Allocating tasks to processors is a well-known NP-Hard problem in distributed computing systems. Due to the lack of practicable exact solutions, it has been attracted by the researchers working on heuristic based suboptimal search algorithms. With the recent inclusion of multiple objectives such as minimizing the cost, maximizing, the throughput and maximizing the reliability, the problem gets even more complex and an efficient approximate method becomes more valuable. In this work, I propose a new solution for the multi-objective task allocation problem. My solution consists in designing a problem-specific neighboring function for an existing metaheuristic algorithm that is proven to be successful in quadratic assignment problems. The neighboring function, namely greedy reassignment with maximum release (GR-MR), provides a dynamic mechanism to switch the preference of the search between the exploration and exploitation. The experiments validate both that the quality of the solutions are close to the optimal and the proposed method performs significantly better comparing to three other metaheuristic algorithms. Neighboring functions being the common reusable components of metaheuristic algorithms, GR-MR can also be utilized by other metaheuristic-based solutions in the future. (C) 2016 Elsevier Ltd. All rights reserved.