Skip to main content

Advertisement

SpringerLink
Log in

Hierarchicity-based (self-similar) hybrid genetic algorithm for the grey pattern quadratic assignment problem

  • Regular Research Paper
  • Published:
Memetic Computing Aims and scope Submit manuscript

Abstract

In this paper, we present a hierarchicity-based (self-similar) hybrid genetic algorithm for the solution of the grey pattern quadratic assignment problem. This is a novel hybrid genetic search-based heuristic algorithm with the original, hierarchical architecture and it is in connection with what is known as self-similarity—this means that an object (in our case, algorithm) is exactly or approximately similar to constituent parts of itself. The two main aspects of the proposed algorithm are the following: (1) the hierarchical (self-similar) structure of the genetic algorithm itself, and (2) the hierarchical (self-similar) form of the iterated tabu search algorithm, which is integrated into the genetic algorithm as an efficient local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Notes

  1. In our work, we consider \(m \le \frac{n}{2}\).

  2. The first m elements of the permutation p determine the locations on the grid where the black squares have to be placed in. The coordinates \((r,s)\) of the black squares are derived according to these formulas: \(r = \frac{{\left( {p\left( i \right) - 1} \right)}}{{n_{2} }} + 1\), \(s = \left( {\left( {p\left( i \right) - 1} \right) \bmod n_{2} } \right) + 1\), \(i = 1, \ldots , m\).

  3. The hierarchical principle is one of the guiding fundamental principles of nature. First of all, this is true for the structural organization of matter (energy), where it can be observed that one physical structures contain other structures within itself—from the largest structures, such as galaxies and star systems, to the tiniest elements such as atoms and quarks. The principle of hierarchy applies to natural processes as well. It is clearly visible if we think a little of motion. For example, the earth orbits around the sun, the sun rotates (albeit relatively slowly) around the massive galaxy center, and so on. Finally, the spirit of hierarchicity can also be felt in the formal systems created by intelligence. One of the shining examples is the system of the types of numbers: the abstract class of complex numbers cover the class of real numbers, real numbers encompass integers, integers—natural numbers.

    These are just a few examples. Even more examples could be found, which makes it possible to speculate that the hierarchical principle is the universal principle of the world. As a result, we conjecture that for both the computational methods and algorithms, this principle may also be deeply inherent and important.

  4. For more detailed description of the basic principles of TS algorithms, we refer the reader to [36].

  5. The source code of the implemented hierarchical genetic algorithm will be available at https://www.personalas.ktu.lt/~alfmise/.

References

  1. Burkard RE, Dell’Amico M, Martello S (2009) Assignment problems. SIAM, Philadelphia

    Book  Google Scholar 

  2. Çela E (1998) The quadratic assignment problem: theory and algorithms. Kluwer, Dordrecht

    Book  Google Scholar 

  3. Taillard ED (1995) Comparison of iterative searches for the quadratic assignment problem. Locat Sci 3:87–105. https://doi.org/10.1016/0966-8349(95)00008-6

    Article  MATH  Google Scholar 

  4. Drezner Z (2006) Finding a cluster of points and the grey pattern quadratic assignment problem. OR Spectrum 28:417–436. https://doi.org/10.1007/s00291-005-0010-7

    Article  MathSciNet  MATH  Google Scholar 

  5. Erkut E (1990) The discrete p-dispersion problem. Eur J Oper Res 46:48–60

    Article  MathSciNet  Google Scholar 

  6. Kuby MJ (1987) Programming models for facility dispersion: the p-dispersion and maxisum dispersion problems. Geogr Anal 19:315–329. https://doi.org/10.1111/j.1538-4632.1987.tb00133.x

    Article  Google Scholar 

  7. Shier DR (1977) A min-max theorem for p-center problems on a tree. Transp Sci 11:243–252

    Article  Google Scholar 

  8. Kuo C-C, Glover F, Dhir KS (1993) Analyzing and modeling the maximum diversity problem by zero-one programming. Decis Sci 24:1171–1185. https://doi.org/10.1111/j.1540-5915.1993.tb00509.x

    Article  Google Scholar 

  9. Drezner Z, Misevičius A, Palubeckis G (2015) Exact algorithms for the solution of the grey pattern quadratic assignment problem. Math Method Oper Res 82:85–105. https://doi.org/10.1007/s00186-015-0505-1

    Article  MathSciNet  MATH  Google Scholar 

  10. Talbi E-G, Hafidi Z, Geib J-M (1999) Parallel tabu search for large optimization problems. In: Voß S, Martello S, Osman IH, Roucairol C (eds) Meta-heuristics: advances and trends in local search paradigms for optimization. Kluwer, Boston, pp 345–358

    Chapter  Google Scholar 

  11. Taillard ED, Gambardella LM (1997) Adaptive memories for the quadratic assignment problem. Technical report IDSIA-87-97, Lugano, Switzerland

  12. Baldé MAMT, Gueye S, Ndiaye BM (2020) A greedy evolutionary hybridization algorithm for the optimal network and quadratic assignment problem. Oper Res. https://doi.org/10.1007/s12351-020-00549-7

    Article  Google Scholar 

  13. Drezner Z, Drezner TD (2020) Biologically inspired parent selection in genetic algorithms. Ann Oper Res 287:161–183. https://doi.org/10.1007/s10479-019-03343-7

    Article  MATH  Google Scholar 

  14. Fatahi M, Moradi S (2020) An FPA and GA-based hybrid evolutionary algorithm for analyzing clusters. Knowl Inf Syst 62:1701–1722. https://doi.org/10.1007/s10115-019-01413-7

    Article  Google Scholar 

  15. Singh K, Sundar S (2019) A new hybrid genetic algorithm for the maximally diverse grouping problem. Int J Mach Learn Cybern 10:2921–2940. https://doi.org/10.1007/s13042-018-00914-1

    Article  Google Scholar 

  16. Zhang H, Liu F, Zhou Y, Zhang Z (2020) A hybrid method integrating an elite genetic algorithm with tabu search for the quadratic assignment problem. Inf Sci 539:347–374. https://doi.org/10.1016/j.ins.2020.06.036

    Article  MathSciNet  Google Scholar 

  17. Misevičius A (2006) Experiments with hybrid genetic algorithm for the grey pattern problem. Informatica-Lithuan 17:237–258

    Article  Google Scholar 

  18. Misevičius A (2011) Generation of grey patterns using an improved genetic-evolutionary algorithm: some new results. Inf Technol Control 40:330–343. https://doi.org/10.5755/j01.itc.40.4.983

    Article  Google Scholar 

  19. Misevičius A, Stanevičienė E (2018) A new hybrid genetic algorithm for the grey pattern quadratic assignment problem. Inf Technol Control 47:503–520. https://doi.org/10.5755/j01.itc.47.3.20728

    Article  Google Scholar 

  20. El-Shorbagy MA, Ayoub AY, Mousa AA, El-Desoky IM (2019) An enhanced genetic algorithm with new mutation for cluster analysis. Comput Stat 34:1355–1392. https://doi.org/10.1007/s00180-019-00871-5

    Article  MathSciNet  MATH  Google Scholar 

  21. Fausto F, Reyna-Orta A, Cuevas E, Andrade ÁG, Perez-Cisneros M (2020) From ants to whales: metaheuristics for all tastes. Artif Intell Rev 53:753–810. https://doi.org/10.1007/s10462-018-09676-2

    Article  Google Scholar 

  22. Ghosh M, Begum S, Sarkar R, Chakraborty D, Maulik U (2019) Recursive memetic algorithm for gene selection in microarray data. Expert Syst Appl 116:172–185. https://doi.org/10.1016/j.eswa.2018.06.057

    Article  Google Scholar 

  23. Tang D, Liu Z, Zhao J, Dong S, Cai Y (2020) Memetic quantum evolution algorithm for global optimization. Neural Comput Appl 32:9299–9329. https://doi.org/10.1007/s00521-019-04439-8

    Article  Google Scholar 

  24. Tzanetos A, Dounias G (2020) Nature inspired optimization algorithms or simply variations of metaheuristics? Artif Intell Rev. https://doi.org/10.1007/s10462-020-09893-8

    Article  Google Scholar 

  25. Zhou Q, Benlic U, Wu Q (2020) An opposition-based memetic algorithm for the maximum quasi-clique problem. Eur J Oper Res 286:63–83. https://doi.org/10.1016/j.ejor.2020.03.019

    Article  MathSciNet  MATH  Google Scholar 

  26. Hussin MS, Stützle T (2009) Hierarchical iterated local search for the quadratic assignment problem. In: Blesa MJ, Blum C, Di Gaspero L, Roli A, Sampels M, Schaerf A (eds) Hybrid metaheuristics, HM 2009. Lecturer notes in computer science, vol 5818. Springer, Berlin, pp 115–129

    Google Scholar 

  27. Lourenco HR, Martin O, Stützle T (2002) Iterated local search. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. Kluwer, Norwell, pp 321–353

    Google Scholar 

  28. Battarra M, Benedettini S, Roli A (2011) Leveraging saving-based algorithms by master–slave genetic algorithms. Eng Appl Artif Intell 24:555–566. https://doi.org/10.1016/j.engappai.2011.01.007

    Article  Google Scholar 

  29. Garai G, Chaudhuri BB (2007) A distributed hierarchical genetic algorithm for efficient optimization and pattern matching. Pattern Recogn 40:212–228. https://doi.org/10.1016/j.patcog.2006.04.023

    Article  MATH  Google Scholar 

  30. Hauschild M, Bhatia S, Pelikan M (2012) Image segmentation using a genetic algorithm and hierarchical local search. In: Soule T (ed) Proceedings of the 14th annual conference on genetic and evolutionary computation, Philadelphia, USA. ACM Press, New York, pp 633–639

  31. Schaefer R, Byrski A, Kołodziej J, Smołka M (2012) An agent-based model of hierarchic genetic search. Comput Math Appl 64:3763–3776. https://doi.org/10.1016/j.camwa.2012.02.052

    Article  MathSciNet  MATH  Google Scholar 

  32. Ahmed AKMF, Sun JU (2018) A novel approach to combine the hierarchical and iterative techniques for solving capacitated location-routing problem. Cogent Eng 5:1463596. https://doi.org/10.1080/23311916.2018.1463596

    Article  Google Scholar 

  33. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Press, Reading

    MATH  Google Scholar 

  34. Drezner Z (2005) Compounded genetic algorithms for the quadratic assignment problem. Oper Res Lett 33:475–480. https://doi.org/10.1016/j.orl.2004.11.001

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhou Y, Hao J-K, Duval B (2017) Opposition-based memetic search for the maximum diversity problem. IEEE Trans Evolut Comput 21:731–745. https://doi.org/10.1109/TEVC.2017.2674800

    Article  Google Scholar 

  36. Glover F, Laguna M (1997) Tabu search. Kluwer, Dordrecht

    Book  Google Scholar 

  37. Dell’Amico M, Trubian M (1998) Solution of large weighted equicut problems. Eur J Oper Res 106:500–521. https://doi.org/10.1016/S0377-2217(97)00287-7

    Article  MATH  Google Scholar 

  38. Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Global Optim 6:109–133. https://doi.org/10.1007/BF01096763

    Article  MathSciNet  MATH  Google Scholar 

  39. Sivanandam SN, Deepa SN (2008) Introduction to genetic algorithms. Springer, Heidelberg

    MATH  Google Scholar 

Download references

Acknowledgements

We would like to thank three anonymous referees for the valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Multimedia Engineering, Kaunas University of Technology, Studentu st. 50, 51368, Kaunas, Lithuania

    Alfonsas Misevičius & Gintaras Palubeckis

  2. Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner

Authors
  1. Alfonsas Misevičius
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gintaras Palubeckis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zvi Drezner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alfonsas Misevičius.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Table 12.

Table 12 Comparison of the results of the branch and bound algorithm [9] and hierarchical genetic algorithm for the GP-QAP
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Misevičius, A., Palubeckis, G. & Drezner, Z. Hierarchicity-based (self-similar) hybrid genetic algorithm for the grey pattern quadratic assignment problem. Memetic Comp. 13, 69–90 (2021). https://doi.org/10.1007/s12293-020-00321-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12293-020-00321-6

Keywords

Search

Navigation