Deep networks as approximators of optimal low-thrust and multi-impulse cost in multitarget missions.

In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate optimal transfer costs to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, the fuel consumption of fuel-optimal low-thrust transfers, and the total Δ v of minimum- Δ v J 2 -perturbed multi-impulse transfers. To generate the training data, both considered categories of low-thrust trajectories are optimized using the indirect method, and the J 2 -perturbed multi-impulse trajectories are optimized using J 2 homotopy and particle swarm optimization. The hyper-parameters of deep networks are determined by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and the generalization capabilities of the developed deep networks for predicting cases well outside the training data are investigated. Applications in multitarget mission design are also investigated. • The mean relative error for low-thrust transfers is less than 0.5%. • The mean relative error for J 2 -perturbed multi-impulse transfers is less than 4%. • Deep networks are superior to other algorithms. • Deep networks show an excellent extrapolation capability. • Applications in multitarget mission design are investigated. [ABSTRACT FROM AUTHOR]