The objective of this study is to propose an intelligent methodology for efficiently optimizing the injection molding parameters when multiple constraints and multiple objectives are involved. Multiple objective functions reflecting the product quality, manufacturing cost and molding efficiency were constructed for the optimization model of injection molding parameters while multiple constraint functions reflecting the requirements of clients and the restrictions in the capacity of injection molding machines were established as well. A novel methodology integrating variable complexity methods (VCMs), constrained non-dominated sorted genetic algorithm (CNSGA), back propagation neural networks (BPNNs) and Moldflow analyses was put forward to locate the Pareto optimal solutions to the constrained multiobjective optimization problem. The VCMs enabled both the knowledge-based simplification of the optimization model and the variable-precision flow analyses of different injection molding parameter schemes. The Moldflow analyses were applied to collect the precise sample data for developing BPNNs and to fine-tune the Pareto-optimal solutions after the CNSGA-based optimization while the approximate BPNNs were utilized to efficiently compute the fitness of every individual during the evolution of CNSGA. The case study of optimizing the mold and process parameters for manufacturing mice with a compound-cavity mold demonstrated the feasibility and intelligence of proposed methodology.