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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
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    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).

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