SpringerLink
Log in

A new evolutionary optimization based on multi-objective firefly algorithm for mining numerical association rules

  • Application of soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Association rule mining (ARM) is a widely used technique in data mining for pattern discovery. However, association rule mining in numerical data poses a considerable challenge. In recent years, researchers have turned to optimization-based approaches as a potential solution. One particular area of interest in numerical association rules mining (NARM) is controlling the length of itemset intervals. In this paper, we propose a novel evolutionary algorithm based on the multi-objective firefly algorithm for efficiently mining numerical association rules (MOFNAR). MOFNAR utilizes Balance, square of cosine (SOC) and comprehensibility as objectives of evolutionary algorithm to assess rules and achieve a rule set that is both simple and accurate. We introduce the Balance measure to effectively control the intervals of numerical itemsets and eliminate misleading rules. Furthermore, we suggest a penalty approach, and the crowding-distance method is employed to maintain high diversity. Experimental results on five well-known datasets show the effectiveness of our method in discovering a simple rule set with high confidence that covers a significant percentage of the data.

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
EUR 32.99 /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 includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig.5
Fig. 6

Similar content being viewed by others

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Agrawal R, Srikant R (1994) 'Fast algorithms for mining association rules' Proc. 20th int. conf. very large data bases, VLDB. Citeseer, pp. 487–499

  • Agrawal R, Imieliński T, Swami A (1993) 'Mining association rules between sets of items in large databases' Proceedings of the 1993 ACM SIGMOD international conference on Management of data. pp. 207–216.

  • Alatas B, Akin E (2006) An efficient genetic algorithm for automated mining of both positive and negative quantitative association rules. Soft Comput 10(3):230–237

    Google Scholar 

  • Alatas B, Akin E (2008) Rough particle swarm optimization and its applications in data mining. Soft Comput 12(12):1205–1218

    Google Scholar 

  • Alatas B, Akin E, Karci A (2008) MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules. Appl Soft Comput 8(1):646–656

    Google Scholar 

  • Almasi M, Abadeh MS (2015) Rare-PEARs: A new multi objective evolutionary algorithm to mine rare and non-redundant quantitative association rules. Knowl-Based Syst 89:366–384

    Google Scholar 

  • Altay EV, Alatas B (2021) Differential evolution and sine cosine algorithm based novel hybrid multi-objective approaches for numerical association rule mining. Inf Sci 554:198–221

    MathSciNet  Google Scholar 

  • Bahri O, Li P, Boubrahimi SF, Hamdi S M. (2022) 'Shapelet-based temporal association rule mining for multivariate time series classification' 2022 IEEE International Conference on Big Data (Big Data). IEEE, pp. 242–251

  • Baró GB, Martínez-Trinidad JF, Rosas RMV, Ochoa JAC, González AYR, Cortés MSL (2020) A PSO-based algorithm for mining association rules using a guided exploration strategy. Pattern Recogn Lett 138:8–15

    Google Scholar 

  • Beiranvand V, Mobasher-Kashani M, Bakar AA (2014) Multi-objective PSO algorithm for mining numerical association rules without a priori discretization. Expert Syst Appl 41(9):4259–4273

    Google Scholar 

  • Berzal F, Blanco I, Sánchez D, Vila M-A (2002) Measuring the accuracy and interest of association rules: a new framework. Intell Data Anal 6(3):221–235

    Google Scholar 

  • Brin S, Motwani R, Ullman JD, Tsur S (1997) 'Dynamic itemset counting and implication rules for market basket data' Proceedings of the 1997 ACM SIGMOD international conference on Management of data. pp. 255–264.

  • Can U, Alatas B (2017) Automatic mining of quantitative association rules with gravitational search algorithm. Int J Software Eng Knowl Eng 27(03):343–372

    Google Scholar 

  • Coello CAC (2007) Evolutionary algorithms for solving multi-objective problems. Springer

    Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Google Scholar 

  • Deng W, Ni H, Liu Y, Chen H, Zhao H (2022) An adaptive differential evolution algorithm based on belief space and generalized opposition-based learning for resource allocation. Appl Soft Comput 127:109419

    Google Scholar 

  • Djenouri Y, Drias H, Habbas Z (2014) Bees swarm optimisation using multiple strategies for association rule mining. Int J Bio-Inspir Comput 6(4):239–249

    Google Scholar 

  • Djenouri Y, Djenouri D, Belhadi A, Fournier-Viger P, Lin JC-W (2018) A new framework for metaheuristic-based frequent itemset mining. Appl Intell 48(12):4775–4791

    Google Scholar 

  • Espadinha-Cruz P, Godina R, Rodrigues EM (2021) A review of data mining applications in semiconductor manufacturing. Processes 9(2):305

    Google Scholar 

  • Fan G, Shi W, Guo L, Zeng J, Zhang K, Gui G (2019) Machine learning based quantitative association rule mining method for evaluating cellular network performance. IEEE Access 7:166815–166822

    Google Scholar 

  • Fister I, Iglesias A, Galvez A, Del Ser J, Osaba E (2018) Differential evolution for association rule mining using categorical and numerical attributes. In: Yin H, Camacho D, Novais P, Tallón-Ballesteros AJ (eds) International conference on intelligent data engineering and automated learning. Springer, Cham, pp 79–88

    Google Scholar 

  • Fister I, Salcedo-Sanz S (2022) 'Time Series numerical association rule mining for assisting smart agriculture' 2022 International Conference on Electrical, Computer and Energy Technologies (ICECET). IEEE, pp. 1–6

  • Freitas AA (2003) A survey of evolutionary algorithms for data mining and knowledge discovery. In: Ghosh A, Tsutsui S (eds) Advances in evolutionary computing. Springer, Berlin, pp 819–845

    Google Scholar 

  • Fung K, Kwong CK, Siu KWM, Yu K (2012) A multi-objective genetic algorithm approach to rule mining for affective product design. Expert Syst Appl 39(8):7411–7419

    Google Scholar 

  • Gao X, He F, Zhang S, Luo J, Fan B (2023) A fast nondominated sorting-based MOEA with convergence and diversity adjusted adaptively. J Supercomput. https://doi.org/10.1007/s11227-023-05516-5

    Article  Google Scholar 

  • Geng L, Hamilton HJ (2007) Choosing the right lens: finding what is interesting in data mining. In: Guillet FJ, Hamilton HJ (eds) Quality measures in data mining. Springer, Berlin, pp 3–24

    Google Scholar 

  • Guvenir HA, Uysal I (2000). Bilkent university function approximation repository. Accessed August, 10, 2015

  • Hadi W, El-Khalili N, AlNashashibi M, Issa G, AlBanna AA (2019) Application of data mining algorithms for improving stress prediction of automobile drivers: a case study in Jordan. Comput Biol Med 114:103474

    Google Scholar 

  • Heraguemi KE, Kamel N, Drias H (2016) Multi-swarm bat algorithm for association rule mining using multiple cooperative strategies. Appl Intell 45(4):1021–1033

    Google Scholar 

  • Holland JH, Booker LB, Colombetti M, Dorigo M, Goldberg DE, Forrest S et al (1999) “What is a learning classifier system?” International Workshop on Learning Classifier Systems. Springer, pp 3–32

    Google Scholar 

  • Hsieh N-C (2004) An integrated data mining and behavioral scoring model for analyzing bank customers. Expert Syst Appl 27(4):623–633

    Google Scholar 

  • Hu Z, Shao M, Liu H, Mi J (2022) Cognitive computing and rule extraction in generalized one-sided formal contexts. Cogn Comput 14(6):2087–2107

    Google Scholar 

  • Jaramillo IF, Garzás J, Redchuk A (2021) Numerical association rule mining from a defined schema using the vmo algorithm. Appl Sci 11(13):6154

    Google Scholar 

  • Kaushik M, Sharma R, Fister Jr, Draheim D (2023). Numerical association rule mining: a systematic literature review. ar**v preprint ar**v:2307.00662

  • Kennedy J, Eberhart R. 4 (1995) 'Particle swarm optimization' Proceedings of ICNN'95-international conference on neural networks. IEEE, pp. 1942–1948

  • Khan WA, Hamadneh NN, Tilahun SL, Ngnotchouye J (2016) A review and comparative study of firefly algorithm and its modified versions. Optim Algorithm-Methods Appl 45:281–313

    Google Scholar 

  • Kumar V, Kumar D (2021) A systematic review on firefly algorithm: past, present, and future. Arch Comput Methods Eng 28:3269–3291

    MathSciNet  Google Scholar 

  • Kuo R-J, Gosumolo M, Zulvia FE (2019) Multi-objective particle swarm optimization algorithm using adaptive archive grid for numerical association rule mining. Neural Comput Appl 31(8):3559–3572

    Google Scholar 

  • Li R, Gong W, Lu C (2022) Self-adaptive multi-objective evolutionary algorithm for flexible job shop scheduling with fuzzy processing time. Comput Ind Eng 168:108099

    Google Scholar 

  • Liang Y, He F, Zeng X, Luo J (2022) An improved loop subdivision to coordinate the smoothness and the number of faces via multi-objective optimization. Integr Comput-Aided Eng 29(1):23–41

    Google Scholar 

  • Luo J, He F, Gao X (2023) An enhanced grey wolf optimizer with fusion strategies for identifying the parameters of photovoltaic models. Integr Comput-Aided Eng 30(1):89–104

    Google Scholar 

  • Ma L, Li N, Guo Y, Wang X, Yang S, Huang M et al (2021) Learning to optimize: reference vector reinforcement learning adaption to constrained many-objective optimization of industrial copper burdening system. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3086501

    Article  Google Scholar 

  • Ma L, Li N, Yu G, Geng X, Cheng S, Wang X et al (2023) Pareto-wise ranking classifier for multi-objective evolutionary neural architecture search. IEEE Trans Evol Comput. https://doi.org/10.1109/TEVC.2023.3314766

    Article  Google Scholar 

  • Ma L, Zhang T, Wang R, Yang G, Zhang Y (2019) 'Pbar: Parallelized brain storm optimization for association rule mining' 2019 IEEE Congress on Evolutionary Computation (CEC). IEEE, pp. 1148–1156

  • Martin D, Rosete A, Alcalá-Fdez J, Herrera F (2013) A new multiobjective evolutionary algorithm for mining a reduced set of interesting positive and negative quantitative association rules. IEEE Trans Evol Comput 18(1):54–69

    Google Scholar 

  • Martín D, Alcalá-Fdez J, Rosete A, Herrera F (2016) Nicgar: a niching genetic algorithm to mine a diverse set of interesting quantitative association rules. Inf Sci 355:208–228

    Google Scholar 

  • Martín D, Martínez-Ballesteros M, García-Gil D, Alcalá-Fdez J, Herrera F, Riquelme-Santos J (2018) MRQAR: a generic MapReduce framework to discover quantitative association rules in big data problems. Knowl-Based Syst 153:176–192

    Google Scholar 

  • Martínez-Ballesteros M, Troncoso A, Martínez-Álvarez F, Riquelme JC (2016) Improving a multi-objective evolutionary algorithm to discover quantitative association rules. Knowl Inf Syst 49(2):481–509

    Google Scholar 

  • McGarry K (2005) A survey of interestingness measures for knowledge discovery. Knowl Eng Rev 20(1):39–61

    Google Scholar 

  • Medjadba Y, Hu D, Liu W, Yu X (2019) Combining graph clustering and quantitative association rules for knowledge discovery in geochemical data problem. IEEE Access 8:40453–40473

    Google Scholar 

  • Merceron A, Yacef K (2008) 'Interestingness measures for association rules in educational data' Educational data mining 2008.

  • Minaei-Bidgoli B, Barmaki R, Nasiri M (2013) Mining numerical association rules via multi-objective genetic algorithms. Inf Sci 233:15–24

    Google Scholar 

  • Park JS, Chen M-S, Yu PS (1995) An effective hash-based algorithm for mining association rules. ACM SIGMOD Rec 24(2):175–186

    Google Scholar 

  • Pazhaniraja N, Sountharrajan S, Kumar BS (2020) High utility itemset mining: a Boolean operators-based modified grey wolf optimization algorithm. Soft Comput 24(21):16691–16704

    Google Scholar 

  • Rokh B, Mirvaziri H, Eftekhari M (2014) 'Proposing an efficient combination of interesting measures for mining association rules via NSGA-II' 2014 International Congress on Technology, Communication and Knowledge (ICTCK). IEEE, pp. 1–7

  • Romero C, Ventura S (2020) Educational data mining and learning analytics: an updated survey. Wiley Interdiscip Rev: Data Min Knowl Discov 10(3):e1355

    Google Scholar 

  • Song W, Huang C (2018) Mining high utility itemsets using bio-inspired algorithms: a diverse optimal value framework. IEEE Access 6:19568–19582

    Google Scholar 

  • Srikant R, Agrawal R (1996) 'Mining quantitative association rules in large relational tables' Proceedings of the 1996 ACM SIGMOD international conference on Management of data. pp. 1–12

  • Su T, Xu H, Zhou X (2019) Particle swarm optimization-based association rule mining in big data environment. IEEE Access 7:161008–161016

    Google Scholar 

  • Tahyudin I, Nambo H (2017) 'The rule extraction of numerical association rule mining using hybrid evolutionary algorithm' 2017 4th International Conference on Electrical Engineering, Computer Science and Informatics (EECSI). IEEE, pp. 1–6

  • Tan P-N, Kumar V, Srivastava J (2002) 'Selecting the right interestingness measure for association patterns' Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining. pp. 32–41

  • Tan P-N, Steinbach M, Kumar V (2016). Introduction to data mining. Pearson Education India

  • Wang G-G, Gao D, Pedrycz W (2022) Solving multiobjective fuzzy job-shop scheduling problem by a hybrid adaptive differential evolution algorithm. IEEE Trans Industr Inf 18(12):8519–8528

    Google Scholar 

  • Yang X-S (2009) Firefly algorithms for multimodal optimization. In: Watanabe O, Zeugmann T (eds) International symposium on stochastic algorithms. Springer, Berlin, pp 169–178

    Google Scholar 

  • Yang X-S (2010a) Engineering optimization: an introduction with metaheuristic applications. John Wiley & Sons

    Google Scholar 

  • Yang X-S (2010b) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspir Comput 2(2):78–84

    Google Scholar 

  • Yang X-S (2010c). Nature-inspired metaheuristic algorithms. Luniver press.

  • Yang X-S (2013) Multiobjective firefly algorithm for continuous optimization. Eng Comput 29(2):175–184

    Google Scholar 

  • Yang XS, Hossein Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483

    Google Scholar 

  • Zhang Y, Zhang L, Nie G, Shi Y (2009) 'A survey of interestingness measures for association rules' 2009 International Conference on Business Intelligence and Financial Engineering. IEEE, pp. 460–463.

  • Zhang A, Shi W (2020) Mining significant fuzzy association rules with differential evolution algorithm. Appl Soft Comput 97:105518

    Google Scholar 

  • Zou J, Fu L, Zheng J, Yang S, Yu G, Hu Y (2018) A many-objective evolutionary algorithm based on rotated grid. Appl Soft Comput 67:596–609

    Google Scholar 

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Department of Computer Engineering, University of Zanjan, Zanjan, Iran

    Babak Rokh

  2. Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Hamid Mirvaziri

  3. Faculty of Engineering, Department of Computer Engineering, University of Gonabad, Gonabad, Iran

    MohammadHossein Olyaee

Authors
  1. Babak Rokh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid Mirvaziri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. MohammadHossein Olyaee
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by all authors. The first draft of the manuscript was written by BR and both the other authors revised and commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to MohammadHossein Olyaee.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Ethical approval

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

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rokh, B., Mirvaziri, H. & Olyaee, M. A new evolutionary optimization based on multi-objective firefly algorithm for mining numerical association rules. Soft Comput 28, 6879–6892 (2024). https://doi.org/10.1007/s00500-023-09558-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-09558-y

Keywords

Search

Navigation