Online Surrogate Models for the Constrained Optimization of Interplanetary Low-Thrust Trajectories

Abstract

The optimization of interplanetary, low-­thrust trajectories is a computationally expensive aspect of
preliminary mission design. To reduce the computational burden associated with it, surrogate models
can be used as cheap approximations of the original fitness function. Training the surrogate models in
a fully online manner can be done to remove the need of having previously generated datasets, which
is another source of computational cost. The Sims­-Flanagan transcription is used to model an Earth-Mars transfer which is optimized through different optimization routines. The development of a C++
library with machine learning tooling was initiated, containing implementations for Generalized Regression Neural Networks (GRNNs) and Radial Basis Function Networks (RBFNs) that are used in global
and local surrogates, respectively, having their hyperparameters tuned through cross-­validation. A
surrogate model was constructed using Differential Evolution (DE) operators and an uncertainty-based
infill criterion for the global search phase, and approximation of the derivative of the original fitness
function which is provided to SNOPT (Sparse Nonlinear Optimizer), in the local search phase. An ablation study was performed to assess how each of the components of the surrogate model contribute
to the results. It was verified that neither the derivative information nor the local search as a whole led
to better results. The surrogate model was also outperformed by the standard optimization strategy
found in literature, Monotonic Basin Hopping (MBH). Two new surrogate models incorporating ideas of
this strategy were created, with one of them outperforming every other model that was tested. Despite
not having performed a full study of the computational effort due to the simulations having been run in a
server with a variable load, the new models present better results for similar amounts of fitness function
evaluations. A Wilcoxon rank-­sum test was performed to assess whether the results have statistical
significance, leading to the conclusion that a surrogate model can be used to improve the optimization
of low-­thrust trajectories modeled with the Sims­-Flanagan transcription when inserted in a monotonic
basin hopping optimization scheme.