Abstract
Performance aspects of a Lagrangian relaxation based heuristic for solving large 0–1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Göteborg, Sweden, based on distributing the variables and a new sequential active set strategy which requires less work and is better adapted to the memory hierachy properties of modern RISC processors. The active set strategy can even be parallelized on networks of workstations.
This work has been supported by the ESPRIT HPCN program, project PAROS.
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P. Alefragis, C. Goumopoulos, E. Housos, P. Sanders, T. Takkula, and D. Wedelin. Parallel crew scheduling in PAROS. In EUROPAR'98, Lecture Notes in Computer Science, 1998. to appear.
E. Andersson, E. Housos, N. Kohl, and D. Wedelin. OR in the Airline Industry, chapter Crew Pairing Optimization, Kluwer Academic Publishers, Boston, London, Dordrecht, 1997.
C. Barnhart and R. G. Shenoi. An alternate model and solution approach for the long-haul crew pairing problem. Jul 1996.
A. Caprara, M. Fischetti, and P. Toth. A heuristic algorithm for the set covering problem. In Lecture Notes in Computer Science, pages 72–84, 1996.
The Carmen System, version 5.1. Carmen Systems AB, Göteborg, Sweden.
S. Ceria, P. Nobili, and A. Sassano. A Lagrangian-based heuristic for large-scale set covering problems. Technical report, Dipartimento di Informatica e Sistemistica, Università di Roma, La Sapienza, Italy, 1995.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. McGraw-Hill, 1990.
G. Desaulniers, J. Desrosiers, Y. Dumas, S. Marc, B. Rioux, M. Solomon, and F. Soumis. Crew pairing at Air France. European Journal of Operational Research, 97:245–259, 1997.
M. L. Fisher. The Lagrangian relaxation method for solving integer programming problems. Management Sciences, 27(1):1–18, 1981.
C. Goumopoulos, P. Alefragis, and E. Housos. Parallel algorithms for airline crew planning on networks of workstations. In International Conference on Parallel Processing, Minneapolis, 1998.
C. Goumopoulos, E. Housos, and O. Liljenzin. Parallel crew scheduling on work-station networks using PVM. In Euro PVM-MPI, number 1332 in LNCS, Cracow, Poland, 1997.
K. L. Hoffman and M. Padberg. Solving airline crew scheduling problems by branch-and-cut. Management Science, 39(6):657–682, 1993.
S. Lavoie, M. Minoux, and E. Odier. A new approach for crew pairing problems by column generation with an application to air transportation. European Journal of Operations Research, 35:45–58, 1988.
R. Marsten. RALPH: Crew Planning at Delta Air Lines. Technical Report. Cutting Edge Optimization, 1997.
J. Motwani and P. Raghavan. Randomized algorithms. Cambridge University Press, 1995.
M. Snir, S. W. Otto, S. Huss-Lederman, D. W. Walker, and J. Dongarra. MPI—the Complete Reference. MIT Press, 1996.
P. H. Vance. Crew Scheduling, Cutting Stock, and Column Generation: Solving Huge Integer Programs. PhD thesis, Georgia Institute of Technology, August 1993.
D. Wedelin. An algorithm for large scale 0–1 integer programming with application to airline crew scheduling. Annals of Operations Research, 57:283–301, 1995.
A. Wool and T. Grossman. Computational experience with approxima-tion algorithms for the set covering problem. Technical Report CS94-25, Weizmann Institute of Science, Faculty of Mathematical Sciences, Jan. 1, 1994.
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© 1999 Springer-Verlag
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Sanders, P., Takkula, T., Wedelin, D. (1999). High performance integer optimization for crew scheduling. In: Sloot, P., Bubak, M., Hoekstra, A., Hertzberger, B. (eds) High-Performance Computing and Networking. HPCN-Europe 1999. Lecture Notes in Computer Science, vol 1593. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0100560
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DOI: https://doi.org/10.1007/BFb0100560
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