Annals of Operations Research

, Volume 147, Issue 1, pp 23–41 | Cite as

Two-phase method and Lagrangian relaxation to solve the Bi-Objective Set Covering Problem

  • Christian Prins
  • Caroline ProdhonEmail author
  • Roberto Wolfler Calvo


This paper deals with the Bi-Objective Set Covering Problem, which is a generalization of the well-known Set Covering Problem. The proposed approach is a two-phase heuristic method which has the particularity to be a constructive method using the primal-dual Lagrangian relaxation to solve single objective Set Covering problems. The results show that this algorithm finds several potentially supported and unsupported solutions. A comparison with an exact method (up to a medium size), shows that many Pareto-optimal solutions are retrieved and that the other solutions are well spread and close to the optimal ones. Moreover, the method developed compares favorably with the Pareto Memetic Algorithm proposed by Jaszkiewicz.


Multi-objective combinatorial optimization Lagrangean relaxation Set covering problem 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Christian Prins
    • 1
  • Caroline Prodhon
    • 1
    • 2
    Email author
  • Roberto Wolfler Calvo
    • 1
  1. 1.Institute Charles DelaunayUniversity of Technology of TroyesTroyes CedexFrance
  2. 2.ISTIT, University of Technology of TroyesTroyes CedexFrance

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