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Lexicographical Order in Integer Programming

Abstract : Forcing lexicographical order in the solutions to an integer programming problem is a possible strategy to avoid symmetric solutions. An orbisack is the convex hull of the lexicographically ordered pairs of n-dimensional binary vectors. In this paper, we present a minimal complete description of orbisacks. In addition, we provide a polynomial formulation with exponential coefficients and a formulation with an exponential number of constraints but with unit coefficients, both of which still force lexicographical order. An exact separation procedure is also described.
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Contributor : Bernard Fortz Connect in order to contact the contributor
Submitted on : Monday, December 19, 2016 - 4:13:53 PM
Last modification on : Tuesday, November 22, 2022 - 2:26:16 PM




Martine Labbé, Alfredo Marín, Antonio M. Rodríguez-Chía. Lexicographical Order in Integer Programming. Vietnam Journal of Mathematics, 2016, ⟨10.1007/s10013-016-0220-0⟩. ⟨hal-01419551⟩



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