In wire arc additive manufacturing (WAAM), a trade-off exists among deposition efficiency, microstructure, and mechanical properties. Addressing this challenge, this work proposes an innovative multi-objective optimization framework tailored for WAAM of AZ31 magnesium alloy components, which integrates deposition efficiency and microstructure as coupled objectives and is resolved through the NSGA-II algorithm. The proposed framework employs quadratic regression to correlate process parameters with deposition efficiency through geometric morphology mediation, while addressing uncertainties in WAAM by integrating theoretical insights with data-driven stacked ensemble learning for grain size prediction, establishing the hybrid physics-informed data method for WAAM microstructure prediction. The optimized process achieved a deposition rate of 6257 mm³/min, with effective width and average layer height maintained at 10.1 mm and 4.13 mm, respectively. Microstructural optimization produced a fine, uniform, fully equiaxed grain structure with an average grain size of 38 μm. These findings underscore the significant industrial potential of intelligent optimization strategies in WAAM for manufacturing lightweight, high-performance components in aerospace and transportation sectors.