This work investigates the possibility of setting up an Earth-asteroid cycler to asteroid 2001AE2 using solar sail technology. An ideal solar sail model with near-future technology levels (𝛽 = 0.05) is implemented alongside the circular restricted three-body problem, two-body problem and the elliptic Hill problem. The spacecraft cycles between the Sun-Earth 𝐿2 point (SE − L2) and the Sun-asteroid 𝐿1 point (Sa − L1). From these equilibrium points, the spacecraft state vector is propagated forwards and backwards with a constant sail attitude to generate solar-sail assisted invariant manifolds. Initial guess trajectories for the outbound and inbound sections of the cycle are generated with a genetic algorithm by searching for optimal sail attitudes for the different dynamical models and departure, connection and arrival times. These initial guess trajectoryies are used to seed the optimization software PSOPT. This pseudospectral collocation method using Legendre-Chebyshev polynomials transforms the infinite dimensional control problem into a finite dimensional non-linear programming problem. This way a continuous control profile can be found that justifies the dynamical models and results in a time-optimal trajectory. The resulting cycler is designed to have a cycle time of 11.04 years, with an outbound trajectory departing from SE − L2 on 01 − 03 − 2036 and arriving at Sa − L1 on 02 − 04 − 2039 and an inbound trajectory departing from Sa − L1 on 04 − 08 − 2043 and arriving back at SE − L2 on 31 − 03 − 2046. This results in dwelling times at SE − L2 of 351 days (0.95y) and at Sa − L1 of 1585 days (4.34y). The trajectories are assumed time-optimal given the assumptions made in the work, but require further refining for non-ideal properties of the solar sail and other higher fidelity models.