Optimal continuous thrust orbit transfer using evolutionary algorithms

In order to calculate the time history of the trajectory properties for an optimal continuous-thrust orbit transfer, the equations of motion and adjoint equations are integrated. For optimality, boundary conditions on the Hamiltonian must be satisfied, subject to meeting the initial and final values of the state vectors. At the beginning of the integration, the initial co-state variables for the adjoint equations are needed. However, the initial costate variables are usually unknown and thus it is necessary to find these variables. In this paper, evolutionary algorithms (EAs) are introduced and applied to find the values of the initial costate variables. Results obtained from the EAs are compared with the results previously published, and it was found that for several low Earth orbit to geostationary Earth orbit transfers, the initial values of the adjoints are comparable to those found using traditional optimization methods. While many traditional optimization methods are very sensitive to initial values of the adjoint variables, the EAs are able to find the initial values of the adjoints from lower and upper bounds that are up to ±25% away from the actual values.