Abstract
Background
Meta-heuristics are high-level methods widely used in different fields of applications. To enhance their performance, they are often combined to concepts borrowed from machine learning and statistics in order to improve the quality of solutions and/or reduce the response time.
Aim
In this paper, we investigate the use of feature selection to speed-up the search process of Bee Swarm Optimisation (BSO) meta-heuristic in solving the MaxSAT problem.The general idea is to extract a subset of the most relevant features that describe an instance of a problem in order to reduce its size.
Proposed approach
We propose to translate a MaxSAT instance into a dataset following one of several representations proposed in this study, and then apply a FS technique to select the most relevant variables or clauses. Two data organizations are proposed depending on whether we want to remove variables or clauses. In addition, two data encodings can be used: binary encoding if we are only interested by the presence or not of a variable in a clause, and ternary encoding if we consider the information that it appears as a positive or negative literal. Moreover, we experiment two feature evaluation approaches: subset evaluation approach which returns the optimal subset, and individual evaluation which ranks the features and lets the user choose the number of features to remove. All possible combinations of data organization, data encoding and features evaluation approach lead to eight (08) variants of the hybrid algorithm, named FS-BSO.
Results
BSO and all the variants of FS-BSO have been applied to several instances of different benchmarks. The analysis of experimental results showed that in terms of solution quality, BSO gives the best results. However, FS-BSO algorithms achieve very good results and are statistically equivalent to BSO for some instances. In terms of execution time, all hybrid variants of FS-BSO are faster. In addition, results showed that removing clauses is slightly more advantageous in terms of solution quality whereas removing variables gives better execution times. Concerning data encoding, the results did not show any difference between the binary and ternary encodings.
Conclusion
In this paper, we investigated the possibility to speed-up BSO meta-heuristic in solving an instance of the MaxSAT problem by extracting a priori knowledge. Feature selection has been used as a preprocessing technique in order to reduce the instance size by selecting a subset of the most relevant vaiables/clauses. Results showed that there is a strong link between the reduction rate and solution quality, and that FS-BSO offers a better quality-time trade off.
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Weka is an environment for knowledge analysis which provides a collection of machine learning algorithms for data mining tasks (http://www.cs.waikato.ac.nz/ml/weka/).
all instances can be downloaded from http://www.cs.ubc.ca/~hoos/SATLIB/benchm.html.
p-value is a probability which is compared to the threshold value \(\alpha \) to quantify the significance of the null hypothesis. If the p-value is less than or equal to \(\alpha \) then the null hypothesis is rejected, else it is accepted.
References
Hussain K, Salleh MNM, Cheng S, Shi Y (2019) Metaheuristic research: a comprehensive survey. Artif Intell Rev 52(4):2191–2233
Guo Y-N, Cheng J, Luo S, Gong D, Xue Y (2017) Robust dynamic multi-objective vehicle routing optimization method. IEEE/ACM Trans Comput Biol Bioinform 15(6):1891–1903
Ji J, Guo Y, Gong D, Tang W (2020) Moea/d-based participant selection method for crowdsensing with social awareness. Appl Soft Comput 87:105981
Jourdan L, Dhaenens C, Talbi E-G (2006) Using datamining techniques to help metaheuristics: a short survey. In: International workshop on hybrid metaheuristics. Springer, pp 57–69
Corne D, Dhaenens C, Jourdan L (2012) Synergies between operations research and data mining: the emerging use of multi-objective approaches. Eur J Oper Res 221(3):469–479
Battiti R, Brunato M, Mascia F (2008) Reactive search and intelligent optimization, vol 45. Springer, Berlin
Battiti R, Brunato M (2010) Reactive search optimization: learning while optimizing. In: Glover FW, Kochenberger GA (eds) Handbook of metaheuristics. Springer, Berlin, pp 543–571
Jabbour S, Sais L, Salhi Y, Uno T (2013) Mining-based compression approach of propositional formulae. In: Proceedings of the 22nd ACM international conference on information and knowledge management. ACM, pp 289–298
Drias H, Sadeg S, Yahi S(2005) Cooperative bees swarm for solving the maximum weighted satisfiability problem. In: Computational intelligence and bioinspired systems. Springer, pp 318–325
Sadeg S, Hamdad L, Haouas M, Abderrahmane K, Benatchba K, Habbas Z (2019) Unsupervised learning bee swarm optimization metaheuristic. In: International work-conference on artificial neural networks. Springer, pp 773–784
Djenouri Y, Chun-Wei LJ, Djenouri D, Belhadi A, Fournier-Viger P (2018) Gbso-rss: Gpu-based BSO for rules space summarization. In: International conference on big data analysis and deep learning applications. Springer, pp 123–129
Sadeg S, Hamdad L, Benatchba K, Habbas Z (2015) Bso-fs: bee swarm optimization for feature selection in classification. In: International work-conference on artificial neural networks. Springer, pp 387–399
Sadeg S, Hamdad L, Remache AR, Karech MN, Benatchba K, Habbas Z(2019) Qbso-fs: a reinforcement learning based bee swarm optimization metaheuristic for feature selection. In: International work-conference on artificial neural networks. Springer, pp 785–796
Djenouri Y, Belhadi A, Belkebir R (2018) Bees swarm optimization guided by data mining techniques for document information retrieval. Exp Syst Appl 94:126–136
Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):3–12
Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1(2):61–70
Santos LF, Martins SL, Plastino A (2008) Applications of the dm-grasp heuristic: a survey. Int Trans Oper Res 15(4):387–416
Jia Y-H, Chen W-N, Tianlong G, Zhang H, Yuan H-Q, Kwong S, Zhang J (2018) Distributed cooperative co-evolution with adaptive computing resource allocation for large scale optimization. IEEE Trans Evol Comput 23(2):188–202
Kira K, Rendell LA (1992) The feature selection problem: traditional methods and a new algorithm. In AAAI, vol 2, pp 129–134
Liu H, Motoda H (2007) Computational methods of feature selection. CRC Press, Boca Raton
Liu H, Motoda H, Setiono R, Zhao Z (2010) Feature selection: an ever evolving frontier in data mining. In: Feature selection in data mining, pp 4–13
Dash M, Liu H (1997) Feature selection for classification. Intell Data Anal 1(1–4):131–156
Guyon I, Elisseeff A (2003) An introduction to variable and feature selection. J Mach Learn Res 3:1157–1182
Lee HD, Monard MC, Wu FC (2006) A fractal dimension based filter algorithm to select features for supervised learning. In: Advances in artificial intelligence-IBERAMIA-SBIA 2006. Springer, pp 278–288
Hall MA (1999) Correlation-based feature selection for machine learning
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report, Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department
Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi Mb (2005) The bees algorithm. Technical note. Manufacturing Engineering Centre, Cardiff University, UK, pp 1–57
Karaboga D, Akay B (2009) A survey: algorithms simulating bee swarm intelligence. Artif Intell Rev 31(1–4):61–85
Anguluri R, Swagatam D, Lynn N, Suganthan PN (2016) Computing with the collective intelligence of honey bees. Swarm Evol Comput 32:25–48 (in press)
Witten IH, Frank E, Hall MA (2011) Data mining: practical machine learning tools and techniques, 3rd edn. Morgan Kaufmann Publishers Inc., San Francisco
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Sadeg, S., Hamdad, L., Chettab, H. et al. Feature selection based bee swarm meta-heuristic approach for combinatorial optimisation problems: a case-study on MaxSAT. Memetic Comp. 12, 283–298 (2020). https://doi.org/10.1007/s12293-020-00310-9
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DOI: https://doi.org/10.1007/s12293-020-00310-9