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Variable Valve Actuation (VVA) technology provides high potential in achieving high performance, low fuel consumption and pollutant reduction. However, more degrees of freedom impose a big challenge for engine characterization and calibration. In this study, a simulation based approach and optimization framework is proposed to optimize the setpoints of multiple independent control variables. Since solving an optimization problem typically requires hundreds of function evaluations, a direct use of the high-fidelity simulation tool leads to the unbearably long computational time. Hence, the Artificial Neural Networks (ANN) are trained with high-fidelity simulation results and used as surrogate models, representing engine's response to different control variable combinations with greatly reduced computational time. To demonstrate the proposed methodology, the cam-phasing strategy at Wide Open Throttle (WOT) is optimized for a dual-independent Variable Valve Timing (VVT) engine.