Distributed Swarm Optimization for the Solution of Boundary Value Problems in Astrodynamics

In this paper, a distributed computing framework that exploits high-performance compute clusters and employs a Distributed Multiple-Swarm Particle Swarm Optimization (DMSPSO) algorithm is proposed for solving two-point boundary-value problems in astrodynamics. The DMSPSO algorithm performs a search of the solution space by attempting to minimize the weighted sum of squares of the boundary condition residuals, generating many guesses for the unknown variables that nearly satisfy the boundary conditions. These guesses are then used to solve the boundary-value problem with a gradient-based algorithm that runs in parallel with the DMSPSO search. The proposed framework is applied to solve two different boundary-value problems in astrodynamics. The first is formulated to compute energy-optimal transfers between a Geostationary Transfer Orbit and an L1 halo orbit using the Calculus of Variations approach, and the second is formulated to compute periodic orbits in the Circular Restricted Three Body Problem model. It is demonstrated that the methodology provides a large speedup over a conventional Particle Swarm Optimization algorithm, can be applied to solve sensitive boundary value problems, and facilitates the discovery of many (if not all) solutions of a given two-point boundary-value problem.