Optimization Letters

, Volume 5, Issue 3, pp 407–419 | Cite as

Experiments with LAGRASP heuristic for set k-covering

  • Luciana S. PessoaEmail author
  • Mauricio G. C. Resende
  • Celso C. Ribeiro
Original Paper


The set k-covering problem (SC k P) is a variant of the classical set covering problem, in which each object is required to be covered at least k times. We describe a hybrid Lagrangean heuristic, named LAGRASP, which combines subgradient optimization and GRASP with path-relinking to solve the SC k P. Computational experiments carried out on 135 test instances show experimentally that by properly tuning the parameters of LAGRASP, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, LAGRASP makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, whereas other strategies fail to find new improving solutions.


GRASP Hybrid heuristics Metaheuristics Path-relinking Lagrangean relaxation Lagrangean heuristics Local search Set covering Set multicovering Set k-covering 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Luciana S. Pessoa
    • 1
    Email author
  • Mauricio G. C. Resende
    • 2
  • Celso C. Ribeiro
    • 3
  1. 1.Department of Informatics and Applied MathematicsUniversidade Federal do Rio Grande do NorteNatalBrazil
  2. 2.Algorithms and Optimization Research DepartmentAT&T Labs ResearchFlorham ParkUSA
  3. 3.Department of Computer ScienceUniversidade Federal FluminenseNiteróiBrazil

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