strategies. In: Proc of IEEE congress on evolutionary computation, mexico, pp 377–383

  3. Chatterjee A, Ghoshal S, Mukherjee V (2012) A maiden application of gravitational search algorithm with wavelet mutation for the solution of economic load dispatch problems. International Journal of Bio-Inspired Computation 4:33–46

    Article  Google Scholar 

  4. Chaos theory and the logistic map - geoff boeing. http://geoffboeing.com/2015/03/chaos-theory-logistic-map/http://geoffboeing.com/2015/03/chaos-theory-logistic-map/, (Accessed on 04/12/2016)

  5. Davarynejad M, Forghany Z, van den Berg J (2012) Mass-dispersed gravitational search algorithm for gene regulatory network model parameter identification. In: Proc of springer asia-pacific conference on simulated evolution and learning, vietnam, pp 62–72

  6. Dhal KG, Ray S, Das A, Das S (2018) A survey on nature-inspired optimization algorithms and their application in image enhancement domain. Archives of Computational Methods in Engineering, pp 1–32

  7. Dixit M, Upadhyay N, Silakari S (2015) An exhaustive survey on nature inspired optimization algorithms. Int J Softw Eng Appl 9:91–104

    Google Scholar 

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

    Article  Google Scholar 

  9. Feng Y, Teng G-F, Wang A-X, Yao Y-M (2007) Chaotic inertia weight in particle swarm optimization. In: Proc of IEEE international conference on innovative computing, information and control, japan, pp 475–480

  10. Giladi C, Sintov A (2020) Manifold learning for efficient gravitational search algorithm. Inf Sci 517:18–36

    Article  MathSciNet  Google Scholar 

  11. Guha R, Ghosh M, Chakrabarti A, Sarkar R, Mirjalili S (2020) Introducing clustering based population in binary gravitational search algorithm for feature selection, Applied Soft Computing, pp 106341

  12. Gupta V, Singh A, Sharma K, Mittal H (2018) A novel differential evolution test case optimisation (detco) technique for branch coverage fault detection. In: Smart Computing and Informatics, Springer, pp 245–254

  13. Han X, Chang X (2012) A chaotic digital secure communication based on a modified gravitational search algorithm filter. Inf Sci 208:14–27

    Article  Google Scholar 

  14. Ibrahim RA, Ewees AA, Oliva D, Abd Elaziz M, Lu S (2019) Improved salp swarm algorithm based on particle swarm optimization for feature selection. Journal of Ambient Intelligence and Humanized Computing 10(8):3155–3169

    Article  Google Scholar 

  15. Jadon SS, Bansal JC, Tiwari R, Sharma H (2014) Artificial bee colony algorithm with global and local neighborhoods. International Journal of System Assurance Engineering and Management 9:1–13

    Google Scholar 

  16. Jiang J, Jiang R, Meng X, Li K (2020) Scgsa: A sine chaotic gravitational search algorithm for continuous optimization problems. Expert Syst Appl 144:113118

    Article  Google Scholar 

  17. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE Internation conference on neural networks

  18. Khajehzadeh M, Taha MR, El-Shafie A, Eslami M (2012) A modified gravitational search algorithm for slope stability analysis. Eng Appl Artif Intell 25:1589–1597

    Article  Google Scholar 

  19. Lei Z, Gao S, Gupta S, Cheng J, Yang G (2020) An aggregative learning gravitational search algorithm with self-adaptive gravitational constants Expert Systems with Applications, pp 113396

  20. Li P, Duan H (2012) Path planning of unmanned aerial vehicle based on improved gravitational search algorithm. Sci China Technol Sci 55:2712–2719

    Article  Google Scholar 

  21. Li C, Li H, Kou P (2014) Piecewise function based gravitational search algorithm and its application on parameter identification of avr system. Neurocomputing 124:139–148

    Article  Google Scholar 

  22. Liu H, Wang Y, Tu L, Ding G, Hu Y (2018) A modified particle swarm optimization for large-scale numerical optimizations and engineering design problems. J Intell Manuf 29:1–27

    Article  Google Scholar 

  23. Liu J, Xing Y, Ma Y, Li Y (2020) Gravitational search algorithm based on multiple adaptive constraint strategy. Computing, pp 1–41

  24. Logistic map – from wolfram mathworld. http://mathworld.wolfram.com/LogisticMap.html, (Accessed on 04/16/2016)

  25. Luo J, Chen H, Xu Y, Huang H, Zhao X, et al. (2018) An improved grasshopper optimization algorithm with application to financial stress prediction. Appl Math Model 64:654–668

    Article  MathSciNet  Google Scholar 

  26. Mirjalili S, Hashim SZM (2010) A new hybrid psogsa algorithm for function optimization. In: Proc of IEEE international conference on computer and information application, china, pp 374–377

  27. Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Comput Applic 25:1569–1584

    Article  Google Scholar 

  28. Mittal H (2018) M. saraswat, ckgsa based fuzzy clustering method for image segmentation of rgb-d images. In: Proc of IEEE international conference on contemporary computing, India

  29. Mittal H, Pal R, Kulhari A, Saraswat M (2016) Chaotic kbest gravitational search algorithm (ckgsa). In: Proc of IEEE international conference on contemporary computing, India

  30. Mittal H, Saraswat M (2018) An optimum multi-level image thresholding segmentation using non-local means 2d histogram and exponential kbest gravitational search algorithm. Eng Appl Artif Intell 71:226–235

    Article  Google Scholar 

  31. Mittal H, Saraswat M (2018) An image segmentation method using logarithmic kbest gravitational search algorithm based superpixel clustering. Evol Intel, pp 1–13

  32. Mittal H, Saraswat M (2019) An automatic nuclei segmentation method using intelligent gravitational search algorithm based superpixel clustering. Swarm and Evolutionary Computation 45:15–32

    Article  Google Scholar 

  33. Mittal H, Saraswat M (2019) Classification of histopathological images through bag-of-visual-words and gravitational search algorithm. In: Soft computing for problem solving, Springer

  34. Mittal H, Saraswat M, Pal R (2020) Histopathological image classification by optimized neural network using igsa. In: International conference on distributed computing and internet technology, Springer, pp 429–436

  35. Mukherjee M, Mitra S, Acharyya S (2020) Mutation-based chaotic gravitational search algorithm. In: Proceedings of the global AI congress 2019, Springer, pp 117–131

  36. Nagaraju S, Reddy AS, Vaisakh K (2019) Shuffled differential evolution-based combined heat and power economic dispatch. In: Proc of springer international conference on soft computing in data analytics, singapore, pp 525–532

  37. Nanda SJ, Panda G (2014) A survey on nature inspired metaheuristic algorithms for partitional clustering. Swarm and Evolutionary Computation 16:1–18

    Article  Google Scholar 

  38. Nayyar A, Garg S, Gupta D, Khanna A (2018) Evolutionary computation: theory and algorithms. In: advances in swarm intelligence for optimizing problems in computer science, Chapman and Hall/CRC, pp 1–26

  39. Nayyar A, Le D-N, Nguyen NG (2018) Advances in swarm intelligence for optimizing problems in computer science. CRC Press

  40. Nayyar A, Nguyen NG (2018) Introduction to swarm intelligence. Advances in Swarm Intelligence for Optimizing Problems in Computer Science, pp 53–78

  41. Niknam T, Golestaneh F, Malekpour A (2012) Probabilistic energy and operation management of a microgrid containing wind/photovoltaic/fuel cell generation and energy storage devices based on point estimate method and self-adaptive gravitational search algorithm. Energy 43:427–437

    Article  Google Scholar 

  42. Olivas F, Valdez F, Melin P, Sombra A, Castillo O (2019) Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm. Inf Sci 476:159–175

    Article  Google Scholar 

  43. Pal R, Saraswat M (2019) Histopathological image classification using enhanced bag-of-feature with spiral biogeography-based optimization. Appl Intell, pp 1–19

  44. Pelusi D, Mascella R, Tallini L, Nayak J, Naik B, Deng Y (2020) Improving exploration and exploitation via a hyperbolic gravitational search algorithm. Knowl-Based Syst 193:105404

    Article  Google Scholar 

  45. Peterjacknaylor/drfns This repository contains the code necessary in order to reproduce the work contained in the submitted paper: segmentation of nuclei in histopathology images by deep regression of the distance map. https://github.com/PeterJackNaylor/DRFNS, (Accessed on 08/06/2020)

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  48. Rashedi E, Rashedi E, Nezamabadi-pour H (2018) A comprehensive survey on gravitational search algorithm. Swarm and Evolutionary Computation 41:141–158

    Article  Google Scholar 

  49. Rawal P, Sharma H, Sharma N (2020) Fast convergent gravitational search algorithm. In: Recent trends in communication and intelligent systems, Springer, pp 1–12

  50. Sabri NM, Puteh M, Mahmood MR (2013) A review of gravitational search algorithm. International Journal of Advances in Soft Computing and its Application 5:1–39

    Google Scholar 

  51. Sarafrazi S, Nezamabadi-Pour H, Saryazdi S (2011) Disruption: a new operator in gravitational search algorithm. Scientia Iranica 18:539–548

    Article  Google Scholar 

  52. Sharma A, Sharma A, Panigrahi BK, Kiran D, Kumar R (2016) Ageist spider monkey optimization algorithm. Swarm and Evolutionary Computation 28:58–77

    Article  Google Scholar 

  53. Shaw B, Mukherjee V, Ghoshal S (2012) A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. International Journal of Electrical Power & Energy Systems 35:21–33

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  56. Tan Z, Zhang D (2020) A fuzzy adaptive gravitational search algorithm for two-dimensional multilevel thresholding image segmentation. Journal of Ambient Intelligence and Humanized Computing, pp 1–12

  57. Thakur AS, Biswas T, Kuila P Binary quantum-inspired gravitational search algorithm-based multi-criteria scheduling for multi-processor computing systems, JOURNAL OF SUPERCOMPUTING

  58. Tsai H-C, Tyan Y-Y, Wu Y-W, Lin Y-H (2013) Gravitational particle swarm. Appl Math Comput 219:9106–9117

    MATH  Google Scholar 

  59. Wang M, Wan Y, Ye Z, Gao X, Lai X (2018) A band selection method for airborne hyperspectral image based on chaotic binary coded gravitational search algorithm. Neurocomputing 273:57–67

    Article  Google Scholar 

  60. Wang Y, Yu Y, Gao S, Pan H, Yang G (2019) A hierarchical gravitational search algorithm with an effective gravitational constant. Swarm and Evolutionary Computation 46:118–139

    Article  Google Scholar 

  61. Whitley D (1994) A genetic algorithm tutorial. Statistics and computing 4:65–85

    Article  Google Scholar 

  62. Wu Z, Yu D (2018) Application of improved bat algorithm for solar pv maximum power point tracking under partially shaded condition. Appl Soft Comput 62:101–109

    Article  Google Scholar 

  63. Yin B, Guo Z, Liang Z, Yue X (2018) Improved gravitational search algorithm with crossover. Computers & Electrical Engineering 66:505–516

    Article  Google Scholar 

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Authors and Affiliations

  1. Jaypee Institute of Information Technology, Noida, India

    Himanshu Mittal, Avinash Chandra Pandey & Raju Pal

  2. Malaviya National Institute of Technology, Jaipur, India

    Ashish Tripathi

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  1. Himanshu Mittal
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Correspondence to Ashish Tripathi.

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Mittal, H., Tripathi, A., Pandey, A.C. et al. Gravitational search algorithm: a comprehensive analysis of recent variants. Multimed Tools Appl 80, 7581–7608 (2021). https://doi.org/10.1007/s11042-020-09831-4

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