Future High Energy Physics experiments require the use of light and stable structures to support their most precise radiation detection elements. These large structures must be light, highly stable, stiff and radiation tolerant in an environment where external vibrations, high radiation levels, material aging, temperature and humidity gradients are not negligible. Unforeseen factors and the unknown result of the coupling of environmental conditions, together with external vibrations, may affect the position stability of the detectors and their support structures compromising their physics performance. Careful optimization of static and dynamic behavior must be an essential part of the engineering design. Genetic Algorithms (GA) belong to the group of probabilistic algorithms, combining elements of direct and stochastic search. They are more robust than existing directed search methods with the advantage of maintaining a population of potential solutions. There is a class of optimization problems for which Genetic Algorithms can be effectively applied. Among them are the ones related to shape control and optimal placement of sensors/actuators for active control of vibrations. In this paper these two problems are addressed and numerically investigated. The finite element method is used for the analysis of the dynamic characteristics. For the case of the optimal placement of sensors/actuators a performance index, proportional to the damping of the system in closed- loop, is used. Genetic algorithms prove their efficiency in this kind of optimization problems.