Available at: https://digitalcommons.calpoly.edu/theses/2404

#### Date of Award

12-2020

#### Degree Name

MS in Aerospace Engineering

#### Department/Program

Aerospace Engineering

#### College

College of Engineering

#### Advisor

Kira Abercromby

#### Advisor Department

Aerospace Engineering

#### Advisor College

College of Engineering

#### Abstract

Critical aspects of spacecraft missions, such as component organization, control algorithms, and trajectories, can be optimized using a variety of algorithms or solvers. Each solver has intrinsic strengths and weaknesses when applied to a given optimization problem. One way to mitigate limitations is to combine different solvers in an island model that allows these algorithms to share solutions. The program Spacecraft Trajectory Optimization Suite (STOpS) is an island model suite of heterogeneous and homogeneous Evolutionary Algorithms (EA) that analyze interplanetary trajectories for multiple gravity assist (MGA) missions. One limitation of STOpS and other spacecraft trajectory optimization programs (GMAT and Pygmo/Pagmo) is that they require a defined encounter body sequence to produce a constant length set of design variables. Early phase trajectory design would benefit from the ability to consider problems with an undefined encounter sequence as it would provide a set of diverse trajectories -- some of which might not have been considered during mission planning. The Hybrid Optimal Control Problem (HOCP) and the concept of hidden genes are explored with the most common EA, the Genetic Algorithm (GA), to compare how the methods perform with a Variable Size Design Space (VSDS). Test problems are altered so that the input to the cost function (the object being optimized) contains a set of continuous variables whose length depends on a corresponding set of discrete variables (e.g. the number of planet encounters determines the number of transfer time variables). Initial testing with a scalable problem (Branin's function) indicates that even though the HOCP consistently converges on an optimal solution, the expensive run time (due to algorithm collaboration) would only escalate in an island model system. The hidden gene mechanism only changes how the GA decodes variables, thus it does not impact run time and operates effectively in the island model. A Hidden Gene Genetic Algorithm ( HGGA) is tested with a simplified Mariner 10 (EVM) problem to determine the best parameter settings to use in an island model with the GTOP Cassini 1 (EVVEJS) problem. For an island model with all GAs there is improved performance when the different base algorithm settings are used. Similar to previous work, the model benefits from migration of solutions and using multiple algorithms or islands. For spacecraft trajectory optimization programs that have an unconstrained fly-by sequence, the design variable limits have the largest impact on the results. When the number of potential fly-by sequences is too large it prevents the solver from converging on an optimal solution. This work demonstrates HGGA is effective in the STOpS environment as well as with GTOP problems. Thus the hidden gene mechanism can be extended to other EAs with members containing design variables that function similarly. It is shown that the tuning of the HGGA is dependent on the specific constraints of the spacecraft trajectory problem at hand, thus there is no need to further explore the general capabilities of the algorithm.