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.
25 in our experiments.
- 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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The authors thank CNPq and FAPEMIG for supporting this research.
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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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