IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v183y2011i1p7-2310.1007-s10479-009-0573-9.html
   My bibliography  Save this article

Adaptive memory programming for matrix bandwidth minimization

Author

Listed:
  • Vicente Campos
  • Estefanía Piñana
  • Rafael Martí

Abstract

In this paper we explore the influence of adaptive memory in the performance of heuristic methods when solving a hard combinatorial optimization problem. Specifically, we tackle the adaptation of tabu search and scatter search to the bandwidth minimization problem. It consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This is a classic problem, introduced in the late sixties, that also has a well-known formulation in terms of graphs. Different exact and heuristic approaches have been proposed for the bandwidth problem. Our contribution consists of two new algorithms, one based on the tabu search methodology and the other based on the scatter search framework. We also present a hybrid method combining both for improved outcomes. Extensive computational testing shows the influence of the different elements in heuristic search, such as neighborhood definition, local search, combination methods and the use of memory. We compare our proposals with the most recent and advanced methods for this problem, concluding that our new methods can compete with them in speed and running time. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Vicente Campos & Estefanía Piñana & Rafael Martí, 2011. "Adaptive memory programming for matrix bandwidth minimization," Annals of Operations Research, Springer, vol. 183(1), pages 7-23, March.
    • Handle: RePEc:spr:annopr:v:183:y:2011:i:1:p:7-23:10.1007/s10479-009-0573-9
    DOI: 10.1007/s10479-009-0573-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0573-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0573-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    2. Pinana, Estefania & Plana, Isaac & Campos, Vicente & Marti, Rafael, 2004. "GRASP and path relinking for the matrix bandwidth minimization," European Journal of Operational Research, Elsevier, vol. 153(1), pages 200-210, February.
    3. Rodriguez-Tello, Eduardo & Hao, Jin-Kao & Torres-Jimenez, Jose, 2008. "An improved simulated annealing algorithm for bandwidth minimization," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1319-1335, March.
    4. Marti, Rafael & Laguna, Manuel & Glover, Fred & Campos, Vicente, 2001. "Reducing the bandwidth of a sparse matrix with tabu search," European Journal of Operational Research, Elsevier, vol. 135(2), pages 450-459, December.
    5. Marti, Rafael & Campos, Vicente & Pinana, Estefania, 2008. "A branch and bound algorithm for the matrix bandwidth minimization," European Journal of Operational Research, Elsevier, vol. 186(2), pages 513-528, April.
    6. Lim, Andrew & Rodrigues, Brian & Xiao, Fei, 2006. "Heuristics for matrix bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 174(1), pages 69-91, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mladenovic, Nenad & Urosevic, Dragan & Pérez-Brito, Dionisio & García-González, Carlos G., 2010. "Variable neighbourhood search for bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 200(1), pages 14-27, January.
    2. Behrooz Koohestani & Riccardo Poli, 2015. "Addressing the envelope reduction of sparse matrices using a genetic programming system," Computational Optimization and Applications, Springer, vol. 60(3), pages 789-814, April.
    3. Rodriguez-Tello, Eduardo & Hao, Jin-Kao & Torres-Jimenez, Jose, 2008. "An improved simulated annealing algorithm for bandwidth minimization," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1319-1335, March.
    4. Michele Samorani & Manuel Laguna, 2012. "Data-Mining-Driven Neighborhood Search," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 210-227, May.
    5. Lim, Andrew & Rodrigues, Brian & Xiao, Fei, 2006. "Heuristics for matrix bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 174(1), pages 69-91, October.
    6. Marti, Rafael & Campos, Vicente & Pinana, Estefania, 2008. "A branch and bound algorithm for the matrix bandwidth minimization," European Journal of Operational Research, Elsevier, vol. 186(2), pages 513-528, April.
    7. Juan Pantrigo & Rafael Martí & Abraham Duarte & Eduardo Pardo, 2012. "Scatter search for the cutwidth minimization problem," Annals of Operations Research, Springer, vol. 199(1), pages 285-304, October.
    8. Sergio Cavero & Eduardo G. Pardo & Abraham Duarte, 2022. "A general variable neighborhood search for the cyclic antibandwidth problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 657-687, March.
    9. S. L. Gonzaga de Oliveira & C. Carvalho, 2022. "Metaheuristic algorithms for the bandwidth reduction of large-scale matrices," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 727-784, May.
    10. Santos, Vinícius Gandra Martins & Carvalho, Marco Antonio Moreira de, 2021. "Tailored heuristics in adaptive large neighborhood search applied to the cutwidth minimization problem," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1056-1066.
    11. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    12. Zi-bin Jiang & Qiong Yang, 2016. "A Discrete Fruit Fly Optimization Algorithm for the Traveling Salesman Problem," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-15, November.
    13. Stefan Poikonen & Bruce Golden, 2020. "The Mothership and Drone Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 249-262, April.
    14. Ting Pong & Hao Sun & Ningchuan Wang & Henry Wolkowicz, 2016. "Eigenvalue, quadratic programming, and semidefinite programming relaxations for a cut minimization problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 333-364, March.
    15. Luca Maria Gambardella & Marco Dorigo, 2000. "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 237-255, August.
    16. Rego, Cesar & Roucairol, Catherine, 1995. "Using Tabu search for solving a dynamic multi-terminal truck dispatching problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 411-429, June.
    17. Wayne Desarbo, 1982. "Gennclus: New models for general nonhierarchical clustering analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 449-475, December.
    18. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    19. Ghosh, Diptesh, 2016. "Exploring Lin Kernighan neighborhoods for the indexing problem," IIMA Working Papers WP2016-02-13, Indian Institute of Management Ahmedabad, Research and Publication Department.
    20. Wex, Felix & Schryen, Guido & Feuerriegel, Stefan & Neumann, Dirk, 2014. "Emergency response in natural disaster management: Allocation and scheduling of rescue units," European Journal of Operational Research, Elsevier, vol. 235(3), pages 697-708.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:183:y:2011:i:1:p:7-23:10.1007/s10479-009-0573-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.