Genetic algorithm (GA) is improved with fast non-dominated sort approach and crowded comparison operator. A new algorithm called parallel multi-objective genetic algorithm (PMGA) is developed with the support of Massage Passing Interface (MPI). Then, PMGA is combined with Artificial Neural Network (ANN) to improve the optimization efficiency. Training samples of the ANN are evaluated based on the two-dimensional Navier-Stokes equation solver of cascade. To demonstrate the feasibility of the hybrid algorithm, an optimization of a controllable diffusion cascade is performed. The optimization results show that the present method is efficient and trustiness.