Aerodynamic noise control is important for various engineering applications, including automobiles. To develop effective control methods for the flow and sound of bluff bodies, flow past a cylinder is usually studied as a simplified problem. In this study, a passive control technique using surface protrusions was developed to suppress the aeolian tone generated by a two-dimensional laminar flow past a circular cylinder. Protrusions were created on the front and rear surfaces of the cylinder using an optimization approach based on the lattice Boltzmann and adjoint methods, allowing the optimization of complex geometries. The computational results revealed that a pair of protrusions on the front surface could stabilize the separated shear layers by fixing the separation points to their tips, whereas a pair of protrusions on the rear surface can stabilize the separated shear layers by interfering with the interaction between the top and bottom shear layers. Consequently, these shapes effectively suppressed the vortex shedding and aeolian tone while decreasing the mean drag. A shape with symmetrical protrusions on the front and rear surfaces reduced the aeolian tone by 3.6 dB.