The potential of low temperature combustion to yield low NOx and soot while maintaining diesel-like thermal efficiencies has been demonstrated through countless studies. Methods of achieving low temperature combustion are just as numerous and they range from using high cetane number fuels, like diesel, with large amounts of exhaust gas recirculation, to completely premixing a high octane number fuel, like gasoline, and approaching an HCCI-like condition. The potential of operating a heavy-duty compression ignition engine fueled with conventional gasoline in a partially premixed combustion mode to have high thermal efficiency and low emissions has been demonstrated in this study. The objective of this work was to optimize the engine using computational tools. The KIVA3V-CHEMKIN code, a multi-dimensional engine CFD model was coupled to a Nondominated Sorting Genetic Algorithm (NSGA II), which is a multi-objective genetic algorithm. Two engine operating conditions were investigated in this study, a mid-load and a high-load point, 11 bar and 21 bar IMEP, respectively. The goal of the optimization study was to simultaneously reduce six objectives, which are soot, NOx, unburned hydrocarbons, carbon monoxide, indicated specific fuel consumption, and ringing intensity, which is related to maximum pressure rise rate. The genetic algorithm was allowed to vary eight engine design parameters that included pilot injection parameters, main injection parameters, injector included angle, number of injector nozzle holes, and swirl ratio. A non-parametric regression analysis tool was used to post-process the optimization results in order to illustrate the effects of the design parameters on the objectives. The results show that gross indicated thermal efficiencies of 50% with low emissions and low ringing intensity are possible at the mid-load condition. The high-load condition yields low NOx emissions, and an efficiency of 50% as well, but indicates that meeting soot emissions and ringing intensity constraints will be a challenge.