In this paper, a sonic boom minimization framework which gathers efficient computational strategies via multi-fidelity and multi-objective optimization methods has been developed to leverage low boom aircraft design concepts. In this multidisciplinary framework, sonic boom prediction requires transfer of the near field pressure data obtained from the aerodynamic solver to the aeroacoustic solver to propagate this pressure signature through the atmosphere to the far-field. For multi-fidelity analyses in the aerodynamic domain, SU2 code is employed as the high-fidelity flow solver through Euler equations, while A502 PANAIR, a higher-order panel code, is employed as the low-fidelity flow solver. For low-fidelity and high-fidelity sonic boom calculations, the linear and non-linear solvers of NASA's sBOOM code are coupled with the near-field pressure data processed from the flow solutions of SU2 and PANAIR codes. For sonic boom minimization, wing planform shape parameters of a supersonic aircraft model are represented by the Class-Shape Transformation method while engineering sketch pad ESP is used for geometric model generation and parametric design update during optimization. As multi-objective optimization algorithm, an in-house code implementing Davidon-Fletcher-Powell Penalty Function method with a multi-start strategy is used for global optimum search. A multi-fidelity surrogate model is constructed with the co-kriging method using linear auto-regressive information fusion scheme and employed in optimization. In-house scripts are developed to couple and drive these analysis tools in this multidisciplinary framework and finally a parametric wing shape design optimization study is conducted for a supersonic wing-body configuration to demonstrate the sonic boom minimization performance.