In the airline industry, the Aircraft Maintenance Routing (AMR) problem has been one of the great successes of operations research. The AMR problem is to determine a particular route for each aircraft to undergo different levels of maintenance checks. The objective is to minimize the total maintenance costs. In this study, our aim is to present a mathematical formulation for the AMR problem which takes into account the case of Aircraft On Ground (AOG). We develop solution approaches based on Particle Swarm Optimization algorithm and Genetic algorithm for solving the problem. The results show the effectiveness of this solution in reducing computational time.