The Linear Programming Relaxation Permutation Symmetry Group of an Orthogonal Array Defining Integer Linear Program
Document Type
Article
Publication Date
6-1-2016
Abstract
There is always a natural embedding of $S_{s}\wr S_{k}$ into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation with equality constraints. The point of this paper is to prove that in the $2$ -level, strength- $1$ case the LP relaxation permutation symmetry group of this formulation is isomorphic to $S_{2}\wr S_{k}$ for all $k$ , and in the $2$ -level, strength- $2$ case it is isomorphic to $S_{2}^{k}\rtimes S_{k+1}$ for $k\geqslant 4$ . The strength- $2$ result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of $S_{2}\wr S_{k}$ . We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation.
DOI
10.1112/S1461157016000085
Source Publication
LMS Journal of Computation and Mathematics
Recommended Citation
Arquette, D. M., & Bulutoglu, D. A. (2016). The linear programming relaxation permutation symmetry group of an orthogonal array defining integer linear program. LMS Journal of Computation and Mathematics, 19(1), 206–216. https://doi.org/10.1112/S1461157016000085
Comments
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Reviewed at MR3507280