In this paper, an approximate method is proposed for solving a multiple knapsack assignment problem(PMKAP) .  An instance of PMKAP is characterized by a set S of n items, and a set M of m knapsacks. Each item j is characterized with its nonnegative profit p and nonnegative weight w. Each knapsack i is characterized by a nonnegative weight c. However, items are divided into r mutually disjoint subsets of items Sk. The goal of the problem is to determine the assignment of all knapsacks to each subset, and to fill knapsacks with items in that subset, so as to maximize the total profit related to the selected items. The iterative algorithm combines descent procedure  with several strategies for anhancing the quality of the solutions. The preliminary experimentation showed that the proposed approach remains competitive, where new bounds have been reached.