An alternative opportunity of future Psyche mission using differential evolution and gravity assists

NASA's Psyche mission will launch in August 2022 and begin a journey of 3.6 years to the metallic asteroid: Psyche, where it will orbits and examine this unique body. This paper presents an alternative opportunity of the Psyche mission as well as the return opportunity to the Earth. It uses Mars's gravity assists to rendezvous with and orbits to the largest metal asteroid in the solar system. The spacecraft orbits around Psyche for approximately 1710 solar days, then starts its return journey. In the outer layer of the proposed methodology, the differential evolution algorithm is used to find the optimal launch, flyby and arrival date. In the inner layer, Lambert's algorithm is used for finding the feasible and optimal space trajectories solution. Considering gravity assists, before the gravity assists impulse, an optimal thrust impulse has been calculated at periapsis of the fly-by planet that gives the maximum $\mathrm{\Delta }{\nu }_2$ to the spacecraft.