Soft Computing

, Volume 22, Issue 3, pp 949–961 | Cite as

A new approach to optimize a hub covering location problem with a queue estimation component using genetic programming

  • Hamid Hasanzadeh
  • Mahdi Bashiri
  • Amirhossein Amiri
Methodologies and Application


Hub locations are NP-hard problems used in transportation systems. In this paper, we focus on a single-allocation hub covering location problem considering a queue model in which the number of servers is a decision variable. We propose a model enhanced with a queue estimation component to determine the number and location of hubs and the number of servers in each hub, and to allocate non-hub to hub nodes according to network costs, including fixed costs for establishing each hub and server, transportation costs, and waiting costs. Moreover, we consider the capacity for a queuing system in any hub node. In addition, we present a metaheuristic algorithm based on particle swarm optimization as a solution method. To evaluate the quality of the results obtained by the proposed algorithm, we establish a tight lower bound for the proposed model. Genetic programming is used for lower bound calculation in the proposed method. The results showed better performance of the proposed lower bound compared to a lower bound obtained by a relaxed model. Finally, the computational results confirm that the proposed solution algorithm performs well in optimizing the model with a minimum gap from the calculated lower bound.


Hub location problem Queuing theory Genetic programming Genetic algorithm Particle swarm optimization 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hamid Hasanzadeh
    • 1
  • Mahdi Bashiri
    • 1
  • Amirhossein Amiri
    • 1
  1. 1.Department of Industrial EngineeringShahed UniversityTehranIran

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