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A Cost-Regular Based Hybrid Column Generation Approach

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Abstract

Constraint Programming (CP) offers a rich modeling language of constraints embedding efficient algorithms to handle complex and heterogeneous combinatorial problems. To solve hard combinatorial optimization problems using CP alone or hybrid CP-ILP decomposition methods, costs also have to be taken into account within the propagation process. Optimization constraints, with their cost-based filtering algorithms, aim to apply inference based on optimality rather than feasibility. This paper introduces a new optimization constraint, cost-regular. Its filtering algorithm is based on the computation of shortest and longest paths in a layered directed graph. The support information is also used to guide the search for solutions. We believe this constraint to be particularly useful in modeling and solving Column Generation subproblems and evaluate its behaviour on complex Employee Timetabling Problems through a flexible CP-based column generation approach. Computational results on generated benchmark sets and on a complex real-world instance are given.

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Authors and Affiliations

  1. École des Mines de Nantes, LINA FRE CNRS 2729, FR-44307, Nantes, France

    Sophie Demassey

  2. Centre for Research on Transportation, École Polytechnique de Montréal, C.P. 6128, succ. Centre-ville, Montreal, H3C 3J7, Canada

    Gilles Pesant & Louis-Martin Rousseau

Authors
  1. Sophie Demassey
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  2. Gilles Pesant
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  3. Louis-Martin Rousseau
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Corresponding author

Correspondence to Sophie Demassey.

Additional information

A preliminary version of this paper appeared as [7]. This research was supported by the Mathematics of Information Technology and Complex Systems (MITACS) Internship program in association with Omega Optimisation Inc. (CA).

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Demassey, S., Pesant, G. & Rousseau, LM. A Cost-Regular Based Hybrid Column Generation Approach. Constraints 11, 315–333 (2006). https://doi.org/10.1007/s10601-006-9003-7

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