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Scatter search for the cutwidth minimization problem

Author

Listed:
  • Juan Pantrigo
  • Rafael Martí
  • Abraham Duarte
  • Eduardo Pardo

Abstract

The cutwidth minimization problem consists of finding a linear layout of a graph so that the maximum linear cut of edges is minimized. This NP-hard problem has applications in network scheduling, automatic graph drawing and information retrieval. We propose a heuristic method based on the Scatter Search (SS) methodology for finding approximate solutions to this optimization problem. This metaheuristic explores solution space by evolving a set of reference points. Our SS method is based on a GRASP constructive algorithm, a local search strategy based on insertion moves and voting-based combination methods. We also introduce a new measure to control the diversity in the search process. Empirical results with 252 previously reported instances indicate that the proposed procedure compares favorably to previous metaheuristics for this problem, such as Simulated Annealing and Evolutionary Path Relinking. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:199:y:2012:i:1:p:285-304:10.1007/s10479-011-0907-2
    DOI: 10.1007/s10479-011-0907-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. Eduardo G. Pardo & Antonio García-Sánchez & Marc Sevaux & Abraham Duarte, 2020. "Basic variable neighborhood search for the minimum sitting arrangement problem," Journal of Heuristics, Springer, vol. 26(2), pages 249-268, April.
    3. Pallavi Jain & Kamal Srivastava & Gur Saran, 2016. "Minimizing cyclic cutwidth of graphs using a memetic algorithm," Journal of Heuristics, Springer, vol. 22(6), pages 815-848, December.
    4. Abraham Duarte & Juan Pantrigo & Eduardo Pardo & Nenad Mladenovic, 2015. "Multi-objective variable neighborhood search: an application to combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 63(3), pages 515-536, November.
    5. Miguel A. González & Juan José Palacios & Camino R. Vela & Alejandro Hernández-Arauzo, 2017. "Scatter search for minimizing weighted tardiness in a single machine scheduling with setups," Journal of Heuristics, Springer, vol. 23(2), pages 81-110, June.

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