The ASTER mission under study by the Brazilian National Institute for Space Research would be the first to explore a triple asteroid system. To find orbits stable in such a perturbed environment, an orbit propagation and optimization programme has been written, which makes use of Evolutionary evolution algorithms. The programme written proves sufficient to identify suitable solutions for several use cases based on various mission phases and scenarios. The solar radiation pressure has been identified as a critical perturbation that prevents the existence of solutions in some scenarios, and often drives existing solutions towards terminator orbits.