Solutions for optimizing an integrated circuit layout for implementation in an integrated circuit are disclosed. In one embodiment, a computer-implemented method is disclosed including: obtaining a plurality of hierarchical constraints in mathematical form, the plurality of hierarchical constraints defining a first integrated circuit layout; partitioning the plurality of hierarchical constraints into groups according to one or more partitioning rules; determining whether a boundary condition exists between two of the groups, and distributing a slack or a gap between the two of the groups in the case that the boundary condition exists; creating a plurality of integer linear programming problems associated with each of the groups; determining a solution for each of the plurality of integer linear programming problems; and integrating each solution together to form a second integrated circuit layout.