Journal of Heuristics

, Volume 18, Issue 6, pp 919–938 | Cite as

Variable neighborhood search with ejection chains for the antibandwidth problem

  • Manuel Lozano
  • Abraham Duarte
  • Francisco Gortázar
  • Rafael MartíEmail author
Original Paper


In this paper, we address the optimization problem arising in some practical applications in which we want to maximize the minimum difference between the labels of adjacent elements. For example, in the context of location models, the elements can represent sensitive facilities or chemicals and their labels locations, and the objective is to locate (label) them in a way that avoids placing some of them too close together (since it can be risky). This optimization problem is referred to as the antibandwidth maximization problem (AMP) and, modeled in terms of graphs, consists of labeling the vertices with different integers or labels such that the minimum difference between the labels of adjacent vertices is maximized. This optimization problem is the dual of the well-known bandwidth problem and it is also known as the separation problem or directly as the dual bandwidth problem. In this paper, we first review the previous methods for the AMP and then propose a heuristic algorithm based on the variable neighborhood search methodology to obtain high quality solutions. One of our neighborhoods implements ejection chains which have been successfully applied in the context of tabu search. Our extensive experimentation with 236 previously reported instances shows that the proposed procedure outperforms existing methods in terms of solution quality.


Metaheuristics VNS Layout problems 



This research has been partially supported by the Ministerio de Ciencia e Innovación of Spain within the OPTSICOM project ( with grant codes TIN2008-05854, TIN2009-07516, TIN2012-35632, and P08-TIC-4173.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Manuel Lozano
    • 1
  • Abraham Duarte
    • 2
  • Francisco Gortázar
    • 2
  • Rafael Martí
    • 3
    Email author
  1. 1.Departamento de Ciencias de la Computación e Inteligencia ArtificialUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Ciencias de la ComputaciónUniversidad Rey Juan CarlosMadridSpain
  3. 3.Departamento de Estadística e Investigación OperativaUniversidad de ValenciaValenciaSpain

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