# Box-inequalities for quadratic assignment polytopes

@article{Jnger2001BoxinequalitiesFQ, title={Box-inequalities for quadratic assignment polytopes}, author={Michael J{\"u}nger and Volker Kaibel}, journal={Mathematical Programming}, year={2001}, volume={91}, pages={175-197} }

Abstract.Linear Programming based lower bounds have been considered both for the general as well as for the symmetric quadratic assignment problem several times in the recent years. Their quality has turned out to be quite good in practice. Investigations of the polytopes underlying the corresponding integer linear programming formulations (the non-symmetric and the symmetric quadratic assignment polytope) have been started during the last decade [34, 31, 21, 22]. They have lead to basic…

## 25 Citations

### The Quadratic Semi-Assignment Polytope

- Mathematics
- 2004

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…

### Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2

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- 2015

The branch-and-cut framework integrated into GloMIQO 2, which addresses mixed-integer quadratically constrained quadratic programs (MIQCQP) to ε-global optimality, is documents.

### A Dual Framework for Lower Bounds of the Quadratic Assignment Problem Based on Linearization

- Computer ScienceComputing
- 2014

A new and more general bounding procedure based on the dual of the linearization of Adams and Johnson is proposed and the computational results indicate that the new bound competes well with existing linearization bounds and yields a good trade off between computation time and bound quality.

### The QAP-polytope and the graph isomorphism problem

- MathematicsJ. Comb. Optim.
- 2018

A geometric approach to solve the Graph Isomorphism (GI in short) problem and defines a partial ordering on each exponential sized family of facet defining inequalities and shows that if there exists a common minimal violated inequality for all points in the feasible region outside the QAP-polytope, then the problem can be solved in polynomial time.

### On the SQAP-Polytope

- MathematicsSIAM J. Optim.
- 2000

A technique is derived for investigating the SQAP-polytope that is based on projecting the (low-dimensional) polytope into a lower dimensional vector-space, where the vertices have a "more convenient" coordinate structure.

### Unbounded convex sets for non-convex mixed-integer quadratic programming

- MathematicsMath. Program.
- 2014

It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a face of a set in the family of unbounded convex sets.

### A comprehensive review of quadratic assignment problem: variants, hybrids and applications

- BusinessJournal of Ambient Intelligence and Humanized Computing
- 2018

QAP is NP-hard problem that is impossible to be solved in polynomial time when the problem size increases, hence heuristic and metaheuristic approaches are utilized for solving the problem instead of exact approaches because these approaches achieve quality in the solution in short computation time.

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