The integration of intermittent renewable energy sources requires hydropower units to operate more flexibly and reliably over a wider load range. However, the flexible operation of Francis turbines, in particular high-head ones, is often constrained by flow instabilities, particularly rotating vortex rope (RVR) induced pressure pulsations under partial-load operating conditions. This study proposes a cost-effective multi-objective optimization framework to identify draft tube adjustable guide vanes (DTGV) configurations that mitigate RVR induced instabilities without compromising hydraulic efficiency under partial load (PL) operation. The framework combines design of experiments, computational fluid dynamics, a back-propagation neural network surrogate model, and a multi-objective genetic algorithm. To accelerate the optimization process, a steady-state mean swirl number is introduced as a practical surrogate indicator for RVR induced pressure pulsations. The close agreement between the back-propagation neural network predicted values and CFD results demonstrates the accuracy and efficiency of the proposed framework. The selected optimized DTGV reduces the low-frequency pressure pulsations amplitude by more than 70% compared to the traditional draft tube. Flow analysis reveals that the DTGV disrupts the main helical RVR into several tip vortices, substantially reduces the tangential velocity and confines flow unsteadiness to the shear layer between the outer and central regions, preventing the RVR formation. These results demonstrate that optimized DTGVs can provide a practical retrofit strategy for enhancing high head Francis's turbine stability and operational flexibility, supporting the integration of renewable energy into power systems.