Power system transient stability can be effectively improved by applying shunt braking resistors. This paper proposes multi-objective heuristics-based optimization for shunt braking resistor sizing. The proposed approach addresses three objectives: transient angle stability, transient voltage response, and mechanical stress of the turbine-generator shaft. The optimization problem was solved using a Python implementation of the multi-objective evolutionary NSGA-II algorithm. Based on the optimization model, comprehensive tests for multimachine IEEE 39-bus power system including single-and multi-objective simulations were performed. Pareto sets for various sets of objectives are obtained and discussed. The results show the complexity of the shunt braking resistor optimization process. Optimization studies were complemented by simulation tests performed for assessing of the impact of optimal shunt braking resistor on power system dynamic response. Detailed discussion of test results has confirmed the correctness of the proposed approach.