MATHEMATICAL ENGINEERING TECHNICAL REPORTS The Quadratic Semi-Assignment Polytope
نویسندگان
چکیده
We study a polytope which arises from a mixed integer programming formulation of the quadratic semi-assignment problem. We introduce an isomorphic projection in order to transform the polytope to another essentially equivalent and tractable polytope. As a result, some basic polyhedral properties, such as the dimension, the affine hull, and the trivial facets, are obtained in quite a simple way. We further present valid inequalities called cliqueand cut-inequalities and give complete characterizations for them to be facet-defining. We also discuss a simultaneous lifting of the clique-type facets. Finally, we show an application of the quadratic semi-assignment problem to hub location problems with some computational experiences.
منابع مشابه
MATHEMATICAL ENGINEERING TECHNICAL REPORTS The Symmetric Quadratic Semi-Assignment Polytope
We deal with quadratic semi-assignment problems with symmetric distances. This symmetry reduces the number of variables in its mixed integer programming formulation. We investigate a polytope arising from the problem, and obtain some basic polyhedral properties, the dimension, the affine hull and certain facets through an isomorphic projection. We also present a nontrivial class of facets. Comp...
متن کاملThe quadratic assignment polytope
We study the quadratic assignment problem (with n variables) from a polyhedral point of view by considering the quadratic assignment polytope that is defined as the convex hull of the solutions of the linearized problem (with n + 2 n 2 n −1 ( ) variables). We give the dimension of the polytope and a minimal description of its affine hull. We also propose a family of facets with a separation alg...
متن کاملAffine maps between quadratic assignment polytopes and subgraph isomorphism polytopes
We consider two polytopes. The quadratic assignment polytope QAP(n) is the convex hull of the set of tensors x⊗x, x ∈ Pn, where Pn is the set of n×n permutation matrices. The second polytope is defined as follows. For every permutation of vertices of the complete graph Kn we consider appropriate (n 2 ) × (n 2 ) permutation matrix of the edges of Kn. The Young polytope P ((n − 2, 2)) is the conv...
متن کاملA Basic Study of the QAP - Polytope
We investigate a polytope (the QAP-Polytope) beyond a \natural" integer programming formulation of the Quadratic Assignment Problem (QAP) that has been used successfully in order to compute good lower bounds for the QAP in the very recent years. We present basic structural properties of the QAP-Polytope, partially independently also obtained by Rijal (1995). The main original contribution of th...
متن کاملThe QAP-polytope and the star transformation
The quadratic assignment problem (QAP) maybe was for a long time the one among the prominent NP-hard combinatorial optimization problems about which the fewest polyhedral results had been known. Recent work of Rijal (1995) and Padberg and Rijal (1996) has on the one hand yielded some basic facts about the associated quadratic assignment polytope, but has on the other hand shown that \naive" inv...
متن کامل