Estimating Bounds for Quadratic Assignment Problems Associated with Hamming and Manhattan Distance Matrices Based on Semidefinit

Quadratic assignment problems (QAPs) with a Hamming distance matrix for a hypercube or a Manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the issue of how to obtain lower bounds for those two classes of QAPs based on semidefinite programming (SDP). By exploiting the data structure of the distance matrix B, we first show that for any permutation matrix X, the matrix Y = E - XBXT is positive semi-definite, where is a properly chosen parameter depending only on the associated graph in the underlying QAP and E = eeT is a rank one matrix whose elements

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Hans D. Mittelmann, Jiming Peng
• Keywords: Distance Matrix, Manhattan Distance Matrix, Quadratic Assignment Problems, SIAMJO 2010