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Separation Strategies for Chvátal-Gomory Cuts in Resource Constrained Project Scheduling Problems: A Computational Study

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Abstract

The Resource Constrained Project Scheduling Problems is a well-known \(\mathcal {N}\mathcal {P}\)-hard combinatorial optimization problem. A solution for RCPSP consists in allocating jobs by selecting execution modes and respecting precedence constraints and resource usage. One of main challenges that exact linear-based programming solution approaches currently face is that compact usually provide weak lower bounds. In this paper we propose use of general purpose Chvátal-Gomory cuts to strengthen the LP-based bounds. We observed that by using proper cut separation strategies, the produced bounds can compete with or improve bounds with those obtained with problem specific cuts.

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Notes

  1. 1.

    25 in our experiments.

  2. 2.

    The relative gap closed is computed as follows: given an obtained dual bound \(\underline{b}\) and the best known upper bound \(\overline{b}\) the relative gap closed is \(\underline{b}/\overline{b}\) if \(\overline{b}\ne 0\) or zero otherwise.

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Acknowledgements

The authors thank CNPq and FAPEMIG for supporting this research.

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Authors and Affiliations

  1. Computing Department, Federal University of Ouro Preto, Ouro Preto, Brazil

    Janniele Aparecida Soares Araujo & Haroldo Gambini Santos

  2. Computing and Systems Department, Federal University of Ouro Preto, João Monlevade, Brazil

    Janniele Aparecida Soares Araujo

Authors
  1. Janniele Aparecida Soares Araujo
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  2. Haroldo Gambini Santos
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Correspondence to Janniele Aparecida Soares Araujo .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Araujo, J.A.S., Santos, H.G. (2017). Separation Strategies for Chvátal-Gomory Cuts in Resource Constrained Project Scheduling Problems: A Computational Study. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10404. Springer, Cham. https://doi.org/10.1007/978-3-319-62392-4_33

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  • DOI: https://doi.org/10.1007/978-3-319-62392-4_33

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