Abstract
The paper describes an optimization procedure for a class of discrete optimization problems which is defined by certain properties of the boundary of the feasible region and level sets of the objective function. It is shown that these properties are possessed, for example, by various scheduling problems, including a number of well known NP-hard problems which play an important role in scheduling theory. For one of these problems the presented optimization procedure is compared with a version of the branch-and-bound algorithm by means of computational experiments.
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References
Garey MR, Johnson DS (1976) Scheduling tasks with nonuniform deadlines on two processors. J ACM 23:461–467
Hoogeveen JA, van de Velde SL, Veltman B (1994) Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Discrete Appl Math 55:259–272
Lenstra JK, Rinnooy Kan AHG (1978) Complexity of scheduling under precedence constraints. Oper Res 26:22–35
Pinedo M (2008) Scheduling: theory, algorithms, and systems, 3rd edn. Springer, Berlin
Ullman JD (1975) NP-complete scheduling problems. J Comput Syst Sci 10:384–393
Zinder Y (2007) The strength of priority algorithms. In: Proceedings, MISTA, pp 531–537
Zinder Y, Roper D (1995) A minimax combinatorial optimization problem on an acyclic directed graph: polynomial-time algorithms and complexity. In: Proceedings, A.C. Aitken centenary conference, pp 391–400
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Zinder, Y., Memar, J. & Singh, G. Discrete optimization with polynomially detectable boundaries and restricted level sets. J Comb Optim 25, 308–325 (2013). https://doi.org/10.1007/s10878-012-9546-z
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DOI: https://doi.org/10.1007/s10878-012-9546-z