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

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Abstract

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.

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References

  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. J. Barutt, T. Hull, Airline crew-scheduling: supercomputers and algorithms, SIAM News 23 (1990) 1–2.

    Google Scholar 

  3. D.R. Bornemann, The evolution of airline crew pairing optimization, AGIFORS Crew Management Study Group Proceedings, Paris, 1982.

  4. I. Gershkoff, Optimizing flight crew schedules, Interfaces 19 (1989) 29–43.

    Google Scholar 

  5. K.L. Hoffman, M. Padberg, Solving airline crew-scheduling problems by branch-and-cut, Management Science 39 (1993) 657–682.

    Google Scholar 

  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. V. Chvatal, A greedy heuristic for the set-covering problem, Mathematics of Operations Research 4 (1979) 233–235.

    Google Scholar 

  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. 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. M.L. Fisher, P. Kedia, Optimal solution of set covering/partitioning problems using dual heuristics, Management Science 36 (1990) 674–688.

    Google Scholar 

  11. J.E. Beasley, A Lagrangean heuristic for set-covering problems, Naval Research Logistics 37 (1990) 151–164.

    Google Scholar 

  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).

  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. 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 

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This research was performed while the author was affiliated with IASI, CNR and Dipartimento di Informatica e Sistemistica, Università di Roma, La Sapienza, Italy.

This research was partially supported by National Research Program “Metodi di Ottimizzazione per le Decisioni”, MURST, Roma, Italy.

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Ceria, S., Nobili, P. & Sassano, A. A Lagrangian-based heuristic for large-scale set covering problems. Mathematical Programming 81, 215–228 (1998). https://doi.org/10.1007/BF01581106

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  • DOI: https://doi.org/10.1007/BF01581106

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