A genetic algorithm optimization methodology is applied to the design of the combustion system of a heavy-duty diesel engine fueled with dimethyl ether (DME). The optimization includes the key combustion system related hardware, bowl geometry and injection nozzle design, together with the most relevant air management and injection settings. The GA was linked to the KIVA computational fluid dynamics code and an automated grid generation tool to perform a single-objective optimization. The optimization target focused on maximizing efficiency, while keeping NOx emissions, peak pressure and maximum pressure rise rate under the baseline engine levels. This research work not only provides the optimum combustion system definition, but also the cause-effect relation between the inputs and outputs under investigation, identifying the most relevant parameters controlling the performance of a DME fueled engine. Piston bowl geometry is found to primarily influence heat transfer and combustion efficiency due to its impact on the surface area and fuel distribution, respectively. Mixing is most affected by the injection system parameters. Finally, the optimum DME engine configuration provides 6.9% absolute net indicated efficiency improvement over the baseline engine fueled with DME. This study confirms the potential of DME as a promising fuel for the future generation of compression ignition engines and demonstrates the need to co-optimize the fuel and combustion system.