Abstract
Particle swarm optimization (PSO) suffers from delayed convergence and stagnation in the local optimal solution, as do most meta-heuristic algorithms. This study proposes a time-based leadership particle swarm-based Salp (TPSOSA) to address the PSO's limitations. The TPSOSA is a novel search technique that addresses population diversity, an imbalance between exploitation and exploration, and the premature convergence of the PSO algorithm. Hybridization in TPSOSA is divided into two stages: The PSO hierarchy of leaders and followers is first represented as a time-varying dynamic structure. Because we need much exploration at the beginning and many exploitative steps at the end, this method raises the number of leaders while decreasing the number of follower particles linearly. In the time-varying form of the PSO (TPSOSA), unlike the PSO, the number of leaders and followers changes over time. PSO's robust search strategy is used to update the leaders' positions. Second, the SSA's powerful exploitation is utilized to update the followers' swarm population position. The purpose of tweaking the particle swarm optimizer algorithm is to aid the fundamental method in avoiding premature convergence and quickly directing the search to the most promising likely search space. The proposed TPSOSA method is tested using the CEC 2017 benchmark, seven CEC2008lsgo test functions with 200, 500, and 1000 decision variables, and 19 datasets (including three high-dimensional datasets and the NSL-KDD Dataset for Intrusion Detection System). In each experiment, TPSOSA is compared to various state-of-the-art metaheuristics methods. Friedman and Wilcoxon rank-sum statistical tests are also used to analyze the data. Experimental data and statistical tests show that the TPSOSA algorithm is very competitive and often superior to the algorithms used in the studies. According to the results, TPSOSA can also find an optimal feature subset that enhances classification accuracy while reducing the number of features employed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- \(TPSOSA\) :
-
Time-based leadership particle swarm-based Salp
- \(IDS\) :
-
Intrusion detection systems
- \(DoS\) :
-
Denial of service
- \(U2R\) :
-
User to root
- \(R2L\) :
-
Remote to local
- \(PSO\) :
-
Particle swarm optimization
- \(SSA\) :
-
Salp swarm optimization
- \(CC\) :
-
Cooperative coevolving
- \(MLCC\) :
-
Multilevel cooperative coevolving technique
- \(LSGO\) :
-
Large-scale global optimization
- \(FEs\) :
-
Function evaluations
- \(pbest\) :
-
Personal best
- \(gbest\) :
-
Global best
- \(x\) :
-
Solution vector
- \({v}_{i}^{t}\) :
-
The velocity of individual \(i\) at iteration \(t\)
- \(w\) :
-
Weighting (inertia) function
- \({c}_{1}\), \({c}_{2}\) :
-
The personal and social learning factors
- \({r}_{1},{r}_{2}\) :
-
Random numbers in the interval of [0,1]
- \({x}_{i}^{t}\) :
-
The current particle \(i\) position at iteration \(t\)
- \(OE\) :
-
Overall effectiveness
- \(W/T/L\) :
-
The number of wins (W), ties (T), and losses (L) for each algorithm
- \(TF\) :
-
Transfer function
- \({z}_{f}\), \({\widetilde{z}}_{fj}\) :
-
The normalized feature value ranged between [0–1]
- \(\mathrm{max}\left({z}_{f }\right),\mathrm{ min}({z}_{f })\) :
-
The maximum and minimum values of the \({f}\text{th}\) (numeric) feature
- \(\left|F\right|\) :
-
The size of identified feature subset
- \(TP\) :
-
True positive rate
- \(TN\) :
-
True negative rate
- \(ROC\) :
-
The area under the receiver operating characteristic
- \({x}_{j}^{1}\) :
-
The chain Salps leader position with \(\mathrm{j}\)th dimension
- \({\mathrm{F}}_{\mathrm{j}}\) :
-
The food position with \(\mathrm{j}\)th dimension
- \({\mathrm{ub}}_{\mathrm{j}}\) :
-
The upper bound
- \({\mathrm{lb}}_{\mathrm{j}}\) :
-
The lower bound
- \({\mathrm{r}}_{2}\), \({\mathrm{r}}_{3}\) :
-
Two scalars chosen at random from the range \([\mathrm{0,1}]\)
- t:
-
The current iteration
- \(Ma{x}_{iteration}\) :
-
The maximum number of iterations
- \({s}_{0}\) :
-
The initial speed
- \(N\) :
-
The population size
- \(L\) :
-
The number of leaders in each iteration
- \({n}_{o}\) :
-
The number of objectives
- \(dim\) :
-
The problem dimension
- \({O}_{f}\) :
-
The objective function
- \(Min\) :
-
Minimum
- \(Max\) :
-
Maximum
- \(Avg\) :
-
Average
- \(std\) :
-
Standard deviation
- \(Med\) :
-
Median
- \({F}_{f}\) :
-
Non-parametric Friedman test
- \(k\) :
-
The number of swarm intelligence algorithms
- \(Rj\) :
-
The average rank of algorithm j
- \({X}_{Binary} \) :
-
The solution to the feature selection problem
- \({N}_{random}\) :
-
Random number used as the threshold
- \(\left|T\right|\) :
-
The total number of features
- \(Err \left(D\right)\) :
-
The classifier error rate
- \(FP\) :
-
False positive rate
- \(FN\) :
-
False negative rate
- \(Acc\) :
-
Classification accuracy
References
Abbassi R, Abbassi A, Heidari AA, Mirjalili S (2019) An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers Manage 179:362–372. https://doi.org/10.1016/j.enconman.2018.10.069
Abdel-Basset M, El-Shahat D, El-henawy I et al (2020) A new fusion of grey wolf optimizer algorithm with a two-phase mutation for feature selection. Expert Syst Appl 139:112824. https://doi.org/10.1016/j.eswa.2019.112824
Abualigah L, Yousri D, Abd Elaziz M et al (2021) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250. https://doi.org/10.1016/J.CIE.2021.107250
Acharya N, Singh S (2018) An IWD-based feature selection method for intrusion detection system. Soft Comput 22:4407–4416. https://doi.org/10.1007/s00500-017-2635-2
Aggarwal P, Sharma SK (2015) Analysis of KDD dataset attributes—class wise for intrusion detection. Procedia Comput Sci 57:842–851. https://doi.org/10.1016/j.procs.2015.07.490
Ahmed S, Mafarja M, Faris H, Aljarah I (2018) Feature selection using salp swarm algorithm with chaos. In: ACM international conference proceeding series. Association for Computing Machinery, New York, New York, USA, pp 65–69
Ait Tchakoucht T, Ezziyyani M (2018) Building a fast intrusion detection system for high-speed-networks: probe and dos attacks detection. Procedia Comput Sci 127:521–530. https://doi.org/10.1016/j.procs.2018.01.151
Akbari R, Ziarati K (2011) A cooperative approach to bee swarm optimization. J Inf Sci Eng 27:799–818
Aljawarneh S, Aldwairi M, Yassein MB (2018) Anomaly-based intrusion detection system through feature selection analysis and building hybrid efficient model. J Comput Sci 25:152–160. https://doi.org/10.1016/j.jocs.2017.03.006
Awad NH, Ali MZ, Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. In: 2017 IEEE Congr Evol Comput CEC 2017—Proc, pp 372–379. https://doi.org/10.1109/CEC.2017.7969336
Bala R (2019) A review on KDD Cup99 and Nsl-Kdd dataset. Int J Adv Res Comput Sci 10:64–67. https://doi.org/10.26483/ijarcs.v10i2.6395
Balasaraswathi VR, Sugumaran M, Hamid Y (2017) Feature selection techniques for intrusion detection using non-bio-inspired and bio-inspired optimization algorithms. J Commun Inf Netw 2:107–119. https://doi.org/10.1007/s41650-017-0033-7
Berchuck A, Iversen ES, Luo J et al (2009) Microarray analysis of early stage serous ovarian cancers shows profiles predictive of favorable outcome. Clin Cancer Res 15:2448–2455. https://doi.org/10.1158/1078-0432.CCR-08-2430
Bharani B, Praveen Prakash A (2016) Fuzzy optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming. Glob J Pure Appl Math 12:170–175
Boubezoul A, Paris S (2012) Application of global optimization methods to model and feature selection. Pattern Recognit 45:3676–3686. https://doi.org/10.1016/j.patcog.2012.04.015
Bradley AP (1997) The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognit 30:1145–1159. https://doi.org/10.1016/S0031-3203(96)00142-2
Brest J, Maučec MS (2011) Self-adaptive differential evolution algorithm using population size reduction and three strategies. Soft Comput 15:2157–2174. https://doi.org/10.1007/s00500-010-0644-5
Chang WD (2015) A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Appl Soft Comput J 33:170–182. https://doi.org/10.1016/j.asoc.2015.04.002
Chegini SN, Bagheri A, Najafi F (2018) PSOSCALF: a new hybrid PSO based on Sine Cosine Algorithm and Levy flight for solving optimization problems. Appl Soft Comput J 73:697–726. https://doi.org/10.1016/j.asoc.2018.09.019
Chen H, Zhu Y, Hu K, He X (2010) Hierarchical swarm model: a new approach to optimization. Discr Dyn Nat Soc. https://doi.org/10.1155/2010/379649
Chen H, Jiang W, Li C, Li R (2013) A heuristic feature selection approach for text categorization by using chaos optimization and genetic algorithm. Math Probl Eng. https://doi.org/10.1155/2013/524017
Cheng R, Jin Y (2015) A competitive swarm optimizer for large scale optimization. IEEE Trans Cybern 45(2):191–204
Colorni A, Dorigo M, Maniezzo V (1991) Distributed Optimization by ant colonies. In: Proceedings of the first European conference on artificial life 142:134–142
Dagal I, Akın B, Akboy E (2022a) MPPT mechanism based on novel hybrid particle swarm optimization and salp swarm optimization algorithm for battery charging through simulink. Sci Rep 12(1):1–17. https://doi.org/10.1038/s41598-022-06609-6
Dagal I, Akın B, Akboy E (2022b) A novel hybrid series salp particle Swarm optimization (SSPSO) for standalone battery charging applications. Ain Shams Eng J 13:101747. https://doi.org/10.1016/J.ASEJ.2022.101747
Dagal I, Akın B, Akboy E (2022c) Improved salp swarm algorithm based on particle swarm optimization for maximum power point tracking of optimal photovoltaic systems. Int J Energy Res 46:8742–8759. https://doi.org/10.1002/ER.7753
Dhanabal L, Shantharajah SP (2015) A study on NSL-KDD dataset for intrusion detection system based on classification algorithms. Int J Adv Res Comput Commun Eng 4:446–452
Eappen G, Shankar T (2020) Hybrid PSO-GSA for energy efficient spectrum sensing in cognitive radio network. Phys Commun 40:101091. https://doi.org/10.1016/j.phycom.2020.101091
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science. IEEE, pp 39–43
Eberhart RC, Shi Y (2001) Particle swarm optimization: developments, applications and resources. Proc IEEE Conf Evol Comput ICEC 1:81–86. https://doi.org/10.1109/cec.2001.934374
edu/ml AF ics. uci., 2010 undefined UCI machine learning repository. ci.nii.ac.jp
Ehteram M, Othman FB, Yaseen ZM et al (2018) Improving the Muskingum flood routing method using a hybrid of particle swarm optimization and bat algorithm. Water (switzerland). https://doi.org/10.3390/w10060807
Fan Y, Wang P, Heidari AA et al (2020) Boosted hunting-based fruit fly optimization and advances in real-world problems. Expert Syst Appl 159:113502. https://doi.org/10.1016/j.eswa.2020.113502
Faris H, Mafarja MM, Heidari AA et al (2018) An efficient binary Salp swarm algorithm with crossover scheme for feature selection problems. Knowl-Based Syst 154:43–67. https://doi.org/10.1016/j.knosys.2018.05.009
Faris H, Heidari AA, Al-Zoubi AM et al (2020) Time-varying hierarchical chains of salps with random weight networks for feature selection. Expert Syst Appl 140:112898. https://doi.org/10.1016/j.eswa.2019.112898
Frank A, Asuncion A (2010) {UCI} Machine learning repository. 15:2. http://archive.ics.uci.edu/ml
Ganapathy S, Kulothungan K, Muthurajkumar S et al (2013) Intelligent feature selection and classification techniques for intrusion detection in networks: a survey. Eurasip J Wirel Commun Netw. https://doi.org/10.1186/1687-1499-2013-271
Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35. https://doi.org/10.1007/s00366-011-0241-y
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. SIMULATION 76:60–68. https://doi.org/10.1177/003754970107600201
Ghasemi M, Aghaei J, Hadipour M (2017) New self-organising hierarchical PSO with jumping time-varying acceleration coefficients. Electron Lett 53:1360–1362. https://doi.org/10.1049/el.2017.2112
Ghasemi M, Akbari E, Rahimnejad A et al (2019) Phasor particle swarm optimization: a simple and efficient variant of PSO. Soft Comput 23:9701–9718. https://doi.org/10.1007/s00500-018-3536-8
Ghosh P, Zafar H, Das S, Abraham A (2011) Hierarchical dynamic neighborhood based particle swarm optimization for global optimization. In: 2011 IEEE Congr Evol Comput CEC, pp 757–764. https://doi.org/10.1109/CEC.2011.5949695
Glover F (1989) Tabu search—part I. ORSA J Comput 1:190–206. https://doi.org/10.1287/ijoc.1.3.190
Goel S, Williams K, Dincelli E (2017) Got phished? Internet security and human vulnerability. J Assoc Inf Syst 18:22–44. https://doi.org/10.17705/1jais.00447
Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3:95–99. https://doi.org/10.1023/A:1022602019183
Gupta S, Deep K (2019) A novel random walk grey wolf optimizer. Swarm Evol Comput 44:101–112. https://doi.org/10.1016/j.swevo.2018.01.001
Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol Comput 11:1–18. https://doi.org/10.1162/106365603321828970
Hegazy AE, Makhlouf MA, El-Tawel GS (2019) Feature selection using chaotic salp swarm algorithm for data classification. Arab J Sci Eng 44:3801–3816. https://doi.org/10.1007/s13369-018-3680-6
Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872. https://doi.org/10.1016/J.FUTURE.2019.02.028
Hou Z, Zhou Y, Li H (2008) Multimodal function optimization based on improved hybrid particle swarm optimization. J Inf Comput Sci 5:2317–2323
Iacca G, dos Santos Junior VC, Veloso de Melo V (2021) An improved Jaya optimization algorithm with Lévy flight. Expert Syst Appl 165:113902. https://doi.org/10.1016/j.eswa.2020.113902
Jiang Y, Wu Q, Zhu S, Zhang L (2022) Orca predation algorithm: a novel bio-inspired algorithm for global optimization problems. Expert Syst Appl 188:116026. https://doi.org/10.1016/J.ESWA.2021.116026
Kabir MM, Shahjahan M, Murase K (2011) A new local search based hybrid genetic algorithm for feature selection. Neurocomputing 74:2914–2928. https://doi.org/10.1016/j.neucom.2011.03.034
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471. https://doi.org/10.1007/s10898-007-9149-x
Ke T, Xiaodong L et al (2010) Benchmark functions for the CEC’2013 special session and competition on large-scale global optimization. Tech report, Univ Sci Technol China, pp 1–21
Khan JA, Jain N (2016) A survey on intrusion detection systems and classification techniques. IJSRSET, India 2:202–208
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680. https://doi.org/10.1126/science.220.4598.671
Kohavi R, John GH (1997) Wrappers for feature subset selection. Artif Intell 97:273–324. https://doi.org/10.1016/s0004-3702(97)00043-x
LaTorre A, Muelas S, Peña JM (2011) A MOS-based dynamic memetic differential evolution algorithm for continuous optimization: a scalability test. Soft Comput 15:2187–2199. https://doi.org/10.1007/s00500-010-0646-3
Li X, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evol Comput 16:210–224. https://doi.org/10.1109/TEVC.2011.2112662
Li C, Yang S (2008) Fast multi-swarm optimization for dynamic optimization problems. In: Proc—4th Int Conf Nat Comput ICNC 2008, vol 7, pp 624–628. https://doi.org/10.1109/ICNC.2008.313
Li S, Chen H, Wang M et al (2020) Slime mould algorithm: a new method for stochastic optimization. Future Gener Comput Syst 111:300–323. https://doi.org/10.1016/j.future.2020.03.055
Liang JJ, Suganthan PN (2005) Dynamic multi-swarm particle swarm optimizer. In: Proc—2005 IEEE Swarm Intell Symp SIS 2005, pp 127–132. https://doi.org/10.1109/SIS.2005.1501611
Liang JJ, Suganthan PN (2006) Dynamic multi-swarm particle swarm optimizer with a novel constraint-handling mechanism. In: 2006 IEEE Congr Evol Comput CEC 2006, pp 9–16. https://doi.org/10.1109/cec.2006.1688284
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10:281–295. https://doi.org/10.1109/TEVC.2005.857610
Lim WH, Mat Isa NA (2014) Particle swarm optimization with adaptive time-varying topology connectivity. Appl Soft Comput J 24:623–642. https://doi.org/10.1016/j.asoc.2014.08.013
Liu B, Wang L, Jin YH et al (2005) Improved particle swarm optimization combined with chaos. Chaos, Solitons Fractals 25:1261–1271. https://doi.org/10.1016/j.chaos.2004.11.095
Liu H, Motoda H (1998) Feature selection for knowledge discovery and data mining. Springer, Boston
Liu H, Yu L (2005) Toward integrating feature selection algorithms for classification and clustering. IEEE Trans Knowl Data Eng 17:491–502. https://doi.org/10.1109/TKDE.2005.66
Liu J, Tang K (2013) Scaling up covariance matrix adaptation evolution strategy using cooperative coevolution. In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics), pp 350–357
Loshchilov I (2017) LM-CMA: an alternative to L-BFGS for large-scale black Box optimization. Evol Comput 25:143–171. https://doi.org/10.1162/EVCO_a_00168
Lourenço HR, Martin OC, Stützle T (2019) Iterated local search: framework and applications. In: International series in operations research and management science. Springer, New York LLC, pp 129–168
Mafarja M, Abdullah S (2015) A fuzzy record-to-record travel algorithm for solving rough set attribute reduction. Int J Syst Sci 46:503–512. https://doi.org/10.1080/00207721.2013.791000
Mahadevan EG (2009) Ammonium nitrate explosives for civil applications: slurries, emulsions and ammonium nitrate fuel oils. Wiley, Hoboken
Masdari M, Tahani M, Naderi MH, Babayan N (2019) Optimization of airfoil based savonius wind turbine using coupled discrete vortex method and salp swarm algorithm. J Clean Prod 222:47–56. https://doi.org/10.1016/j.jclepro.2019.02.237
Mendes R, Kennedy J, Neves J (2004) The fully informed particle swarm: Simpler, maybe better. IEEE Trans Evol Comput 8:204–210. https://doi.org/10.1109/TEVC.2004.826074
Miller NJ, Aliasgari M (2018) Benchmarks for evaluating anomaly based intrusion detection solutions. Int J Netw Secur Appl. https://doi.org/10.5121/ijnsa.2018.10501
Mirjalili S, Hashim SZM (2010) A new hybrid PSOGSA algorithm for function optimization. In: Proc ICCIA 2010–2010 Int Conf Comput Inf Appl, pp 374–377. https://doi.org/10.1109/ICCIA.2010.6141614
Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput 9:1–14. https://doi.org/10.1016/j.swevo.2012.09.002
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf Optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Mirjalili S, Gandomi AH, Mirjalili SZ et al (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002
Mirjalili SZ, Mirjalili S, Saremi S et al (2018) Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48:805–820. https://doi.org/10.1007/s10489-017-1019-8
Nadimi-Shahraki MH, Taghian S, Mirjalili S, Faris H (2020) MTDE: an effective multi-trial vector-based differential evolution algorithm and its applications for engineering design problems. Appl Soft Comput J 97:106761. https://doi.org/10.1016/j.asoc.2020.106761
Niu B, Li L (2008) A novel PSO-DE-based hybrid algorithm for global optimization. Lect Notes Comput Sci (including Subser Lect Notes Artif Intell Lect Notes Bioinformatics) 5227 LNAI:156–163. https://doi.org/10.1007/978-3-540-85984-0_20
Niu B, Zhu Y, He X (2005) Multi-population cooperative particle swarm optimization. Lect Notes Comput Sci (including Subser Lect Notes Artif Intell Lect Notes Bioinformatics) 3630 LNAI:874–883. https://doi.org/10.1007/11553090_88
Niu B, Zhu Y, He X, Wu H (2007) MCPSO: a multi-swarm cooperative particle swarm optimizer. Appl Math Comput 185:1050–1062. https://doi.org/10.1016/j.amc.2006.07.026
Panda N, Majhi SK (2020) Improved Salp swarm algorithm with space transformation search for training neural network. Arab J Sci Eng 45:2743–2761. https://doi.org/10.1007/s13369-019-04132-x
Parsopoulos KE, Vrahatis MN (2019) UPSO: a unified particle swarm optimization scheme. Int Conf Comput Methods Sci Eng 2004 (ICCMSE 2004) 868–873. https://doi.org/10.1201/9780429081385-222
Paulauskas N, Auskalnis J (2017) Analysis of data pre-processing influence on intrusion detection using NSL-KDD dataset. In: 2017 Open Conf Electr Electron Inf Sci eStream 2017—Proc Conf. https://doi.org/10.1109/eStream.2017.7950325
Peng CC, Chen CH (2015) Compensatory neural fuzzy network with symbiotic particle swarm optimization for temperature control. Appl Math Model 39:383–395. https://doi.org/10.1016/j.apm.2014.05.040
Pitakaso R, Sethanan K, Jamrus T (2020) Hybrid PSO and ALNS algorithm for software and mobile application for transportation in ice manufacturing industry 3.5. Comput Ind Eng 144:106461. https://doi.org/10.1016/j.cie.2020.106461
Potter MA, Jong KA (1994) A cooperative coevolutionary approach to function optimization. In: Lecture notes in computer science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer, pp 249–257
Qais MH, Hasanien HM, Alghuwainem S (2019) Enhanced salp swarm algorithm: application to variable speed wind generators. Eng Appl Artif Intell 80:82–96. https://doi.org/10.1016/j.engappai.2019.01.011
Qaraad M, Amjad S, Hussein NK, Elhosseini MA (2022) Addressing constrained engineering problems and feature selection with a time-based leadership salp-based algorithm with competitive learning. J Comput Des Eng. https://doi.org/10.1093/JCDE/QWAC095
Robinson J, Sinton S, Rahmat-Samii Y (2002) Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. IEEE Antennas Propag Soc AP-S Int Symp 1:314–317. https://doi.org/10.1109/aps.2002.1016311
Sumathi S, Hannah G (2020) A novel distance measure for microarray dataset using entropy. Mater Today Proc. https://doi.org/10.1016/j.matpr.2020.10.520
Sadek RA, Soliman MS, Elsayed HS (2013) Effective anomaly intrusion detection system based on neural network with indicator variable and rough set reduction. IJCSI Int J Comput Sci 10:227–233
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/J.ADVENGSOFT.2017.01.004
Sheng-Ta H, Tsung-Ying S, Chan-Cheng L, Shang-Jeng T, Hsieh ST, Sun TY, Liu CC, Tsai SJ (2008) Solving large scale global optimization using improved particle swarm optimizer. In: 2008 IEEE congress on evolutionary computation (IEEE World Congress on Computational Intelligence). IEEE, pp 1777–1784
Singh G, Singh U, Salgotra R (2021) Effect of parametric enhancements on naked mole-rat algorithm for global optimization. Eng Comput. https://doi.org/10.1007/s00366-021-01344-4
Singh N, Son LH, Chiclana F, Magnot JP (2020) A new fusion of salp swarm with sine cosine for optimization of non-linear functions. Eng Comput 36:185–212. https://doi.org/10.1007/s00366-018-00696-8
Storn R, Price K (1996) Minimizing the real functions of the ICEC’96 contest by differential evolution. Proc IEEE Conf Evol Comput. https://doi.org/10.1109/icec.1996.542711
Talbi EG (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8:541–564. https://doi.org/10.1023/A:1016540724870
Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. IEEE Congr Evol Comput CEC 2013:71–78. https://doi.org/10.1109/CEC.2013.6557555
Tang C, Sun W, Wu W, Xue M (2019) A hybrid improved whale optimization algorithm. In: IEEE Int Conf Control Autom ICCA 2019, pp 362–367. https://doi.org/10.1109/ICCA.2019.8900003
Tanweer MR, Suresh S, Sundararajan N (2016) Dynamic mentoring and self-regulation based particle swarm optimization algorithm for solving complex real-world optimization problems. Inf Sci (NY) 326:1–24. https://doi.org/10.1016/j.ins.2015.07.035
Tavallaee M, Bagheri E, Lu W, Ghorbani AA (2009) A detailed analysis of the KDD CUP 99 data set. IEEE Symp Comput Intell Secur Def Appl CISDA. https://doi.org/10.1109/CISDA.2009.5356528
Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput 10:673–686. https://doi.org/10.1007/s00500-005-0537-1
Tu Q, Chen X, Liu X (2019) Multi-strategy ensemble grey wolf optimizer and its application to feature selection. Appl Soft Comput J 76:16–30. https://doi.org/10.1016/j.asoc.2018.11.047
Tubishat M, Idris N, Shuib L et al (2020) Improved Salp Swarm Algorithm based on opposition based learning and novel local search algorithm for feature selection. Expert Syst Appl 145:113122. https://doi.org/10.1016/j.eswa.2019.113122
van den Bergh F, Engelbrecht AP (2004) A cooperative approach to participle swam optimization. IEEE Trans Evol Comput 8:225–239. https://doi.org/10.1109/TEVC.2004.826069
Van Den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci (NY) 176:937–971. https://doi.org/10.1016/j.ins.2005.02.003
Wang XH, Li JJ (2004) Hybrid particle swarm optimization with simulated annealing. In: Proc 2004 Int Conf Mach Learn Cybern, vol 4, pp 2402–2405. https://doi.org/10.1109/icmlc.2004.1382205
Wilcoxon F (1992) Individual comparisons by ranking methods. Springer, New York, pp 196–202
Yang XS (2010) A new metaheuristic bat-inspired algorithm. Stud Comput Intell 284:65–74. https://doi.org/10.1007/978-3-642-12538-6_6
Yang XS, He X (2016) Nature-inspired optimization algorithms in engineering: overview and applications. In: studies in Computational intelligence. Springer, pp 1–20
Yang Z, Tang K, Yao X (2007) Differential evolution for high-dimensional function optimization. In: 2007 IEEE Congr Evol Comput CEC 2007, pp 3523–3530. https://doi.org/10.1109/CEC.2007.4424929
Yang Z, Tang K, Yao X (2008a) Multilevel cooperative coevolution for large scale optimization. In: 2008 IEEE Congr Evol Comput CEC 2008, pp 1663–1670. https://doi.org/10.1109/CEC.2008.4631014
Yang Z, Tang K, Yao X (2008b) Large scale evolutionary optimization using cooperative coevolution. Inf Sci (NY) 178:2985–2999. https://doi.org/10.1016/j.ins.2008.02.017
Yang Z, Tang K, Yao X (2011) Scalability of generalized adaptive differential evolution for large-scale continuous optimization. Soft Comput 15:2141–2155. https://doi.org/10.1007/s00500-010-0643-6
Yang B, Zhong L, Zhang X et al (2019) Novel bio-inspired memetic salp swarm algorithm and application to MPPT for PV systems considering partial shading condition. J Clean Prod 215:1203–1222. https://doi.org/10.1016/j.jclepro.2019.01.150
Yen GG, Daneshyari M (2008) Diversity-based information exchange among multiple swarms in particle swarm optimazation. Int J Comput Intell Appl 7:57–75. https://doi.org/10.1142/S1469026808002144
Zhao SZ, Liang JJ, Suganthan PN, Tasgetiren MF (2008a) Dynamic multi-swarm particle swarm optimizer with local search for large scale global optimization. In: 2008a IEEE congress on evolutionary computation, CEC 2008a, pp 3845–3852
Zhao SZ, Liang JJ, Suganthan PN, Tasgetiren MF (2008b) Dynamic multi-swarm particle swarm optimizer with local search for large scale global optimization. In: 2008b IEEE Congr Evol Comput CEC 2008b, pp 3845–3852. https://doi.org/10.1109/CEC.200.4631320
Zuech R, Khoshgoftaar TM (2015) A survey on feature selection for intrusion detection. In: Proc—21st ISSAT Int Conf Reliab Qual Des, pp 150–155
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix
Appendix 1: CEC 2017 benchmark function.
Type | Fun | Function name | Fmin |
|---|---|---|---|
U | F1 | Shifted and Rotated Bent Cigar Function | 100 |
U | F2 | Shifted and Rotated Zakharov | 300 |
M | F3 | Shiftedv and Rotated Rosenbrock’s | 400 |
M | F4 | Shifted and Rotated Rastrigin’s | 500 |
M | F5 | Shifted and Rotated Expanded Scaffer’s F6 | 600 |
M | F6 | Shifted and Rotated Lunacek Bi_Rastrigin | 700 |
M | F7 | Shifted and Rotated Non-Continuous Rastrigin’s | 800 |
M | F8 | Shifted and Rotated Levy | 900 |
M | F9 | Shifted and Rotated Schwefel’s | 1000 |
H | F10 | Hybrid Function 1 (N = 3) | 1100 |
H | F11 | Hybrid Function 2 (N = 3) | 1200 |
H | F12 | Hybrid Function 3 (N = 3) | 1300 |
H | F13 | Hybrid Function 4 (N = 4) | 1400 |
H | F14 | Hybrid Function 5 (N = 4) | 1500 |
H | F15 | Hybrid Function 6 (N = 4) | 1600 |
H | F16 | Hybrid Function 6 (N = 5) | 1700 |
H | F17 | Hybrid Function 6 (N = 5) | 1800 |
H | F18 | Hybrid Function 6 (N = 5) | 1900 |
H | F19 | Hybrid Function 6 (N = 6) | 2000 |
C | F20 | Composition Function 1 (N = 3) | 2100 |
C | F21 | Composition Function 2 (N = 3) | 2200 |
C | F22 | Composition Function 3 (N = 4) | 2300 |
C | F23 | Composition Function 4 (N = 4) | 2400 |
C | F24 | Composition Function 5 (N = 5) | 2500 |
C | F25 | Composition Function 6 (N = 5) | 2600 |
C | F26 | Composition Function 7 (N = 6) | 2700 |
C | F27 | Composition Function 8 (N = 6) | 2800 |
C | F28 | Composition Function 9 (N = 3) | 2900 |
C | F29 | Composition Function 10(N = 3) | 3000 |
Range [− 100, 100] D |
Appendix 2: CEC 2008lsgo benchmark function.
Fun | Function name | Characteristics |
|---|---|---|
F1 | Shifted Sphere | Separable |
F2 | Schwefel Problem | Non-separable |
F3 | Shifted Rosenbrock | Non-separable |
F4 | Shifted Rastrigin | Separable |
F5 | Shifted Griewank | Non-Separable/separable |
F6 | Shifted Ackley | Separable |
F7 | Fast Fractal | Non-Separable |
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Qaraad, M., Amjad, S., Hussein, N.K. et al. An innovative time-varying particle swarm-based Salp algorithm for intrusion detection system and large-scale global optimization problems. Artif Intell Rev 56, 8325–8392 (2023). https://doi.org/10.1007/s10462-022-10322-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-022-10322-1