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Results for “gradient-free optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Q-Law for Rapid Assessment of Low Thrust Cislunar Trajectories Via Automatic Differentiation

Q-Law is a Lyapunov-based control law used to determine optimal controls for a low thrust trajectory. One major issue with its use is the difficult derivatives re-quired for calculating optimal controls at a given time. In this paper, an implementation of Q-Law with automatic differentiation via a Python package called JAX is applied. With automatic differentiation, the difficult derivatives for Q-Law’s optimal controls are calculated with ease, and derivatives of final states with respect to Q-Law’s weights are found enabling gradient-based optimization of Q-Law for the first time. Different search and optimization methods for finding optimal weights are then compared using the LEO to GEO problem, and it was found that gradient-free methods like design of experiments and genetic algorithm produced the best results, but they took the longest time to get a solution, while the gradient-based method found a locally optimal result in a much faster time. Overall, the run time for a single propagation is manageable and well-suited for a mission designer to use as an initial guess generator for trajectory optimization, or for simple orbit transfer analysis.

Nathan Steffen↗
NASA NTRS2011

Closed-Form and Numerically-Stable Solutions to Problems Related to the Optimal Two-Impulse Transfer Between Specified Terminal States of Keplerian Orbits

The first part of the paper presents some closed-form solutions to the optimal two-impulse transfer between fixed position and velocity vectors on Keplerian orbits when some constraints are imposed on the magnitude of the initial and final impulses. Additionally, a numerically-stable gradient-free algorithm with guaranteed convergence is presented for the minimum delta-v two-impulse transfer. In the second part of the paper, cooperative bargaining theory is used to solve some two-impulse transfer problems when the initial and final impulses are carried by different vehicles or when the goal is to minimize the delta-v and the time-of-flight at the same time.

Senent, Juan↗
NASA NTRS2010

Multifidelity Analysis and Optimization for Supersonic Design

Supersonic aircraft design is a computationally expensive optimization problem and multifidelity approaches over a significant opportunity to reduce design time and computational cost. This report presents tools developed to improve supersonic aircraft design capabilities including: aerodynamic tools for supersonic aircraft configurations; a systematic way to manage model uncertainty; and multifidelity model management concepts that incorporate uncertainty. The aerodynamic analysis tools developed are appropriate for use in a multifidelity optimization framework, and include four analysis routines to estimate the lift and drag of a supersonic airfoil, a multifidelity supersonic drag code that estimates the drag of aircraft configurations with three different methods: an area rule method, a panel method, and an Euler solver. In addition, five multifidelity optimization methods are developed, which include local and global methods as well as gradient-based and gradient-free techniques.

Kroo, Ilan↗