  The Quadratic Assignment Problem, QAP, is a classic combinatorial
optimization problem, classified as NP-hard and widely studied. This problem
consists in assigning N facilities to N locations obeying the relation of 1 to
1, aiming to minimize costs of the displacement between the facilities. The
application of Reformulation and Linearization Technique, RLT, to the QAP leads
to a tight linear relaxation but large and difficult to solve. Previous works
based on level 3 RLT needed about 700GB of working memory to process one large
instances (N = 30 facilities). We present a modified version of the algorithm
proposed by Adams et al. which executes on heterogeneous systems (CPUs and
GPUs), based on level 2 RLT. For some instances, our algorithm is up to 140
times faster and occupy 97% less memory than the level 3 RLT version. The
proposed algorithm was able to solve by first time two instances: tai35b and
tai40b.
