This work proposes a novel polarization-maintaining hollow-core anti-resonant fiber structure characterized by high birefringence and low transmission loss. To address the inherent trade-off between birefringence and confinement loss, a Pareto-front-based multi-objective optimization algorithm is introduced into the geometrical design of the ARF. The optimal fiber design achieves a birefringence exceeding $1\times {10}^{-4}$ and a confinement loss of approximately 1 dB/m at the telecommunication wavelength of 1.55 $\mathsf{\mu }$m. In particular, the asymmetric wall thickness configuration further improves the trade-off, enabling confinement loss as low as 0.15 dB/m while maintaining birefringence on the order of $1\times {10}^{-4}$. This approach significantly reduces computational cost and exhibits strong potential for applications in polarization-maintaining communications, precision sensing, and high-power laser delivery.