In this work, a stability-constrained biobjective (aerodynamic drag and heating) design optimization for the hypersonic spiked bodies is conducted. The shape optimization includes both the forebody shape and the spike/aerodisk shape through a generic parametric representation of the geometry. The NSGA-II multi-objective algorithm is coupled with the kriging surrogates that are constructed based on numerical solutions of laminar VISCOUS flows around the geometries. The optimization reveals that the two objectives, minimum drag and minimum heating, are competing for spiked forebodies such that a set of Pareto front solutions are obtained. On the minimum-drag and maximum-aeroheating extreme, the optimal designs are characterized by highly blunt, nearly flat forebodies with the possibility of flow unsteadiness. On the other extreme, the optimal designs are commonly of slender forebodies with small bluntness. Between the two extremes, a variety of nondominant designs can be found.