Since the discovery of Ceres, asteroids have been of immense scientific interest and intrigue. They hold answers to many of the fundamental questionsabout the formation and evolution of the Solar System. Therefore, a missionsurveying the asteroid belt with close encounter of carefully chosen asteroidswould be of immense scientific benefit. The trajectory of such an asteroidtour mission needs to be designed such that asteroids of a wide range ofcompositions and sizes are encountered; all with an extremely limited ∆Vbudget.This thesis presents a novel heuristic algorithm to optimize trajectoriesfor an asteroid tour mission with close range flybys (≤ 1000 km). The coresearch algorithm efficiently decouples combinatorial (i.e. choosing the asteroids to flyby)and continuous optimization (i.e. optimizing critical maneuversand events) of what is essentially a mixed integer programming problem.Additionally, different methods to generate a healthy initial population forthe combinatorial optimization are presented.The algorithm is used to generate a set of 1800 feasible trajectories withina 2029+ launch frame. A statistical analysis of these set of trajectories isperformed and important metrics for the search are set based on the statistics.Trajectories allowing flybys to prominent families of asteroids like Flora andNysa with ∆V as low as 4.99 km/s are obtained.Two modified implementations of the algorithm are presented. In a firstiteration, a large sample of trajectories is generated with a limited numberof encounters to the most scientifically interesting targets. While, a posteriori, trajectories are filled in with as many small targets as possible. Thisis achieved in two different ways, namely single step extension and multiplestep extension. The former fills in the trajectories with small targets in onestep, while the latter optimizes the trajectory by filling in with one asteroid per step. The thesis also presents detection of asteroids for successfullyperforming flybys. A photometric filter is developed which prunes out badlyilluminated asteroids. The best trajectory is found to perform well againstthis filter such that nine out of the ten planned flybys are feasible.