We present a framework for optimizing sparse quadratic assignment problems. We propose an iterative algorithm that dynamically generates the quadratic part of the assignment problem and, thus, solves a sparsified linearization of the original problem in every iteration. This procedure results in a hierarchy of lower bounds and, in addition, provides heuristic primal solutions in every iteration. This framework was motivated by the task of the French government to design the French keyboard standard, which included solving sparse quadratic assignment problems with over $100$ special characters; a size not feasible for many commonly used approaches. Designing a new standard often involves multiple stakeholders having conflicting opinions and, hence, no agreement on a single well-defined objective function to be used for an extensive one-shot optimization. Since the process of designing the standard is highly interactive, it demands rapid prototyping, e.g., quick primal solutions, on-the-fly evaluation of manual changes, and prompt assessments of solution quality. Particularly concerning the latter aspect, our algorithm is able to provide high-quality lower bounds for these problems within only a few minutes.