Journal of Heuristics

, Volume 22, Issue 4, pp 507–537 | Cite as

Hybrid meta-heuristics with VNS and exact methods: application to large unconditional and conditional vertex \(p\)-centre problems

  • Chandra Ade Irawan
  • Said Salhi
  • Zvi Drezner


Large-scale unconditional and conditional vertex \(p\)-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with \(p\) varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex \(p\)-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems.


Large unconditional and conditional vertex \(p\)-centre Aggregation Variable neighbourhood search Exact method 



The authors would like to thank both referees for their useful suggestions that improved both the content as well as the presentation of the paper. We are also grateful to the Indonesian Government and Department of Industrial Engineering—ITENAS Bandung, Indonesia for the sponsorship of the first author.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Centre for Operational Research and Logistics (CORL), Department of MathematicsUniversity of PortsmouthLion TerraceUK
  2. 2.Department of Industrial EngineeringInstitut Teknologi NasionalBandungIndonesia
  3. 3.Centre for Logistics & Heuristic Optimization (CLHO)Kent Business School, University of KentCanterburyUK
  4. 4.Department of Information Systems and Decision Sciences, Steven G. Mihaylo College of Business and EconomisCalifornia State University-FullertonFullertonUSA

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