It is well known that Parallel Kinematic Mechanisms (PKMs) have an intrinsic dynamic potential (very high speed and acceleration) with high precision and high stiffness. Nevertheless, the choice of optimal dimensions that provide the best performances remains a difficult task, since performances strongly depend on dimensions. On the other hand, there are many criteria of performance that must be taken into account for dimensional synthesis, and which are sometimes antagonist. This paper presents an approach of multiobjective optimization for PKMs that takes into account several criteria of performance simultaneously that have a direct impact on the dimensional synthesis of PKMs. We first present some criteria of performance such as the workspace, transmission speeds, stiffness, dexterity, precision, as well as dynamic dexterity. Secondly, we present the problem of dimensional synthesis, which will be defined as a multiobjective optimization problem. The method of genetic algorithms is used to solve this type of multiobjective optimization problem by means of NSGA-II and SPEA-II algorithms. Finally, based on a linear Delta architecture, we present an illustrative application of this methodology to a 3-axis machine tool in the context of manufacturing of automotive parts.