Multi-objective optimization of magnetorheological polishing fluids formulation for K9 glass using BP neural network and crested porcupine optimizer

Magnetorheological polishing (MRP) of K9 glass faces an inherent trade-off: high material removal rate (MRR) versus low surface roughness (Sa), as well as by the strongly nonlinear coupling effects among multiple fluid components. To address this challenge, this study develops a BP neural network-assisted multi-objective optimization framework for reconciling MRR and Sa by optimizing the MRP fluids formulation. A water-based MRP fluid was formulated with variable carbonyl iron (22–62 vol%), polishing powder (4–12 vol%), five abrasives, and pH (2–12). Rheological and single-factor performance tests determined the optimal additive concentrations and revealed the influence of each component on MRR and Sa. A 25-run L 25 (5 6 ) orthogonal experiment provided the training and validation dataset. A three-layer BP neural network (8-10-2 architecture, Levenberg-Marquardt training) was constructed, achieving validation R 2 values of 0.9323 for MRR and 0.9217 for Sa. Using the trained network as the fitness function, the multi-objective crested porcupine optimizer (MOCPO) was compared against MOPSO and MOWOA. MOCPO outperformed the others in hypervolume (2.88 × 10 5 ), IGD (0.025), and spacing (0.048). The Pareto front yielded an optimal formulation: carbonyl iron 52.4 vol%, polishing powder 10.2 vol%, cerium oxide abrasive, and pH 7.5, giving a predicted MRR of 558 nm/min and Sa of 6.6 nm. Three independent validation experiments confirmed the predictions with average errors of 1.14% for MRR and 3.5% for Sa. The proposed BP-MOCPO framework provides a highly accurate and efficient solution for multi-objective optimization of MRP fluids formulation, effectively balancing MRR and Sa for K9 glass polishing.