Mathematical Programming

, Volume 81, Issue 2, pp 215–228 | Cite as

A Lagrangian-based heuristic for large-scale set covering problems

  • Sebastián Ceria
  • Paolo Nobili
  • Antonio Sassano


We present a new Lagrangian-based heuristic for solving large-scale set-covering problems arising from crew-scheduling at the Italian Railways (Ferrovie dello Stato). Our heuristic obtained impressive results when compared to state-of-the-art codes on a test-bed provided by the company, which includes instances with sizes ranging from 50,000 variables and 500 constraints to 1,000,000 variables and 5000 constraints. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.


Set covering Crew scheduling Primal-dual lagrangian Subgradient algorithms 0–1 programming Approximate solutions Railways 


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  1. [1]
    R. Anbil, E. Gelman, B. Patty, R. Tanga, Recent advances in crew pairing optimization at American Airlines, Interfaces 21 (1991) 62–74.Google Scholar
  2. [2]
    J. Barutt, T. Hull, Airline crew-scheduling: supercomputers and algorithms, SIAM News 23 (1990) 1–2.Google Scholar
  3. [3]
    D.R. Bornemann, The evolution of airline crew pairing optimization, AGIFORS Crew Management Study Group Proceedings, Paris, 1982.Google Scholar
  4. [4]
    I. Gershkoff, Optimizing flight crew schedules, Interfaces 19 (1989) 29–43.Google Scholar
  5. [5]
    K.L. Hoffman, M. Padberg, Solving airline crew-scheduling problems by branch-and-cut, Management Science 39 (1993) 657–682.Google Scholar
  6. [6]
    S. Lavoie, M. Minoux, E. Odier, A new approach for crew pairing problems by column generation with application to air transportation, European Journal of Operations Research 35 (1988) 45–58.Google Scholar
  7. [7]
    V. Chvatal, A greedy heuristic for the set-covering problem, Mathematics of Operations Research 4 (1979) 233–235.Google Scholar
  8. [8]
    E. Balas, A. Ho, Set covering algorithms using cutting planes, heuristics, and subgradient optimization: a computational study, Mathematical Programming Study 12 (1980) 37–60.Google Scholar
  9. [9]
    T.A. Feo, M.G.C. Resende, A probabilistic heuristic for a computationally difficult set covering problem, Operations Research Letters 8 (1989) 67–71.Google Scholar
  10. [10]
    M.L. Fisher, P. Kedia, Optimal solution of set covering/partitioning problems using dual heuristics, Management Science 36 (1990) 674–688.Google Scholar
  11. [11]
    J.E. Beasley, A Lagrangean heuristic for set-covering problems, Naval Research Logistics 37 (1990) 151–164.Google Scholar
  12. [12]
    E. Balas, M. Carrera, A dynamic subgradient-based branch-and-bound procedure for set covering, Management Science Research Report No. 568, Carnegie Mellon University, 1992, Operations Research (to appear).Google Scholar
  13. [13]
    L.W. Jacobs, M.J. Brusco, A simulated annealing-based heuristic for the set-covering problem, Working Paper, Operations Management and Information System Department, Northern Illinois University, Dekalb, IL60115, USA, 1993.Google Scholar
  14. [14]
    J.E. Beasley, P.C. Chu, A genetic algorithm for the set covering problem, Working Paper, The Management School, Imperial College, London SW7 2AZ, England, 1994.Google Scholar

Copyright information

© The Mathematical Programming Society, Inc. 1998

Authors and Affiliations

  • Sebastián Ceria
    • 1
  • Paolo Nobili
    • 2
  • Antonio Sassano
    • 3
  1. 1.Graduate School of BusinessColumbia UniversityNew YorkUSA
  2. 2.Istituto di Analisi dei Sistemi ed Informatica, CNRItaly
  3. 3.Dipartimento di Informatica e SistemisticaUniversità di RomaLa SapienzaItaly

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