During the launch, the transported payload can be subjected to a severe vibratory environment especially during the atmospheric crossing, or when the engines are turned on/off. These vibrations, mainly transmitted to the satellite by its base, can, by the resonance factor, lead to intense local loads which may damage the payload and compromise its mission. It is essential to predict them with the maximum of precision because any overestimation would lead to an excessive over-dimensioning of the structures of the satellite to the detriment of the useful mass. For this, the control of the vibro-acoustic environment of its passengers is essential. Because of incompatibility between the payload envelopes of the launch vehicles and the desirable external shapes of the communication satellites in orbital configuration, use of expandable structures in such payload designs is necessary. Therefore conceptions of expandable structures are dependent on the constraints due to limited possibilities of launchers and the needs of large structures to fulfill the requirements of space programs. In this paper a new formulation has been developed, which combines the mass of the satellite, the satellite and the launcher fairing geometry, axial frequency, and one-third octave band center frequency. In this paper a Gravitational Search Algorithm (GSA) based on the law of gravity and mass interactions, is introduced. In this algorithm, the searcher agents are a collection of masses which interact with each other based on the Newtonian gravity and the laws of motion. The purpose of the paper is to analyze various parameters relating the satellite's mass with its geometry, the lateral frequency, the acoustic frequency, the fill factor and the fairing geometry with new formulation using GSA algorithm.