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Column generation approaches for the software clustering problem

Author

Listed:
  • Hugo Harry Kramer

    (Universidade Federal Fluminense)

  • Eduardo Uchoa

    (Universidade Federal Fluminense)

  • Marcia Fampa

    (Universidade Federal do Rio de Janeiro)

  • Viviane Köhler

    (Universidade Federal de Santa Maria)

  • François Vanderbeck

    (Université de Bordeaux & Inria Bordeaux Sud-Ouest)

Abstract

This work presents the application of branch-and-price approaches to the automatic version of the Software Clustering Problem. To tackle this problem, we apply the Dantzig–Wolfe decomposition to a formulation from the literature. Given this, we present two Column Generation (CG) approaches to solve the linear programming relaxation of the resulting reformulation: the standard CG approach, and a new approach, which we call Staged Column Generation (SCG). Also, we propose a modification to the pricing subproblem that allows to add multiple columns at each iteration of the CG. We test our algorithms in a set of 45 instances from the literature. The proposed approaches were able to improve the literature results solving all these instances to optimality. Furthermore, the SCG approach presented a considerable performance improvement regarding computational time, number of iterations and generated columns when compared with the standard CG as the size of the instances grows.

Suggested Citation

  • Hugo Harry Kramer & Eduardo Uchoa & Marcia Fampa & Viviane Köhler & François Vanderbeck, 2016. "Column generation approaches for the software clustering problem," Computational Optimization and Applications, Springer, vol. 64(3), pages 843-864, July.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:3:d:10.1007_s10589-015-9822-9
    DOI: 10.1007/s10589-015-9822-9
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    References listed on IDEAS

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    1. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    2. Viviane Köhler & Marcia Fampa & Olinto Araújo, 2013. "Mixed-Integer Linear Programming Formulations for the Software Clustering Problem," Computational Optimization and Applications, Springer, vol. 55(1), pages 113-135, May.
    3. Dorit S. Hochbaum, 2013. "A Polynomial Time Algorithm for Rayleigh Ratio on Discrete Variables: Replacing Spectral Techniques for Expander Ratio, Normalized Cut, and Cheeger Constant," Operations Research, INFORMS, vol. 61(1), pages 184-198, February.
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