Box-inequalities for quadratic assignment polytopes

Michael Jünger, Volker Kaibel
2001 Mathematical programming  
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. They have 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 by lead to basic knowledge on these polytopes concerning questions like their
more » ... a ne hulls, and trivial facets. However, no large class of (facet-de ning) inequalities that could be used in cutting plane procedures had been found. We present in this paper the rst such class of inequalities, the box inequalities, which have an interesting origin in some well-known hypermetric inequalities for the cut polytope. Computational experiments with a cutting plane algorithm based on these inequalities show that they are very useful with respect to the goal of solving quadratic assignment problems to optimality or to compute tight lower bounds. The most e ective ones among the new inequalities turn out to be indeed facet-de ning for both the non-symmetric as well as for the symmetric quadratic assignment polytope.
doi:10.1007/s101070100251 fatcat:4ixsykdwvbhetdidmw56fupste