A multiobjective optimization has been developed for the design of the fuselage of a supersonic business jet. The attention is focused on the coupling between the CFD solver (Num3sis) developed at INRIA and the acoustic propagation code TRAPS in use at ONERA. The accuracy of the propagation prediction over the entire domain is fundamental for obtaining a valuable solution. In order to achieve this objective an iterative procedure for unstructured mesh adaptation is developed. Mesh adaptation has the potential to reduce the computational time increasing the density of the mesh only where required. After a brief introduction of the different tools required to solve the problem in analysis, the optimization is carried out in a hybrid process in which an evolutionary strategy (ES) is used first (exploration), and a gradient based method second for improve the accuracy (exploitation). The Pareto optimal curve is evaluated using the Pareto Archive Evolutionary Strategy[17] and with a classical Adapted Weighted Sum method[18] in order to compare the final results. This design methodology has the ability to generate non intuitive configuration that do not rely on the engineer's experience. Combining CAD modeling, CFD, acoustic propagation analysis and shape multicriterion optimization enhance the potential of investigation of such a complex physical phenomenon.