In top-down, constraint-based variational design environment, user expresses his design intent through a series of construction steps that will be further transferred to design variants maintained by the system. Persistent naming techniques build a bridge between design variants and user design intent. The graph-based coding and decoding method together with parameter information, presented in this paper successfully maintain the user design intent in constraint-based variational design. Besides, the energy of parameter vector field decoding method gives a mathematical definition on comparability between original model and regenerated model.