AN ANALYTICAL SURVEY FOR THE QUADRATIC ASSIGNMENT PROBLEM

The quadratic assignment problem (QAP), one of the most difficult problems in the NP-hard class, models many applications in several areas such as operational research, parallel and distributed computing, and combinatorial data analysis. Other optimization combinatorial problems such as the traveling salesman problem, maximal clique, isomorphism and graph partitioning can be formulated as a QAP. In this paper, we survey some of the most important formulations available and classify them according to their mathematical sources. We also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms, including those formulated according to metaheuristic strategies. Finally, we analyze the extension of the contributions brought about by the study of different approaches.