Variable Neighborhood Descent

  • Abraham DuarteEmail author
  • Jesús Sánchez-Oro
  • Nenad Mladenović
  • Raca Todosijević
Reference work entry


Local search heuristic that explores several neighborhood structures in a deterministic way is called variable neighborhood descent (VND). Its success is based on the simple fact that different neighborhood structures do not usually have the same local minimum. Thus, the local optima trap problem may be resolved by deterministic change of neighborhoods. VND may be seen as a local search routine and therefore could be used within other metaheuristics. In this chapter, we discuss typical problems that arise in developing VND heuristic: what neighborhood structures could be used, what would be their order, what rule of their change during the search would be used, etc. Comparative analysis of usual sequential VND variants is performed in solving traveling salesman problem.


Variable neighborhood descent Local search Intensification Deterministic exploration 



The works of Nenad Mladenović and Raca Todosijević are partly supported by the Ministry of Education and Science, Republic of Kazakhstan (Institute of Information and Computer Technologies), project number 0115PK00546, and also by the Ministry of Education, Science and Technological Development of Serbia, project number 174010. The works of Abraham Duarte and Jesús Sánchez-Oro are partly supported by the Spanish “Ministerio de Economía y Competitividad” and by “Comunidad de Madrid” with grants refs. TIN2012-35632-C02 and S2013/ICE-2894, respectively.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Abraham Duarte
    • 1
    Email author
  • Jesús Sánchez-Oro
    • 2
  • Nenad Mladenović
    • 3
    • 4
    • 5
  • Raca Todosijević
    • 6
  1. 1.Department of Ciencias de la ComputaciónUniversidad Rey Juan CarlosMóstoles (Madrid)Spain
  2. 2.Universidad Rey Juan CarlosMóstoles (Madrid)Spain
  3. 3.GERAD and Ecole des Hautes Etudes CommercialesMontréalCanada
  4. 4.LAMIHUniversity of ValenciennesFamarsFrance
  5. 5.LAMIH, France and Mathematical Institute, SANUUniversité de ValenciennesBelgradeSerbia
  6. 6.LAMIH, France and Mathematical Institute, SANUUniversité de ValenciennesBelgradeSerbia

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