Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

An ecological space based hybrid swarm-evolutionary algorithm for software reliability model parameter estimation

  • Original Article
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

Reliability analysis of the software has attracted a lot of attention of the software developers and researchers due to rapid growing need of software in routine life. The software reliability prediction by mathematical models is entirely centered on the estimation of parameter values, and the parameter estimation of the models poses a non-differential, nonlinear, and multimodal problem. A new algorithm based on the concept of ecological space, method of differential evolution (DE) and intelligent behavior of artificial bee colony (ABC) for optimizing the parameter values has been proposed in this paper. The exploration capability in ABC algorithm has been improved by introducing the concept of ecological space. Ecological space is one of the important factors for evolution and reflects the expansion of individual bee in search space. DE technique provides the diversity of bee’s population and faster convergence. The proposed algorithm has been tested with four standard failure datasets. Proficiency of proposed algorithm is also compared with other meta-heuristic algorithms namely ABC, genetic algorithm and particle swarm optimization. Further validation of proposed algorithm is done through comparing its efficiency with hybrid partilce swarm optimization and gravitational search Algorithm. Simulation results verify that proposed hybrid algorithm is very much effective in field of software reliability estimation and would be a competitive one among meta-heuristic optimization algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 14

Similar content being viewed by others

Abbreviations

ABC:

Artificial bee colony

DE:

Differential evolution

PSO:

Particle swarm optimization

GSA:

Gravitational search algorithm

GA:

Genetic algorithm

SSE:

Sum of squared errors

MSE:

Mean square error

GO:

Goel Okummotto

PTZ:

Zhang Tang and Pham model

References

  • Ab Wahab MN, Nefti-Meziani S, Atyabi A (2015) A comprehensive review of swarm optimization algorithms. PLoS ONE 10(5):e0122827

    Google Scholar 

  • Abraham A, Jatoth RK, Rajasekhar A (2012) Hybrid differential artificial bee colony algorithm. J Comput Theor Nanosci 9(2):249–257

    Google Scholar 

  • Abu-Mouti FS, El-Hawary ME (2012) Overview of artificial bee colony (abc) algorithm and its applications. In: 2012 IEEE International Systems Conference (SysCon). IEEE, pp 1–6

  • Akay B, Karaboga D (2017) Artificial bee colony algorithm variants on constrained optimization. Int J Optim Control 7(1):98

    MathSciNet  MATH  Google Scholar 

  • Ashish T, Kapil S, Manju B (2018) Parallel bat algorithm-based clustering using mapreduce. In: Networking communication and data knowledge engineering. Springer, pp 73–82

  • Bi W, Dandy GC, Maier HR (2015) Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge. Environ Model Softw 69:370–381

    Google Scholar 

  • Chakri A, Khelif R, Benouaret M, Yang XS (2017) New directional bat algorithm for continuous optimization problems. Expert Syst Appl 69:159–175

    Google Scholar 

  • Chaudhary A, Agarwal AP, Rana A, Kumar V (2019) Crow search optimization based approach for parameter estimation of SRGMs. In: 2019 amity international conference on artificial intelligence (AICAI). IEEE, pp 583–587

  • Cheng L, Wu Xh, Wang Y (2018) Artificial flora (AF) optimization algorithm. Appl Sci 8(3):329

    Google Scholar 

  • Eberhart R, Kennedy J (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural network. Perth, Australia, pp 1942–1948

  • Goel AL, Okumoto K (1979) Time-dependent error-detection rate model for software reliability and other performance measures. IEEE Trans Reliab 28(3):206–211

    MATH  Google Scholar 

  • Haryono T, et al. (2016) Novel binary pso algorithm based optimization of transmission expansion planning considering power losses. In: IOP conference series: materials science and engineering, IOP Publishing, vol 128, p 012023

  • Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184

    MathSciNet  Google Scholar 

  • Holland J (1992) Genetic algorithm. Nat Sci Am 267(1):66–72. https://doi.org/10.1038/scientificamerican0792-66

    Article  Google Scholar 

  • Hsu CJ, Huang CY (2010) A study on the applicability of modified genetic algorithms for the parameter estimation of software reliability modeling. In: 2010 IEEE 34th annual computer software and applications conference (COMPSAC). IEEE, pp 531–540

  • IEEE (1983) IEEE standard glossary of software engineering terminology, IEEE STD. 729-19833, IEEE CS Order No. 729

  • Ismail M, Moghavvemi M, Mahlia T (2014) Genetic algorithm based optimization on modeling and design of hybrid renewable energy systems. Energy Convers Manag 85:120–130

    Google Scholar 

  • Jadon SS, Tiwari R, Sharma H, Bansal JC (2017) Hybrid artificial bee colony algorithm with differential evolution. Appl Soft Comput 58:11–24

    Google Scholar 

  • Jelinski Z, Moranda P (1972) Software reliability research. In: Statistical computer performance evaluation. Elsevier, pp 465–484

  • Jin C, Jin SW (2016) Parameter optimization of software reliability growth model with s-shaped testing-effort function using improved swarm intelligent optimization. Appl Soft Comput 40:283–291

    Google Scholar 

  • Kapur P, Younes S (1996) Modelling an imperfect debugging phenomenon in software reliability. Microelectron Reliab 36(5):645–650

    Google Scholar 

  • Karaboğa D, Baştürk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. LNCS Adv Soft Comput Found Fuzzy Logic Soft Comput 4529:789–798

    MATH  Google Scholar 

  • Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697

    Google Scholar 

  • Karaboga D, Ozturk C (2011) A novel clustering approach: artificial bee colony (ABC) algorithm. Appl Soft Comput 11(1):652–657

    Google Scholar 

  • Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mechanica 213(3–4):267–289

    MATH  Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Google Scholar 

  • Kumar V, Mathur P, Sahni R, Anand M (2016a) Two-dimensional multi-release software reliability modeling for fault detection and fault correction processes. Int J Reliab Qual Saf Eng 23(03):1640002

    Google Scholar 

  • Kumar V, Sahni R, Shrivastava A (2016b) Two-dimensional multi-release software modelling with testing effort, time and two types of imperfect debugging. Int J Reliab Saf 10(4):368–388

    Google Scholar 

  • Li C, Chen Y (2006) Application of improved differential evolution calculation method based on contious power flow to analyasis of marginal static voltage stability. Power Eng 26:756–760

    Google Scholar 

  • Li Y, Wang Y, Li B (2013) A hybrid artificial bee colony assisted differential evolution algorithm for optimal reactive power flow. Int J Electr Power Energy Syst 52:25–33

    Google Scholar 

  • Lim WH, Isa NAM (2014) Teaching and peer-learning particle swarm optimization. Appl Soft Comput 18:39–58

    Google Scholar 

  • Littlewood B, Sofer A (1987) A bayesian modification to the Jelinski–Moranda software reliability growth model. Softw Eng J 2(2):30–41

    Google Scholar 

  • Liu F, Zhou Z (2014) An improved QPSO algorithm and its application in the high-dimensional complex problems. Chemom Intell Lab Syst 132:82–90

    Google Scholar 

  • Mahapatra G, Roy P (2012) Modified Jelinski–Moranda software reliability model with imperfect debugging phenomenon. Int J Comput Appl 48(18):38–46

    Google Scholar 

  • Majumdar R, Kapur P, Khatri SK, Shrivastava A (2019) Effort-based software release and testing stop time decisions. Int J Reliab Saf 13(3):179–193

    Google Scholar 

  • Malhotra R, Negi A (2013) Reliability modeling using particle swarm optimization. Int J Syst Assur Eng Manag 4(3):275–283

    Google Scholar 

  • Mirjalili S, Wang GG, Coelho LdS (2014) Binary optimization using hybrid particle swarm optimization and gravitational search algorithm. Neural Comput Appl 25(6):1423–1435

    Google Scholar 

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

  • Musa JD, Okumoto K (1984) A logarithmic Poisson execution time model for software reliability measurement. In: Proceedings of the 7th international conference on software engineering. IEEE Press, pp 230–238

  • Myung IJ (2003) Tutorial on maximum likelihood estimation. J Math Psychol 47(1):90–100

    MathSciNet  MATH  Google Scholar 

  • Ohba M (1984) Inflection s-shaped software reliability growth model. In: Stochastic models in reliability theory. Springer, pp 144–162

  • Pachauri B, Kumar A, Dhar J (2014) Software reliability growth modeling with dynamic faults and release time optimization using GA and MAUT. Appl Math Comput 242:500–509

    Google Scholar 

  • Pham H (2006) Springer handbook of engineering statistics. Springer, Berlin

    MATH  Google Scholar 

  • Pham T, Pham H (2019) A generalized software reliability model with stochastic fault-detection rate. Ann Oper Res 277(1):83–93

    MathSciNet  MATH  Google Scholar 

  • Rana R, Staron M, Berger C, Hansson J, Nilsson M, Torner F (2013) Comparing between maximum likelihood estimator and non-linear regression estimation procedures for NHPP software reliability growth modelling. In: 2013 joint conference of the 23rd international workshop on software measurement and the 2013 eighth international conference on software process and product measurement (IWSM-MENSURA). IEEE, pp 213–218

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Google Scholar 

  • Roy P, Mahapatra G, Dey K (2014) An NHPP software reliability growth model with imperfect debugging and error generation. Int J Reliab Qual Saf Eng 21(02):1450008

    Google Scholar 

  • Sahney S, Benton MJ, Ferry PA (2010) Links between global taxonomic diversity, ecological diversity and the expansion of vertebrates on land. Biol Lett 6(4):544–547

    Google Scholar 

  • Santosh KG (2015) Numerical methods for engineer, 3rd edn. Age New International, New Delhi

    Google Scholar 

  • Sayed GI, Darwish A, Hassanien AE (2018) A new chaotic multi-verse optimization algorithm for solving engineering optimization problems. J Exp Theor Artif Intell 30(2):293–317

    Google Scholar 

  • Shah-Hosseini H (2011) Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation. Int J Comput Sci Eng 6(1–2):132–140

    Google Scholar 

  • Shayeghi H, Mahdavi M, Bagheri A (2010) Discrete PSO algorithm based optimization of transmission lines loading in TNEP problem. Energy Convers Manag 51(1):112–121

    Google Scholar 

  • Sheta A, Al-Salt J (2007) Parameter estimation of software reliability growth models by particle swarm optimization. Management 7:14

    Google Scholar 

  • Smidts C, Stutzke M, Stoddard RW (1998) Software reliability modeling: an approach to early reliability prediction. IEEE Trans Reliab 47(3):268–278

    Google Scholar 

  • Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  • Tripathi AK, Sharma K, Bala M (2018a) Dynamic frequency based parallel k-bat algorithm for massive data clustering (DFBPKBA). Int J Syst Assur Eng Manag 9(4):866–874

    Google Scholar 

  • Tripathi AK, Sharma K, Bala M (2018b) A novel clustering method using enhanced grey wolf optimizer and mapreduce. Big Data Res 14:93–100

    Google Scholar 

  • Xiang J, Machida F, Tadano K, Maeno Y (2015) An imperfect fault coverage model with coverage of irrelevant components. IEEE Trans Reliab 64(1):320–332

    Google Scholar 

  • Yamada S, Osaki S (1985) Software reliability growth modeling: models and applications. IEEE Trans Softw Eng 12:1431–1437

    Google Scholar 

  • Yamada S, Ohba M, Osaki S (1983) S-shaped reliability growth modeling for software error detection. IEEE Trans Reliab 32(5):475–484

    Google Scholar 

  • Yamada S, Ohba M, Osaki S (1984) S-shaped software reliability growth models and their applications. IEEE Trans Reliab 33(4):289–292

    Google Scholar 

  • Yamada S, Ohtera H, Narihisa H (1986) Software reliability growth models with testing-effort. IEEE Trans Reliab 35(1):19–23

    Google Scholar 

  • Yamada S, Ohtera H, Ohba M (1992) Testing-domain dependent software reliability models. Comput Math Appl 24(1–2):79–86

    MathSciNet  MATH  Google Scholar 

  • Yang XS (2010b) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74

  • Yang XS (2012a) Flower pollination algorithm for global optimization. In: International conference on unconventional computing and natural computation. Springer, pp 240–249

  • Yang XS (2012b) Nature-inspired mateheuristic algorithms: success and new challenges. arXiv preprint arXiv:12116658

  • Yang XS (2010a) Nature-inspired metaheuristic algorithms. Luniver Press, Bristol

    Google Scholar 

  • Zhang X, Teng X, Pham H (2003) Considering fault removal efficiency in software reliability assessment. IEEE Trans Syst Man Cybern Part A Syst Hum 33(1):114–120

    Google Scholar 

  • Zhu G, Kwong S (2010) Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl Math Comput 217(7):3166–3173

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Maharaja Surajmal Institute, Delhi Technological University, Delhi, 110042, India

    Sangeeta

  2. Department of Information Technology, Delhi Technological University, Delhi, 110042, India

    Kapil Sharma

  3. Department of Computer Science, Indraprastha College for Women, Delhi University, Delhi, 110054, India

    Manju Bala

Authors
  1. Sangeeta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kapil Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manju Bala
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kapil Sharma.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with animals performed by any of the authors. This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sangeeta, Sharma, K. & Bala, M. An ecological space based hybrid swarm-evolutionary algorithm for software reliability model parameter estimation. Int J Syst Assur Eng Manag 11, 77–92 (2020). https://doi.org/10.1007/s13198-019-00926-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-019-00926-2

Keywords

Search

Navigation