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Contributions to the Minimum Linear Arrangement Problem: On a Binary Distance Model for the Minimum Linear Arrangement Problem,Used
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The Minimum Linear Arrangement problem consists in finding an ordering of the nodes of a weighted graph, such that the sum of the weighted edge lengths is minimized. We report on the usefulness of a new model within a branchandcutandprice algorithm for solving Minimum Linear Arrangement problems to optimality. The key idea is to introduce binary variables d_{ijk}, that are equal to 1 if nodes i and j have distance k in the permutation. We present formulations for complete and for sparse graphs and explain the realization of a branchandcutandprice algorithm. Furthermore, its different settings are discussed and evaluated. To the study of the theoretical aspects concerning the Minimum Linear Arrangement problem, we contribute a characterization of a relaxation of the corresponding polyeder.
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