Secondary power system based on gas turbine engine is usually used for starting the aircraft main engine at ground, and finds similar application in air during the emergency. The secondary power system comprises of an Auxiliary Power Unit (APU) and an Air Starter. APU provides stand alone power to the main engine sub-systems and air to the air starter for starting main engine. The main rotor system of APU is to be designed for safe operation during the ground critical speed crossing and maneuver loading. The weight of such a rotor system is an important design criterion. In the current work, multi-objective optimization using Hybrid Genetic Algorithm (HGA) is employed for simultaneously minimizing the response at critical speed, the response during maneuvering and shaft weight of the APU rotor system used in secondary power system of an aircraft. The shaft considered is a stepped one and is modeled using Rayleigh beam elements with three discs. Effects due to gyroscopic effect are also included in the analysis. A Pareto front is generated and subsequently an optimal solution is selected for the problem. The comparison with typical two-objective optimization result, having response at critical speed and shaft weight as objectives and response during maneuvering as constraint, has shown that the three objective optimization has provided the designer with improved design choices for the selection of final compromise solution.