Computational design of menu systems has been solved in limited cases such as the linear menu (list) as an assignment task, where commands are assigned to menu positions while optimizing for for users selection performance and distance of associated items. We show that this approach falls short with larger, hierarchically organized menu systems, where one must also take into account how users navigate hierarchical structures. This paper presents a novel integer programming formulation that models hierarchical menus as a combination of the exact set covering problem and the assignment problem. It organizes commands into ordered groups of ordered groups via a novel objective function based on information foraging theory. It minimizes, on the one hand, the time required to select a command whose location is known from previous usage and, on the other, the time wasted in irrelevant parts of the menu while searching for commands whose location is not known. The convergence of these two factors yields usable, well-ordered command hierarchies from a single model. In generated menus, the lead (first) elements of a group or tab are good indicators of the remaining contents, thereby facilitating the search process. In a controlled usability evaluation, the performance of computationally designed menus was 25 faster than existing commercial designs with respect to selection time. The algorithm is efficient for large, representative instances of the problem. We further show applications in personalization and adaptation of menu systems.