Abstract
Column generation is a state-of-the-art method for optimally solving difficult large-scale optimization problems such as airline crew assignment. We show how to apply column generation even if those problems have complex constraints that are beyond the scope of pure OR methods. We achieve this by formulating the subproblem as a constraint satisfaction problem (CSP). We also show how to efficiently treat the special case of shortest path problems by introducing an efficient path constraint that exploits dual values from the master problem to exclude nodes that will not lead to paths with negative reduced costs. We demonstrate that this propagation significantly reduces the time needed to solve crew assignment problems.
The production of this paper was supported by the Parrot project, partially funded by the ESPRIT programme of the Commission of the European Union as project number 24 960. The partners in the project are ILOG (F), Lufthansa Systems (D), Carmen Systems (S), Olympic Airways (GR), University of Paderborn (D), University of Athens (GR). This paper re.ects the opinions of the authors and not necessarily those of the consortium.
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Junker, U., Karisch, S.E., Kohl, N., Vaaben, B., Fahle, T., Sellmann, M. (1999). A Framework for Constraint Programming Based Column Generation. In: Jaffar, J. (eds) Principles and Practice of Constraint Programming – CP’99. CP 1999. Lecture Notes in Computer Science, vol 1713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48085-3_19
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DOI: https://doi.org/10.1007/978-3-540-48085-3_19
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