Abstract
IBM ILOG CP Optimizer is a constraint solver that implements a model-and-run paradigm. For scheduling problems, CP Optimizer provides a relatively simple but very expressive modeling language based on the notion of interval variables. This paper presents the temporal linear relaxation (TLR) used to guide the automatic search when solving scheduling problems that involve temporal and resource allocation costs. We give the rationale of the TLR, describe its integration in the automatic search of CP Optimizer, and present the relaxation of most of the constraints and expressions of the model. An experimental study on a set of classical scheduling benchmarks shows that using the TLR is essential for problems with irregular temporal costs and generally helps for problems with resource allocation costs.
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Notes
It is to be noted that \(x(a)\), \(s(a)\), \(e(a)\), and \(l(a)\) are not proper decision variables of the problem, and we use them here only for the purpose of defining interval variables. In the model, interval variables are basic variables, and they are not an assembly of lower level variables. The different features of an interval variable (presence status, start, end, and length) are constrained via some expressions that we will see later (Table 1).
Subscript \(p\) stands for presence value as this is the value of the expression in case the interval variable is present.
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Laborie, P., Rogerie, J. Temporal linear relaxation in IBM ILOG CP Optimizer. J Sched 19, 391–400 (2016). https://doi.org/10.1007/s10951-014-0408-7
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DOI: https://doi.org/10.1007/s10951-014-0408-7