A Low-Dimensional Semidefinite Relaxation for the Quadratic Assignment Problem
نویسندگان
چکیده
منابع مشابه
A Low-Dimensional Semidefinite Relaxation for the Quadratic Assignment Problem
The quadratic assignment problem (QAP) is arguably one of the hardest NP-hard discrete optimization problems. Problems of dimension greater than 25 are still considered to be large scale. Current successful solution techniques use branch-and-bound methods, which rely on obtaining strong and inexpensive bounds. In this paper, we introduce a new semidefinite programming (SDP) relaxation for gener...
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The quadratic assignment problem (QAP ) is arguably one of the hardest of the NP-hard discrete optimization problems. Problems of dimension greater than 20 are considered to be large scale. Current successful solution techniques depend on branch and bound methods. However, it is difficult to get strong and inexpensive bounds. In this paper we introduce a new semidefinite programming (SDP ) rela...
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Recent progress in solving quadratic assignment problems (QAPs) from the QAPLIB test set has come from mixed integer linear or quadratic programming models that are solved in a branchand-bound framework. Semide nite programming bounds for QAP have also been studied in some detail, but their computational impact has been limited so far, mostly due to the restrictive size of the early relaxations...
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Semideenite programming (SDP) relaxations for the quadratic assignment problem (QAP) are derived using the dual of the (homogenized) Lagrangian dual of appropriate equivalent representations of QAP. These relaxations result in the interesting, special, case where only the dual problem of the SDP relaxation has strict interior, i.e. the Slater constraint qualii-cation always fails for the primal...
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It was recently demonstrated that a well-known eigenvalue bound for the Quadratic Assignment Problem (QAP) actually corresponds to a semideenite programming (SDP) relaxation. However, for this bound to be computationally useful the assignment constraints of the QAP must rst be eliminated, and the bound then applied to a lower-dimensional problem. The resulting \projected eigenvalue bound" is on...
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2009
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.1090.0419