Abstract
In this paper we propose an algorithm for the vertex separator problem (VSP) based on Lagrangian Relaxation and on cutting planes derived from valid inequalities presented in [3]. The procedure is used as a preprocessing for the branch-and-cut (B&C) algorithm implemented for VSP in [12], aiming to generate an initial pool of cutting planes and a strong primal bound for the latter. Computational experiments show that the exact method obtained in that way outperforms the pure B&C algorithm recently introduced by de Souza and Balas in [12]. Besides, we show that the Lagrangian phase is a very effective heuristic for the VSP, often producing optimal solutions extremely fast.
Research supported by grants CNPq-307773/2004-3 and FAPESP-03/09925-5.
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Cavalcante, V.F., de Souza, C.C. (2007). Lagrangian Relaxation and Cutting Planes for the Vertex Separator Problem. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_42
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DOI: https://doi.org/10.1007/978-3-540-74450-4_42
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