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.
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References
Billionnet, A., Djebali, K.: Résolution d’un problème combinatoire fractionnaire par la programmation linéaire mixte. RAIRO. Recherche opérationnelle 40(2), 97–111 (2006)
Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)
Doval, D., Mancoridis, S., Mitchell, B.S.: Automatic clustering of software systems using a genetic algorithm. In: Proceedings of the Software Technology and Engineering Practice, pp. 73–81. IEEE (1999)
Gauthier, R., Pont, S.: Designing Systems Programs. Prentice-Hall, Englewood Cliffs (1970)
Harman, M., Hierons, R.M., Proctor, M.: A new representation and crossover operator for search-based optimization of software modularization. GECCO 2, 1351–1358 (2002)
Hochbaum, D.S.: Polynomial time algorithms for ratio regions and a variant of normalized cut. IEEE Trans. Pattern Anal. Mach. Intell. 32(5), 889–898 (2010)
Hochbaum, D.S.: A polynomial time algorithm for rayleigh ratio on discrete variables: Replacing spectral techniques for expander ratio, normalized cut, and cheeger constant. Oper. Res. 61(1), 184–198 (2013)
Jeet, K., Dhir, R.: Software architecture recovery using genetic black hole algorithm. ACM SIGSOFT Softw. Eng. Notes 40(1), 1–5 (2015)
Kazem, A.A.P., Lotfi, S.: A modified genetic algorithm for software clustering problem. In: Proceedings of the 6th WSEAS International Conference on Applied Informatics and Communications, pp. 306–311. World Scientific and Engineering Academy and Society (WSEAS) (2006)
Kazem, A.A.P., Lotfi, S.: An evolutionary approach for partitioning weighted module dependency graphs. In: 4th International Conference on Innovations in Information Technology, 2007. IIT’07, pp. 252–256. IEEE (2007)
Köhler, V., Fampa, M., Araújo, O.: Mixed-integer linear programming formulations for the software clustering problem. Comput. Optim. Appl. 55(1), 1–23 (2013)
Mahdavi, K., Harman, M., Hierons, R.M.: Finding building blocks for software clustering. Lecture Notes in Computer Science, vol, 2724, pp. 2513–2514 (2003)
Mahdavi, K., Harman, M., Hierons, R.M.: A multiple hill climbing approach to software module clustering. In: Proceedings of the International Conference on Software Maintenance, pp. 315–324. IEEE (2003)
Mamaghani, A.S., Meybodi, M.R.: Clustering of software systems using new hybrid algorithms. In: Proceedings of the 2009 IEEE International Conference on Computer and Information Technology (CIT’09), vol. 1, pp. 20–25 (2009)
Mancoridis, S., Mitchell, B.S., Chen, Y., Gansner, E.R.: Bunch: A clustering tool for the recovery and maintenance of software system structures. In: Proceedings of the IEEE International Conference on Software Maintenance, pp. 50–59. IEEE (1999)
Mancoridis, S., Mitchell, B.S., Rorres, C., Chen, Y., Gansner, E.R.: Using automatic clustering to produce high-level system organizations of source code. In: Proceedings of the 6th International Workshop on Program Comprehension, 1998. IWPC’98. pp. 45–52. IEEE (1998)
Mitchell, B.S.: A heuristic search approach to solving the software clustering problem. Ph.D. thesis, Drexel University (2002)
Mitchell, B.S., Mancoridis, S.: Using heuristic search techniques to extract design abstractions from source code. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1375–1382. Morgan Kaufmann Publishers Inc. (2002)
Parnas, D.L.: On the criteria to be used in decomposing systems into modules. Commun. ACM 15(12), 1053–1058 (1972)
Parsa, S., Bushehrian, O.: A new encoding scheme and a framework to investigate genetic clustering algorithms. J. Res. Pract. Inf. Technol. 37(1) (2005)
Räihä, O.: A survey on search-based software design. Comput. Sci. Rev. 4(4), 203–249 (2010)
Ryan, D.M., Foster, B.A.: An integer programming approach to scheduling. Computer scheduling of public transport urban passenger vehicle and crew scheduling, pp. 269–280 (1981)
Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)
Vanderbeck, F.: Branching in branch-and-price: a generic scheme. Math. Program. 130(2), 249–294 (2011)
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HH Kramer was financially supported by CNPq/CsF Grant No. 246661/2012-7 and CAPES
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Kramer, H.H., Uchoa, E., Fampa, M. et al. Column generation approaches for the software clustering problem. Comput Optim Appl 64, 843–864 (2016). https://doi.org/10.1007/s10589-015-9822-9
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DOI: https://doi.org/10.1007/s10589-015-9822-9