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Solving RCPSP/max by lazy clause generation

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Abstract

We present a generic exact method for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedence relations (Rcpsp/max). This is a very general scheduling model with applications areas such as project management and production planning. Our method uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply no-good learning and conflict-driven search to the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solution and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. In comparison to other methods, our method is able to find better solutions faster on the Rcpsp/max benchmarks. Indeed, our method closes 573 open problem instances and generates better solutions in most of the remaining instances. Surprisingly, although ours is an exact method, it outperforms the published non-exact methods on these benchmarks in terms of the quality of solutions.

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Notes

  1. In the literature, Rcpsp/max is also called as Rcpsp with temporal precedences, arbitrary precedences, minimal and maximal time lags, and time windows.

  2. Conflict sets are set of activities for which their execution might overlap in time and violate at least one resource constraint if they are executed at the same time.

  3. Results from Schwindt (1998a) are taken from Dorndorf et al. (2000)

  4. The missing propagators are not available in the G12 Constraint Programming Platform.

  5. No machine details are given in Oddi and Rasconi (2009).

  6. The paper (Schwindt 1998a) was not accessible for us, so that here the reported results are taken from Cesta et al. (2002).

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Acknowledgements

We are thankful to the reviewers for their helpful comments and suggestions. NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.

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Authors and Affiliations

  1. National ICT Australia, Department of Computing and Information Systems, The University of Melbourne, Melbourne, Victoria, 3010, Australia

    Andreas Schutt, Thibaut Feydy & Peter J. Stuckey

  2. Faculty of Information Technology, Monash University, Caulfield, Victoria, 3145, Australia

    Mark G. Wallace

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  1. Andreas Schutt
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  2. Thibaut Feydy
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  4. Mark G. Wallace
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Correspondence to Andreas Schutt.

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Schutt, A., Feydy, T., Stuckey, P.J. et al. Solving RCPSP/max by lazy clause generation. J Sched 16, 273–289 (2013). https://doi.org/10.1007/s10951-012-0285-x

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