IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v22y2011i4d10.1007_s10878-010-9306-x.html
   My bibliography  Save this article

Revised GRASP with path-relinking for the linear ordering problem

Author

Listed:
  • W. Art Chaovalitwongse

    (Rutgers University)

  • Carlos A. S. Oliveira

    (Princeton Consultants Inc.)

  • Bruno Chiarini
  • Panos M. Pardalos

    (University of Florida)

  • Mauricio G. C. Resende

    (AT&T Labs Research)

Abstract

The linear ordering problem (LOP) is an $\mathcal{NP}$ -hard combinatorial optimization problem with a wide range of applications in economics, archaeology, the social sciences, scheduling, and biology. It has, however, drawn little attention compared to other closely related problems such as the quadratic assignment problem and the traveling salesman problem. Due to its computational complexity, it is essential in practice to develop solution approaches to rapidly search for solution of high-quality. In this paper we propose a new algorithm based on a greedy randomized adaptive search procedure (GRASP) to efficiently solve the LOP. The algorithm is integrated with a Path-Relinking (PR) procedure and a new local search scheme. We tested our implementation on the set of 49 real-world instances of input-output tables (LOLIB instances) proposed in Reinelt (Linear ordering library (LOLIB) 2002). In addition, we tested a set of 30 large randomly-generated instances proposed in Mitchell (Computational experience with an interior point cutting plane algorithm, Tech. rep., Mathematical Sciences, Rensellaer Polytechnic Institute, Troy, NY 12180-3590, USA 1997). Most of the LOLIB instances were solved to optimality within 0.87 seconds on average. The average gap for the randomly-generated instances was 0.0173% with an average running time of 21.98 seconds. The results indicate the efficiency and high-quality of the proposed heuristic procedure.

Suggested Citation

  • W. Art Chaovalitwongse & Carlos A. S. Oliveira & Bruno Chiarini & Panos M. Pardalos & Mauricio G. C. Resende, 2011. "Revised GRASP with path-relinking for the linear ordering problem," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 572-593, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9306-x
    DOI: 10.1007/s10878-010-9306-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-010-9306-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-010-9306-x?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. Leung, J. & Lee, J., 1994. "More facets from fences for linear ordering and acyclic subgraph polytopes," LIDAM Reprints CORE 1087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Vicente Campos & Manuel Laguna & Rafael Martí, 2005. "Context-Independent Scatter and Tabu Search for Permutation Problems," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 111-122, February.
    3. Wanpracha Chaovalitwongse & Dukwon Kim & Panos M. Pardalos, 2003. "GRASP with a New Local Search Scheme for Vehicle Routing Problems with Time Windows," Journal of Combinatorial Optimization, Springer, vol. 7(2), pages 179-207, June.
    4. Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1984. "A Cutting Plane Algorithm for the Linear Ordering Problem," Operations Research, INFORMS, vol. 32(6), pages 1195-1220, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kim, Jiyoung & Nakano, Satoshi & Nishimura, Kazuhiko, 2016. "Productivity growth and the structure of production," IDE Discussion Papers 624, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    2. Satoshi Nakano & Kazuhiko Nishimura, 2017. "Structural propagation in a production network with restoring substitution elasticities," Papers 1701.02216, arXiv.org, revised Apr 2018.
    3. Kim, Jiyoung & Nakano, Satoshi & Nishimura, Kazuhiko, 2017. "Multifactor CES elasticity and productivity growth : a cross-sectional approach," IDE Discussion Papers 632, Institute of Developing Economies, Japan External Trade Organization(JETRO).

    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. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    2. P. Detti & D. Pacciarelli, 2001. "A branch and bound algorithm for the minimum storage‐time sequencing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(4), pages 313-331, June.
    3. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    4. Michael J. Brusco & Douglas Steinley & Ashley L. Watts, 2022. "Disentangling relationships in symptom networks using matrix permutation methods," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 133-155, March.
    5. Miles William W & Fowks Gary T & Coulter Lisa O, 2010. "AccuV College Football Ranking Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(3), pages 1-17, July.
    6. Akbari, Sina & Escobedo, Adolfo R., 2023. "Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties," Omega, Elsevier, vol. 119(C).
    7. Angel Juan & Javier Faulin & Albert Ferrer & Helena Lourenço & Barry Barrios, 2013. "MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 109-132, April.
    8. Potts, C. N. & Whitehead, J. D., 2001. "Workload balancing and loop layout in the design of a flexible manufacturing system," European Journal of Operational Research, Elsevier, vol. 129(2), pages 326-336, March.
    9. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    10. Miguel F. Anjos & Anthony Vannelli, 2008. "Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 611-617, November.
    11. Fung, Richard Y.K. & Liu, Ran & Jiang, Zhibin, 2013. "A memetic algorithm for the open capacitated arc routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 50(C), pages 53-67.
    12. Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. Tan, K.C. & Chew, Y.H. & Lee, L.H., 2006. "A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 172(3), pages 855-885, August.
    14. Daniel Porumbel & Jin-Kao Hao, 2020. "Distance-guided local search," Journal of Heuristics, Springer, vol. 26(5), pages 711-741, October.
    15. Fred Glover & Gary Kochenberger & Weihong Xie & Jianbin Luo, 2019. "Diversification methods for zero-one optimization," Journal of Heuristics, Springer, vol. 25(4), pages 643-671, October.
    16. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.
    17. T. Christof & G. Reinelt, 1996. "Combinatorial optimization and small polytopes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 1-53, June.
    18. Vicky Mak & Andreas Ernst, 2007. "New cutting-planes for the time- and/or precedence-constrained ATSP and directed VRP," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 69-98, August.
    19. B. Jay Coleman, 2005. "Minimizing Game Score Violations in College Football Rankings," Interfaces, INFORMS, vol. 35(6), pages 483-496, December.
    20. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.

    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:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9306-x. 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.