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

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Abstract

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.

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Authors and Affiliations

  1. Institute Charles Delaunay, University of Technology of Troyes, BP 2060, 10010, Troyes Cedex, France

    Christian Prins, Caroline Prodhon & Roberto Wolfler Calvo

  2. ISTIT, University of Technology of Troyes, BP 2060, 10010, Troyes Cedex, France

    Caroline Prodhon

Authors
  1. Christian Prins
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  2. Caroline Prodhon
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  3. Roberto Wolfler Calvo
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Correspondence to Caroline Prodhon.

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Prins, C., Prodhon, C. & Calvo, R.W. Two-phase method and Lagrangian relaxation to solve the Bi-Objective Set Covering Problem. Ann Oper Res 147, 23–41 (2006). https://doi.org/10.1007/s10479-006-0060-5

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  • DOI: https://doi.org/10.1007/s10479-006-0060-5

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