On the Applicability of Lower Bounds for Solving Rectilinear Quadratic Assignment Problems in Parallel

The quadratic assignment problem (QAP) belongs to the hard core of N P-hard optimization problems. After almost forty years of research only relatively small instances can be solved to optimality. The reason is that the quality of the lower bounds available for exact methods is not suucient. Recently, lower bounds based on decomposition were proposed for the so called rectilinear QAP that proved to be the strongest for a large class of problem instances. We investigate a) the diiculty of incorporating new bound functions devised and implemented by one research team in a parallel code devised and implemented by another team, and b) the strength of these bounds when applied not only at the root node of a search tree but as the bound function used in a Branch-and-Bound code solving large scale QAPs.