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Genetic algorithm based approach to solve the Clustered Steiner Tree Problem

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Abstract

In a complex network application, a set of nodes might be partitioned into multiple local clusters with different functions, properties, or communication protocols, and the communication is restricted between nodes of the same cluster to maximize efficiency and other security concern. Thus, there has been a rise in network design problems with additional constraints regarding the clustering of vertices, one of them being Clustered Steiner Tree Problem—a variant of the Steiner Tree Problem. Recently, a heuristic-based algorithm was proposed to solve the problem. However, its obtained result is limited in terms of solution quality when applied to the problem in the Euclidean case. This paper proposes a Genetic Algorithm called Shortest-Path Genetic Algorithm for solving the CluSteiner. In the proposal, a permutation-based individual representation that reduces the dimensionality of chromosomes to the number of clusters is devised. The proposed algorithm can solve the problem in both Euclidean and non-Euclidean cases. Experiment results compared to existing works in the literature are analyzed in detail to prove the effectiveness of the proposed algorithm.

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References

  1. Prömel HJ, Steger A. The Steiner tree problem a tour through graphs, algorithms, and complexity

  2. Wu BY, Lin CW (2015) On the Clustered Steiner Tree Problem. J Comb Optim 30:370–386. https://doi.org/10.1007/s10878-014-9772-7

    Article  MathSciNet  MATH  Google Scholar 

  3. Chisman JA (1975) The clustered traveling salesman problem. Comput Op Res 2(2):115–119

    Article  Google Scholar 

  4. D’Emidio M, Forlizzi L, Frigioni D, Leucci S, Proietti G (2016) On the clustered shortest-path tree problem. In: ICTCS, pp 263–268

  5. Lin C-W, Wu BY (2017) On the minimum routing cost clustered tree problem. J Comb Optim 33(3):1106–1121

    Article  MathSciNet  MATH  Google Scholar 

  6. Menéndez HD, Barrero DF, Camacho D (2014) A genetic graph-based approach for partitional clustering. Int J Neural Syst 24(03):1430008

    Article  Google Scholar 

  7. Ding C, Cheng Y, He M (2007) Two-level genetic algorithm for clustered traveling salesman problem with application in large-scale TSPS. Tsinghua Sci Technol 12(4):459–465

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen L, Abdellatif S, Gayraud T, Berthou P (2017) A Steiner tree based approach for the efficient support of multipoint communications in a multi-domain context. In: 2017 IEEE symposium on computers and communications (ISCC), pp 316–321 https://doi.org/10.1109/ISCC.2017.8024549

  9. Haghighat AT, Faez K, Dehghan M, Mowlaei A, Ghahremani Y (2002) A genetic algorithm for Steiner tree optimization with multiple constraints using prüfer number. In: EurAsia-ICT 2002: information and communication technology, pp 272–280 https://doi.org/10.1007/3-540-36087-5_32

  10. Hesser J, Männer R, Stucky O (1989) Optimization of steiner trees using genetic algorithms. In: Third international conference on genetic algorithms, pp 231–236

  11. Julstrom B (1993) A genetic algorithm for the rectilinear steiner problem. In: 5th international conference on genetic algorithms, pp 474–480

  12. Kapsalis A, Rayward-Smith V, Smith G (1993) Solving the graphical Steiner tree problem using genetic algorithms. J Op Res Soc 44:397–406. https://doi.org/10.1038/sj/jors/0440408

    Article  MATH  Google Scholar 

  13. Esbensen H (1995) Computing near-optimal solutions to the Steiner problem in a graph using a genetic algorithm. Networks. https://doi.org/10.1002/net.3230260403

    Article  MATH  Google Scholar 

  14. Mitchell M (1998) An introduction to genetic algorithms. MIT Press, Cambridge. https://doi.org/10.7551/mitpress/3927.001.0001

    Book  MATH  Google Scholar 

  15. D’Emidio M, Forlizzi L, Frigioni D, Leucci S, Proietti G (2018) Hardness, approximability, and fixed-parameter tractability of the clustered shortest-path tree problem. J Comb Optim 38:165–184. https://doi.org/10.1007/s10878-018-00374-x

    Article  MathSciNet  MATH  Google Scholar 

  16. Thanh PD, Binh HTT, Trung TB (2020) An efficient strategy for using multifactorial optimization to solve the clustered shortest path tree problem. Appl Intell 50(4):1233–1258

    Article  Google Scholar 

  17. Thanh PD, Binh HTT, Long NB et al (2019) A heuristic based on randomized greedy algorithms for the clustered shortest-path tree problem. In: 2019 IEEE congress on evolutionary computation (CEC), IEEE, pp 2915–2922

  18. Binh HTT, Thanh PD, Trung TB et al (2018) Effective multifactorial evolutionary algorithm for solving the cluster shortest path tree problem. In: 2018 IEEE congress on evolutionary computation (CEC), IEEE, pp 1–8

  19. Thanh PD, Dung DA, Tien TN, Binh HTT (2018) An effective representation scheme in multifactorial evolutionary algorithm for solving cluster shortest-path tree problem. In: 2018 IEEE congress on evolutionary computation (CEC), IEEE, pp 1–8

  20. Binh HTT, Thanh PD, Thang TB (2019) New approach to solving the clustered shortest-path tree problem based on reducing the search space of evolutionary algorithm. Knowl-Based Syst 180:12–25. https://doi.org/10.1016/j.knosys.2019.05.015

    Article  Google Scholar 

  21. Lin CW, Wu BY (2017) On the minimum routing cost clustered tree problem. J Comb Optim 33:1106–1121. https://doi.org/10.1007/s10878-016-0026-8

    Article  MathSciNet  MATH  Google Scholar 

  22. Trung T, Thanh L, Hieu L, Pham Dinh T, Binh H (2019) Multifactorial evolutionary algorithm for clustered minimum routing cost problem, pp 170–177 https://doi.org/10.1145/3368926.3369712

  23. Thang TB, Long NB, Hoang NV, Binh HTT (2021) Adaptive knowledge transfer in multifactorial evolutionary algorithm for the clustered minimum routing cost problem. Appl Soft Comput 105:107253

    Article  Google Scholar 

  24. Pham Dinh T (2019) Cluspt instances, mendeley data, v3. https://doi.org/10.17632/b4gcgybvt6.3

  25. Carrasco J, García S, Rueda MM, Das S, Herrera F (2020) Recent trends in the use of statistical tests for comparing swarm and evolutionary computing algorithms: practical guidelines and a critical review. Swarm Evolut Comput 54:100665

    Article  Google Scholar 

  26. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  27. Stakic Z (2021) Anokic: a reduced variable neighborhood search approach to the heterogeneous vector bin packing problem. J ICT 50(4):808–826

    Google Scholar 

  28. BAN H-B (2021) Applying metaheuristic for time-dependent traveling salesman problem in postdisaster. Int J Comput Intell Syst 14(1):1087–1107

    Article  Google Scholar 

  29. BAN H-B (2021) A metaheuristic for the delivery man problem with time windows. J Comb Optim 41(4):794–816

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work is funded by the Ministry of Education and Training of Vietnam for Do Tuan Anh under project code B2023-BKA-05. It also was funded by Office Naval of Research under grant number N62909-23-1-2018 for Huynh Thi Thanh Binh. In addition, Nguyen Binh Long is funded by Vingroup JSC and supported by the Master, Ph.D. Scholarship Programme of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VINIF.2021.ThS.BK.02.

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Authors and Affiliations

  1. School of Information and Communication Technology, Hanoi University of Science and Technology, Dai Co Viet, Hanoi, Vietnam

    Tuan Anh Do, Ha-Bang Ban, Thi Thanh Binh Huynh, Minh Tu Le & Binh Long Nguyen

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  1. Tuan Anh Do
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  2. Ha-Bang Ban
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  3. Thi Thanh Binh Huynh
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  4. Minh Tu Le
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Contributions

DTA: Methodology, Algorithms, Coding, Writing the manuscript. H-BB: Methodology, Algorithms, Coding, Writing the manuscript. HTTB: Methodology, Algorithms, Writing the manuscript. MTL: Algorithms, Coding, Writing the manuscript. BLN: Methodology, Coding, Writing the manuscript.

Corresponding author

Correspondence to Ha-Bang Ban.

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The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

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Appendix

Appendix

See Tables 

Table 14 Results obtained by SPMST, BSPH and SPGA on instances in Type_1_Small
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Table 15 Results obtained by SPMST, BSPH and SPGA on instances in Type_1_Large
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Table 16 Results obtained by SPMST, BSPH and SPGA on instances in Type_3_Large
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Table 17 Results obtained by SPMST, BSPH and SPGA on instances in Type_5_Small
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Table 18 Results obtained by SPMST, BSPH and SPGA on instances in Type_5_Large
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Table 19 Results obtained by SPMST, BSPH and SPGA on instances in Type_6_Small
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Table 20 Results obtained by SPMST, BSPH and SPGA on instances in Type_6_Large
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Do, T.A., Ban, HB., Huynh, T.T.B. et al. Genetic algorithm based approach to solve the Clustered Steiner Tree Problem. Evol. Intel. (2023). https://doi.org/10.1007/s12065-023-00848-w

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