The Multiple Knapsack Assignment Problem (MKAP) is a generalization of the Multiple Knapsack Problem (MKP), in which some additional assignment restrictions must be met. In this paper, we develop an efficient adaptive memetic algorithm to solve MKAP. The adaptive memetic algorithm (AMA) is obtained by integrating a powerful local search (LS) procedure within the framework of a genetic algorithm characterized by a dynamically adjusted mutation rate during the evolution process. Preliminary computational experiments have been performed on existing instances from the literature. The results achieved prove that our developed AMA performs better compared to the classical memetic algorithm (MA) and is highly competitive compared to the state-of-the-art approaches.