Aerospikes can reduce both drag and aeroheating for hypersonic vehicles with blunt forebodies. However, the performance of the spike depends largely upon its design and the forebody geometry. Balancing the design for drag and aeroheating reduction can be competing. For some design combinations, the flow can be unstable which invokes undesirable consequence. In this work, a stability-constrained bi-objective design optimization for the hypersonic spiked bodies was conducted. The multi-objective algorithm was coupled with the Kriging surrogates that were constructed based on numerical solutions of laminar viscous flows around the geometries.