The Quadratic Assignment Problem (QAP) is one of the most challenging NP-Hard combinatorial optimization problems. Circuit-layout design, transportation/traffic engineering, and assigning gates to airplanes are some of the interesting applications of the QAP. In this study, we introduce an enhanced version of a recent local search heuristic, Breakout Local Search Algorithm (BLS), by using the Levenshtein Distance metric for checking the similarity of the new starting points to previously explored QAP permutations. The similarity-checking process prevents the local search algorithm, BLS, from getting stuck in already-explored areas. In addition, the proposed BLS Algorithm (BLS-OpenMP) incorporates multi-threaded computation using OpenMP. The stagnation-aware search for the optimal solutions of the QAP is executed concurrently on several cores with diversified trajectories while considering their similarity to already-discovered local optima. The exploration of the search space is improved by selecting the starting points intelligently and speeding up the fitness evaluations linearly with number of processors/threads. BLS-OpenMP has been tested on the hardest 59 problem instances of the QAPLIB, and it obtained 57 of the best known results. The overall deviation of the achieved solutions from the best known results is 0.019% on average, which is a significant improvement compared with state-of-the-art algorithms. (C) 2016 Elsevier Ltd. All rights reserved.