This study proposes a new global gas dynamics optimization method which was applied to a multi-objective optimization task of centrifugal compressor performance with the aim of determining the improvement probability for achieving high efficiency across a wide operating range. Initially, the original Nondominated Neighbor Immune Algorithm (NNIA) was extended to solve constrained multi-objective optimization problems for the first time, which mainly incorporated a procedure for handling inequality and equality constraints without additional parameters. Subsequently, an adaptive topological Back-propagation Multilayer Feed-forward Artificial Neural Network (BP-MLFANN) was trained using the modified NNIA to quickly evaluate the fitness value of the centrifugal compressor stage performance during the optimization. The feasibility of the method was validated using the first stage of a refrigeration centrifugal compressor. The results indicated a substantial enhancement in the stage efficiency of the optimized impeller at the Near-stall, Design, and Near-choke operating points, with increasement of 1.8%, 1.9%, and 4%, respectively, as compared to the baseline stage. The flow field analysis shows that the impact loss at impeller leading edge and flow separation in the passage reduced greatly, the mixing process between the leakage flow and mainstream in the channel is significantly weakened, thus the flow field becomes more uniform after optimization. The new global gas dynamics optimization method provides a reference for the development of efficient and rapid optimization techniques for centrifugal compressor.