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The application of the Reformulation Linearization Technique (RLT) to theQuadratic Assignment Problem (QAP) leads to a tight linear relaxation with hugedimensions that is hard to solve. Previous works found in the literature showthat these relaxations combined with branch-and-bound algorithms belong to thestate-of-the-art of exact methods for the QAP. For the level 3 RLT (RLT3),using this relaxation is prohibitive in conventional machines for instanceswith more than 22 locations due to memory limitations. This paper presents adistributed version of a dual ascent algorithm for the RLT3 QAP relaxation thatapproximately solves it for instances with up to 30 locations for the firsttime. Although, basically, the distributed algorithm has been implemented ontop of its sequential conterpart, some changes, which improved not only theparallel performance but also the quality of solutions, were proposed here.When compared to other lower bounding methods found in the literature, ouralgorithm generates the best known lower bounds for 26 out of the 28 testedinstances, reaching the optimal solution in 18 of them.

Improving Lower Bounds for the Quadratic Assignment Problem by applying a Distributed Dual Ascent Algorithm