Free-piston Vuilleumier heat pumps (VHPs) provide unique advantages for residential heating and cooling but require careful selection of machine design parameters to operate correctly, which is the focus of this work. A dynamic model for a free-piston VHP is first developed. Forces including mechanical spring, pressure, friction, gravity, and viscous damping are included. Ten machine design parameters, including displacer masses and spring constants, are optimized using the dynamic model combined with a non-dominated Sorting Genetic Algorithm. An initial design and experimental data for a prototype free-piston VHP is used as the starting point for the optimization. Several sets of optimized machine parameters are found that produce the desired machine motion profile, with little to no external energy input. The optimization results also suggest an improved design that eliminates one of the displacer springs, reducing overall system cost and complexity. The developed optimization approach is applicable to similar free-piston VHPs.