, Volume 11, Issue 1, pp 57–73 | Cite as

Variable neighborhood search for the travelling deliveryman problem

  • Nenad Mladenović
  • Dragan UroševićEmail author
  • Saïd Hanafi
Research Paper


A travelling deliveryman needs to find a tour such that the total waiting time of all the customers he has to visit is minimum. The deliveryman starts his tour at a depot, travelling at constant velocity. In this paper we suggest a general variable neighborhood search based heuristic to solve this NP-hard combinatorial optimization problem. We combine several classical neighborhood structures and design data structure to store and update the incumbent solution efficiently. In this way, we are able to explore neighborhoods as efficiently as when solving the travelling salesman problem. Computational results obtained on usual test instances show that our approach outperforms recent heuristics from the literature.


Combinatorial optimization Routing Travelling deliveryman problem Metaheuristics Variable neighborhood search 

Mathematics Subject Classification (2000)

90C059 90C27 



The present research work has been supported by Research Grants 174010 and III 044006 of the Serbian Ministry of Education, Science and Technological Development. The present research work has been also supported by International Campus on Safety and Intermodality in Transportation the Nord-Pas-de-Calais Region, the European Community, the Regional Delegation for Research and Technology, the Ministry of Higher Education and Research, and the National Center for Scientific Research. The authors gratefully acknowledge the support of these institutions.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Nenad Mladenović
    • 1
  • Dragan Urošević
    • 2
    Email author
  • Saïd Hanafi
    • 3
  1. 1.School of MathematicsBrunel UniversityUxbridgeUK
  2. 2.Mathematical InstituteBelgradeSerbia
  3. 3.LAMIH-Université de ValenciennesValenciennesFrance

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