It is well known that, in general, exact algorithms for the Quadratic Assignment Problem (QAP) cannot solve problems of size N>15. Therefore, it is necessary to use heuristic approaches for solving large-scale QAPs. In this paper, we consider a class of heuristic approaches based on local search criteria. In particular, we selected four algorithms; CRAFT, Simulated Annealing, TABU search and the Graph Partitioning (GP) approach and studied their relative performance in terms of the quality of solutions and CPU times. All of these algorithms performed roughly the same, based on the results of two sets of test problems executed on an IBM ES/3090-600S computer.