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Mixed-Integer Linear Programming Formulations for the Software Clustering Problem

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Abstract

The clustering problem has an important application in software engineering, which usually deals with large software systems with complex structures. To facilitate the work of software maintainers, components of the system are divided into groups in such a way that the groups formed contain highly-interdependent modules and the independent modules are placed in different groups. The measure used to analyze the quality of the system partition is called Modularization Quality (MQ). Designers represent the software system as a graph where modules are represented by nodes and relationships between modules are represented by edges. This graph is referred in the literature as Module Dependency Graph (MDG). The Software Clustering Problem (SCP) consists in finding the partition of the MDG that maximizes the MQ.

In this paper we present three new mathematical programming formulations for the SCP. Firstly, we formulate the SCP as a sum of linear fractional functions problem and then we apply two different linearization procedures to reformulate the problem as Mixed-Integer Linear Programming (MILP) problems. We discuss a preprocessing technique that reduces the size of the original problem and develop valid inequalities that have been shown to be very effective in tightening the formulations. We present numerical results that compare the formulations proposed and compare our results with the solutions obtained by the exhaustive algorithm supported by the freely available Bunch clustering tool, for benchmark problems.

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Acknowledgements

This research has been supported in part by CNPq and FAPERJ (Brazil). The authors thank Ali S. Mamaghani and Brian S. Mitchell for providing the instances used on the computational experiments and thank the anonymous reviewers, whose comments greatly improve the structure of the presentation.

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Authors and Affiliations

  1. COPPE, Federal University of Rio de Janeiro, C.P. 68530, 21945-970, Rio de Janeiro, Brazil

    Viviane Köhler & Marcia Fampa

  2. CTISM, Federal University of Santa Maria, Santa Maria, Rio Grande do Sul, Brazil

    Olinto Araújo

Authors
  1. Viviane Köhler
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  2. Marcia Fampa
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  3. Olinto Araújo
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Correspondence to Marcia Fampa.

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Köhler, V., Fampa, M. & Araújo, O. Mixed-Integer Linear Programming Formulations for the Software Clustering Problem. Comput Optim Appl 55, 113–135 (2013). https://doi.org/10.1007/s10589-012-9512-9

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  • DOI: https://doi.org/10.1007/s10589-012-9512-9

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