Journal of Global Optimization

, Volume 63, Issue 3, pp 515–536 | Cite as

Multi-objective variable neighborhood search: an application to combinatorial optimization problems

  • Abraham Duarte
  • Juan J. Pantrigo
  • Eduardo G. Pardo
  • Nenad Mladenovic


Solutions to real-life optimization problems usually have to be evaluated considering multiple conflicting objectives. These kind of problems, known as multi-objective optimization problems, have been mainly solved in the past by using evolutionary algorithms. In this paper, we explore the adaptation of the Variable Neighborhood Search (VNS) metaheuristic to solve multi-objective combinatorial optimization problems. In particular, we describe how to design the shake procedure, the improvement method and the acceptance criterion within different VNS schemas (Reduced VNS, Variable Neighborhood Descent and General VNS), when two or more objectives are considered. We validate these proposals over two multi-objective combinatorial optimization problems.


Multi-objective VNS Multi-objective optimization Antibandwidth Cutwidth Knapsack 



This research has been partially supported by the Spanish Ministry of “Economía y Competitividad”, Grants Ref. TIN2011-28151, and TIN2012-35632-C02, and the Government of the Community of Madrid, Grant Ref. S2009/TIC-1542.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Abraham Duarte
    • 1
  • Juan J. Pantrigo
    • 1
  • Eduardo G. Pardo
    • 1
  • Nenad Mladenovic
    • 2
  1. 1.Dept. Ciencias de la ComputaciónUniversidad Rey Juan CarlosMóstoles, MadridSpain
  2. 2.Laboratory of Industrial and Human Automation control, Mechanical Engineering and Computer Science (LAMIH)Université de ValenciennesValenciennesFrance

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