This work investigates the potential improvements in vehicle fuel economy possible by optimizing gear shift strategies to leverage a novel boosting device, an electrically assisted variable speed supercharger (EAVS), also referred to as a power split supercharger (PSS). Realistic gear shift strategies, resembling those commercially available, have been implemented to control upshift and downshift points based on torque request and engine speed. Using a baseline strategy from a turbocharged application of a MY2015 Ford Escape, a vehicle gas mileage of 34.4 mpg was achieved for the FTP75 drive cycle before considering the best efficiency regions of the supercharged engine. Overlaying predicted speed and load visitation points from the FTP75, HWY and US06 drive cycles with the engine’s brake specific fuel consumption (BSFC) map, reveals how to manipulate the gear shift curves so that the visitation points concentrate at the speed and load conditions where BSFC is lowest, or where the engine runs most efficiently. The shift strategy curve was moved incrementally to test for the optimal position at which the average gas mileage would be highest for each drive cycle. Additionally, the times between gear shifts were varied for both the upshift and the downshift. Since shortening the minimum interval time between shifts allows the engine to rapidly shift to a more fuel-efficient gear but also increases the number of gear shifts, during which some power is lost, there is an optimal minimum interval time, identified here as 0.2 seconds. When these optimization strategies are combined, a 2.63% increase in fuel efficiency during the FTP75 drive cycle for the EAVS engine was achieved. Interestingly, this strategy did not involve aggressive downspeeding of the engine at high loads.