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

Abstract 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 J2-perturbed multi-impulse transfers. To generate the training data, both considered categories of low-thrust trajectories are optimized using the indirect method, and the J2-perturbed multi-impulse trajectories are optimized using J2 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.