A new strategy for the design and optimization of regenerative cycles (e.g. Stirling or Vuilleumier cycles) is presented. It is based on a simplex algorithm and is organized in a hierarchical structure, sorting the independent parameters in order of decreasing influence on the global design and defining them in a way which minimizes their mutual interaction. It was successfully applied to the design of a 20 kW Vuilleumier heat pump for residential heating applications within in joint German government-funded R&D-project. The experimental results are well reproduced by the simulation code if a few resonable assumptions for hardly predictable parameters are made.