The optimization of mixed-integer problems is a classic problem with many industrial and design applications. A number of algorithms exist for the numerical optimization of these problems, but the robust optimization of mixed-integer problems has been explored to a far lesser extent. We present here a general methodology for the robust optimization of mixed-integer problems using nonuniform rational B-spline (NURBs) based metamodels and graph theory concepts. The use of these techniques allows for a new and powerful definition of robustness along integer variables. In this work, we define robustness as an invariance in problem structure, as opposed to insensitivity in the dependent variables. The application of this approach is demonstrated on two test problems. We conclude with a performance analysis of our new approach, comparisons to existing approaches, and our views on the future development of this technique.