Analysis of Global Optimization Algorithms for Costate Initialization of Minimum-Time Spiral Transfers

Costate initialization with stochastic global optimization (SGO) algorithms has proven successful in alleviating some of the difficulties associated with solving spacecraft trajectory optimal control problems with the indirect method. Although many SGO algorithms are applicable to this task, only particle swarm optimization (PSO) has been systematically analyzed for its costate initialization performance to date. In this work, we seek to analyze several variants of Differential Evolution (DE) and Monotonic Basin Hopping (MBH) for costate initialization of low-thrust minimum-time spiral transfer problems. We apply these algorithms to two transfer scenarios: (i) from a geostationary transfer orbit to an L1 halo orbit, and (ii) from a low-altitude polar lunar orbit to a near-rectilinear halo orbit. The performance of these algorithms is compared against PSO through the use of several metrics, aimed at capturing their ability to generate a guess that results in successful convergence to an optimal transfer solution. Certain variants of DE and MBH tend to perform better than others, though general algorithm performance is found to vary significantly based on the transfer scenario.