With rapid development of airlines, airports today become much busier and more complicated than previous days. The assignment of aircraft arriving on schedule to available gate is a major issue during the daily airline operations. In this project, we consider the over-constrained airport gate assignment problem (AGAP) where the number of flights exceeds the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distance or connection times. The procedures which are used to do this project are to create a mathematical model formulation and then Identify decision variables and finally identify constraints and objective function. In addition, we will consider in the AGAP the size of each gate in the terminal and also the towing process for the aircrafts. We will use greedy algorithm and Tabu search metaheuristic to solve the problem. The greedy algorithm minimizes ungated flights while providing initial feasible solutions while we devise a new neighborhood search technique, the interval exchange move, which allow us flexibility in seeking good solutions, especially in case when flight schedules are dense in time. Experiments conducts give good results.