Mathematical model of hierarchical menu structure optimization

A mathematical model is proposed to optimize the structure of hierarchical menus and directories. The model considers each element popularity. The problem of discrete optimization is solved regarding the choice of menu structure minimizing the average search time. It is demonstrated that optimal menu panels should provide the user with identical number of options having popularity levels split in the same proportion. It is indicated that the model allows for comparing the types of menu, as well as for choosing the best one. A certain algorithm is developed to design optimal menu, taking into account both semantic constraints and results of optimization. Application of the algorithm is illustrated using mobile phone menu optimization as an example.