Methods and systems for migrating circuit layouts. A floorplan layout is built for a target circuit using a subset of constraints that characterize a layout structure of an original circuit. Shape-constraint-based scaling is used on the floorplan layout by scaling parts of the floorplan layout in accordance with a plurality of different scaling ratios such that portions of the floorplan layout are concurrently scaled with the plurality of different scaling ratios. Cells are placed at locations defined by the floorplan layout. The floorplan layout is checked with shape-constraint-based legalization using all of the constraints to produce a migrated layout.