A method of assigning a plurality of input/output (I/O) objects of a circuit design to banks of a programmable integrated circuit (IC) using integer linear programming can include storing a plurality of constraints that depend upon a plurality of variables, wherein the plurality of constraints regulate assignment of each of the plurality of I/O objects to banks of the programmable IC (125-184), and storing a linear function that depends upon the plurality of constraints and a plurality of cost metrics, wherein each cost metric imposes a penalty when a selected I/O object of the circuit design is assigned to a bank of the programmable IC that is different from a bank to which the selected I/O object is assigned within a reference solution that is infeasible (190). A result indicating whether a feasible solution exists for assignment of the plurality of I/O objects of the circuit design to banks of the target programmable IC can be determined by minimizing the linear function (192) subject to the plurality of constraints and outputting the result (196, 198).