Cam-phasing is increasingly considered as a feasible Variable Valve Timing (VVT) technology for production engines. Additional independent control variables in a dual-independent VVT engine increase the complexity of the system, and achieving its full benefit depends critically on devising an optimum control strategy. A traditional approach relying on hardware experiments to generate set-point maps for all independent control variables leads to an exponential increase in the number of required tests and prohibitive cost. Instead, this work formulates the task of defining actuator set-points as an optimization problem. In our previous study, an optimization framework was developed and demonstrated with the objective of maximizing torque at full load. This study extends the technique and uses the optimization framework to minimize fuel consumption of a VVT engine at part load. By adding a penalty term for NOx emissions in the optimization objective, the tradeoff of fuel consumption and NOx emissions is explored. The methodology relies on high-fidelity simulations for pre-optimality studies and as means of generating data that characterize engine behavior in the multidimensional space. Artificial Neural Networks (ANN) are then trained on sets of high-fidelity simulation data and used as surrogate models, thus enabling optimization runs requiring hundreds of function evaluations. A case study performed for a DaimlerChrysler 2.4 liter fourcylinder SI engine demonstrates the use of the algorithm for minimizing fuel consumption while simultaneously meeting NOx emission targets.