Solving the Quadratic Assignment Problem on heterogeneous environment (CPUs and GPUs) with the application of Level 2 Reformulation and Linearization Technique

Abstract: 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.