In engineering, optimizing parameters often involves computationally expensive tasks, especially when dealing with multi-dimensional variables and multiple performance metrics. This falls under the category of multi-objective black-box optimization. To address this, we propose two optimization algorithms for low and medium-dimensional spaces, incorporating relaxation conditions for hyperplane segmentation. For the specific parameter optimization of HC-ARF, we employed a two-stage approach. It combines a BP neural network as a surrogate model with a hyperplane separation optimization algorithm. This method efficiently optimizes both confinement loss (CL) and birefringence, using a weighted sum approach to identify their Pareto sets. We validate the effectiveness and stability of the surrogate model by comparing it with traditional optimization algorithms. Exhaustive experiments confirm the superiority of this algorithm and the results show that our optimized structure achieves impressive performance metrics, including a loss of 0.8 dB/m, a birefringence of 2.2×10-4, and a critical bending radius of 0.5 cm under optimal parameters.