In this paper, modified non-dominated sorting genetic algorithm-II (MNSGA-II)-based optimal damping control of unified power flow controller (UPFC) has been designed to enhance the damping of low frequency oscillations in power systems. The robust damping of UPFC controller design is formulated as a multi-objective optimisation problem, thereby minimising the integral squared error (ISE) of speed deviation and input control signal (u) under a wide range of operating conditions. The effectiveness of the proposed controller is confirmed through nonlinear time domain simulation and Eigen value analysis. The results are compared with NSGA-II and conventional method. Simulation result reveals that the obtained Pareto-front using MNSGA-II-based UPFC controllers are better and uniformly distributed due to the controlled elitism and dynamic crowding distance concepts. The proposed modulation index of shunt inverter (mE)-based damping controller is superior to the other damping controllers under different loading conditions and improves the stability of system.