The greatest fuel efficiency advantages of gasoline direct injection (GDI) engines are achieved under the so-called mixed mode boosting, where mixture characteristics are properly adapted to the specific working condition. In particular, in the medium range of load and speed, overall lean mixtures are suitable of being used in the so-called direct injection stratified charge operation. Present paper reports the results of numerical optimization analyses aimed at increasing the energetic efficiency of a GDI engine equipped with a high pressure multi-hole injector under both single and double injection events. In moderate-load moderate-speed lean conditions, the single or double injection synchronization in the working cycle is effected through a procedure that couples a 3D numerical model of the in-cylinder processes with an optimization tool. The choice of both the start of the injection events and the time of spark advance is realized to maximize the engine work. The optimal double injection solution is shown to increase the engine energy efficiency with respect to the case injection is realized in one shot, thus confirming that split injections improve the quality of the charge stratification under lean operation. The effect on the major pollutants is also discussed. (C) 2012 Elsevier Ltd. All rights reserved.