It is not possible to configure yEd in such a way that it automatically calculates a layout for its loaded graph. See Layout on starting yEd for reasons.
That said, it is possible to dock the dialog of any layout algorithm. If you do so, the corresponding layout settings will stay docked even if you quit and restart yEd. With the layout settings docked, it is only one extra click to calculate a new layout after opening a graph instead of having to navigate through the layout menu.