Simulated annealing (SA) is a well-known metaheuristic commonly used to solve a great variety of NP-hard problems such as the quadratic assignment problem (QAP). As commonly known, the choice and size of neighborhoods can have a considerable impact on the performance of SA. In this work, we investigate and propose a SA variant that considers variable neighborhood structures driven by the state of the search. In the computational experiments, we assess the contribution of this SA variant in comparison with the state-of-the-art SA for the QAP applied to printed circuit boards and conclude that our approach is able to report better solutions by means of short computational times.