Waverider is a hypersonic vehicle that improves the lift-to-drag ratio using the shockwave attached to the leading edge of the lifting surface. Owing to its superior aerodynamic performance, it exhibits a viable external configuration in hypersonic flight conditions. Most of the existing studies on waverider employ the inverse design method to generate vehicle configuration. However, the waverider inverse design method exhibits two limitations; inaccurate definition of design space and unfeasible performance estimation during the design process. To address these issues, a novel framework to directly optimize the waverider is proposed in this paper. The osculating cone theory is adopted as a waverider inverse design method. A general methodology to define the design space is suggested by analyzing the design curves of the osculating cone theory. The performance of the waverider is estimated accurately and rapidly via combining a high-fidelity computational fluid dynamics solver and a surrogate model. A comparison study shows that the proposed direct optimization framework enables a more accurate design space and efficient performance estimation. The framework is applied to the multi-objective optimization problem, which maximizes internal volume and minimizes aerodynamic drag. Finally, general characteristics for waverider are presented by analyzing the optimized results with data mining methods such as K-means.