The increased concern of global climate change and lack of sustainability of fossil fuels in the projected future has prompted further research into alternative fuel vehicles, or advanced vehicles, in an effort to combat vehicle emissions and fuel consumption. One of the many areas of advanced vehicles being researched includes the electrification and hybridization of vehicles. As the technology for hybrid-electric vehicles has increased, so has the need for more advanced control scheme for the vehicles. This includes the development and optimization of a shift schedule for the automatic transmission in a hybrid powertrain. The focus of this work is to demonstrate how to develop and analyze the benefits and shortcomings of two different shift schedules for a position 3 parallel hybrid-electric vehicle: a traditional two-parameter shift schedule that operates as a function of the driver's accelerator position and the vehicle's speed (SOC independent shift schedule), and a three-parameter shift schedule that also adapts to fluctuations in the state of charge of the high voltage batteries (SOC dependent shift schedule). The shift schedules were generated using an exhaustive search coupled with a fitness function to evaluate all possible vehicle operating points. The generated shift schedules were then tested in the software-in-the-loop (SIL) environment and the vehicle-in-the-loop (VIL) environment and compared to each other, as well as to the stock 8L45 8-speed transmission shift schedule. The results show that both generated shift schedules improved upon the stock transmission shift schedule used in the hybrid powertrain in component efficiency, vehicle efficiency, engine fuel economy, and vehicle fuel economy. However, there were few differences between the two shift schedules. A sensitivity analysis was then performed on the generated SOC dependent shift schedule by varying the initial SOC in the SIL environment in an attempt to explore more of the shift schedule's solution space. The sensitivity analysis showed little difference in vehicle energy consumption, engine fuel economy, and vehicle fuel economy during the executed driving cycle as initial SOC varied. Additionally, the analysis showed that the gear commanded from the SOC dependent shift schedule between the three cases were almost identical with the exception of at the start of the simulation. Once the control algorithm achieved and sustained the target SOC, the SOC dependent shift schedule contributed little as deviations in SOC were minute. iii DEDICATION This thesis is dedicated to my old family, new family, and friends. I want to thank my dad, James Connelly, for his patience with me and constant support through my college career. Without him I would not be where I am today. I want to thank my mom, Judi Connelly, who has been a pillar of support and always believed I can be better than I am. I want to thank my little sister, Sarah, for always keeping me on the right track.