Operations Research and Enterprise Systems: 4th by Dominique De Werra, Greg H. Parlier, Begoña Vitoriano PDF

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Extra resources for Operations Research and Enterprise Systems: 4th International Conference, ICORES 2015, Lisbon, Portugal, January 10-12, 2015, Revised Selected Papers

Example text

More precisely, it must be executed on: – all the machines of C b – either all the machines of Cb,1 , or all the machines of Cb,2 – one machine of M Note that relying on cliques is not necessary to make this analogy with multiprocessor scheduling, another option could be to define a machine for each binary constraint, but relying on cliques allows to take into account several constraints simultaneously, just like global constraints in constraint programming. In the example of Fig. 2, for the beam number 1 with the notations C1 = {c1,1 , c1,2 }, C1,1 = {c1,1,1 , c1,1,2 } and C1,2 = {c1,2,1 , c1,2,2 }, we have: – c1,1 and c1,2 associated to the cliques/machines {1, 2} and {1, 3} of G – c1,1,1 and c1,1,2 associated to the machines of first polarization for the cliques {1, 2, 3} and {1, 3, 4} in G – c1,2,1 and c1,2,2 associated to the machines of second polarization for the cliques {1, 2, 3} and {1, 3, 4} in G – m1 the machine in M used by the beam 1 In the example, the two carriers required in beam 1 use the second and third frequency channels and the first kind of polarization.

See the references section of [3] for more). However, their approach is almost exclusively aimed on interval solutions, that is on payoff distributions consisting of intervals and thus containing another uncertainty. This is in contrast with selections – possible outcomes of an interval game with no additional uncertainty. Selection-based approach was never systematically studied and not very much is known. This paper is trying to fix c Springer International Publishing Switzerland 2015 D. de Werra et al.

A global constraint [2] is a set of constraints for which it is preferable to treat that set of constraints as a whole than to treat all the constraints of that conjunction of constraints individually. Using global constraints is a way to have a better view on the structure of the problem, which is then exploited with powerful filtering algorithms. On that regard, a very significant example is the all different constraint [15] alldifferent(X) that forces all the variables of the array X to be different.

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