A method (300) and system (500) for optimizing a circuit layout based on layout constraints (308) and objectives (312). The method includes solving a linear program so as to obtain a rational solution whose variables are either whole or half integer. The tight constraints and objectives involving variables whose solution are a half integer are reduced to a 2-SAT problem, which is analyzed to determine its satisfiability. If the 2-SAT problem is not satisfiable, one or more objectives are removed so as to make the 2-SAT problem satisfiable. Any half-integer results of the linear program are rounded according to the truth assignment that satisfies the 2-SAT problem. The rounded results are used to create the circuit layout.