Abstract
Software reliability growth model (SRGM) with modified testing-effort function (TEF) is a function to evaluate and foresee the parameters of the data. Reliability of software is portrayed as the distinct possibility that for a predefined time, a software package will continue to run on an advance domain without frustration. SRGM utilized a few optimization procedure algorithms to advance the parameters by bifurcating them into a few stages however to upgrade the technique by using all of the parameters at the same time, the algorithm utilized is the chaotic grey wolf optimization algorithm (CGWO). CGWO is an advanced heuristic system for portraying the execution by achieving complex parameter optimization and designing application issues. Different parametric reliabilities rely upon the attributes or characteristics of the data. The parameters are predicted using the Pham–Zhang (PZ) model. Tandem computer software dataset DS1 and DS2 are used to compare the predicted parameter of SRGM obtained by Pham–Zhang (PZ) model using testing effort functions (TEFs) based on the evaluation metrics mean square error (MSE), relative error (RE) and coefficient of determination (R2). To enhance the reliability of SRGM, the parameters of SRGM estimated using TEF and enhanced using chaotic maps to improve search performance. By using the constrained benchmark functions the results of chaotic maps are obtained. Based on the chaotic graph results, the Chebyshev graph shows a good convergence rate of 78%. Overall, 86% of the results revealed an association between the choice variable and fitness criteria for CGWO. In the SRGM using CGWO, the expected result is completely mechanized and does not require any client necessity.
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Abd-Elkader AG, Saleh SM, Eiteba MM (2018) A passive islanding detection strategy for multi-distributed generations. Int J Electr Power Energy Syst 99:146–155. https://doi.org/10.1016/j.ijepes.2018.01.005
Cascone A, Manzo R, Piccoli B, Rarità L (2008) Optimization versus randomness for car traffic regulation. Phys Rev E 78(2):026113. https://doi.org/10.1103/PhysRevE.78.026113
Cheng M, Wu G, Yuan M, Wan H (2016) Semi-supervised software defect prediction using task-driven dictionary learning. Chin J Electron 25(6):1089–1096. https://doi.org/10.1049/cje.2016.08.034
Choudhary A, Baghel A, Sangwan O (2017) Efficient parameter estimation of software reliability growth models using harmony search. IET Softw 11(6):286–291. https://doi.org/10.1049/iet-sen.2015.0171
Cutolo A, De Nicola C, Manzo R, Rarità L (2012) Optimal paths on urban networks using travelling times prevision. Model Simul Eng. https://doi.org/10.1155/2012/564168
D’Apice C, Manzo R, Rarità L (2011) Splitting of traffic flows to control congestion in special events. Int J Math Math Sci. https://doi.org/10.1155/2011/563171
Decoderz (2019) Behavior of grey wolf optimization (GWO) algorithm using meta-heuristics method. Transpire Online. https://transpireonline.blog/2019/08/09/behavior-of-grey-wolf-optimization-gwo-algorithm-using-meta-heuristics-method/. Accessed Sept 2010
Diwaker C, Tomar P, Poonia R, Singh V (2018) Prediction of software reliability using bio inspired soft computing techniques. J Med Syst. https://doi.org/10.1007/s10916-018-0952-3
Fera M, Fruggiero F, Lambiase A, Macchiaroli R, Todisco V (2018) A modified genetic algorithm for time and cost optimization of an additive manufacturing single-machine scheduling. Int J Ind Eng Comput 9(4):423–438. https://doi.org/10.5267/j.ijiec.2018.1.001
Jin C, Jin S (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. https://doi.org/10.1016/j.asoc.2015.11.041
Kim T, Lee K, Baik J (2015) An effective approach to estimating the parameters of software reliability growth models using a real-valued genetic algorithm. J Syst Softw 102:134–144. https://doi.org/10.1016/j.jss.2015.01.001
Kohli M, Arora S (2018) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Des Eng 5(4):458–472. https://doi.org/10.1016/j.jcde.2017.02.005
Lakshmanan I, Ramasamy S (2015) An artificial neural-network approach to software reliability growth modeling. Procedia Comput Sci 57:695–702. https://doi.org/10.1016/j.procs.2015.07.450
Li Q, Li H, Lu M (2015) Incorporating S-shaped testing-effort functions into NHPP software reliability model with imperfect debugging. J Syst Eng Electron 26(1):190–207. https://doi.org/10.1109/JSEE.2015.00024
Li Z, Jing X, Zhu X (2018) Progress on approaches to software defect prediction. IET Softw 12(3):161–175. https://doi.org/10.1049/iet-sen.2017.0148
Mallikharjuna K, Anuradha K (2015) An efficient method for software reliability growth model selection using modified particle swarm optimization technique. Int Rev Comput Softw 10(12):1169. https://doi.org/10.15866/irecos.v10i12.8089
Mirjalili S, Mirjalili S, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Packianather MS, Yuce B, Mastrocinque E, Fruggiero F, Pham DT, Lambiase A (2014) Novel Genetic Bees Algorithm applied to single machine scheduling problem. In: 2014 World Automation Congress (WAC). IEEE, pp 906–911. https://doi.org/10.1109/wac.2014.6936194
Rarità L, D’Apice C, Piccoli B, Helbing D (2010) Sensitivity analysis of permeability parameters for flows on Barcelona networks. J Differ Equ 249(12):3110–3131. https://doi.org/10.1016/j.jde.2010.09.006
Riaz S, Arshad A, Jiao L (2018) Rough noise-filtered easy ensemble for software fault prediction. IEEE Access 6:46886–46899. https://doi.org/10.1049/iet-sen.2014.0108
Roy P, Mahapatra G, Dey K (2017) An efficient particle swarm optimization-based neural network approach for software reliability assessment. Int J Reliab Qual Saf Eng 24(04):1750019. https://doi.org/10.1109/ACCESS.2018.2865383
Singh L, Tripathi A, Vinod G (2015) Approach for parameter estimation in Markov model of software reliability for early prediction: a case study. IET Softw 9(3):65–75. https://doi.org/10.1109/TNSM.2018.2848105
Vizarreta P, Trivedi K, Helvik B, Heegaard P, Blenk A, Kellerer W, Mas Machuca C (2018) Assessing the maturity of SDN controllers with software reliability growth models. IEEE Trans Netw Serv Manag 15(3):1090–1104. https://doi.org/10.1109/TR.2018.2804922
Wu F, Jing X, Sun Y, Sun J, Huang L, Cui F, Sun Y (2018) Cross-project and within-project semisupervised software defect prediction: a unified approach. IEEE Trans Reliab 67(2):581–597. https://doi.org/10.1109/TR.2018.2804922
Yang X, Tang K, Yao X (2015) A learning-to-rank approach to software defect prediction. IEEE Trans Reliab 64(1):234–246. https://doi.org/10.1016/j.asoc.2016.08.006
Yazdanbakhsh O, Dick S, Reay I, Mace E (2016) On deterministic chaos in software reliability growth models. Appl Soft Comput 49:1256–1269. https://doi.org/10.1007/s12293-017-0247-0
Yu Y, Gao S, Cheng S, Wang Y, Song S, Yuan F (2017) CBSO: a memetic brain storm optimization with chaotic local search. Memet Comput 10(4):353–367. https://doi.org/10.1109/TR.2016.2570557
Zeephongsekul P, Jayasinghe C, Fiondella L, Nagaraju V (2016) Maximum-likelihood estimation of parameters of NHPP software reliability models using expectation conditional maximization algorithm. IEEE Trans Reliab 65(3):1571–1583. https://doi.org/10.1109/TR.2016.2570557
Zhu M, Pham H (2018) A two-phase software reliability modeling involving with software fault dependency and imperfect fault removal. Comput Lang Syst Struct 53:27–42. https://doi.org/10.1016/j.cl.2017.12.002
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Dhavakumar, P., Gopalan, N.P. An efficient parameter optimization of software reliability growth model by using chaotic grey wolf optimization algorithm. J Ambient Intell Human Comput 12, 3177–3188 (2021). https://doi.org/10.1007/s12652-020-02476-z
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DOI: https://doi.org/10.1007/s12652-020-02476-z