This research addresses scalable flow optimization in networks for emergency evacuation for natural disasters in socially vulnerable communities, a critical task given the increasing frequency of disasters. We propose a novel multi-origin/multi-destination Integer Linear Optimization (ILO) model, managing discrete assignments and structural robustness. The methodology includes pre-optimal identification and post-optimal tracking and sensitivity algorithms. Implemented in AIMMS, the model demonstrates reliability and scalability in extensive simulations. It achieved optimal solutions in 98.7% of cases with fast times (average 0.12s) for complex instances (up to 132,203 variables, 8,771 constraints), evacuating up to 4,885 people. A volcanic evacuation case study with real data showed applicability and performance. Sensitivity analysis revealed critical cost variabilities by family size/starting points, informing resilient adaptive strategies.