Algorithms on a variable-size rectangular interface

The purpose of this paper is to elaborate approximate algorithms capable of generating two-dimensional interfaces that contain a given set of services adapted to the user’s context. The proposed methods give good solutions that minimize the used surface, by taking in consideration the placement and the positioning of the tiles. The obtained interface from packing all the tiles into a variable-size bin should be adapted and very simple to use. In order to increase the usability of these solutions (configurations) we develop a mathematical modeling incorporating different Human-Computer Interaction constraints for an exact resolution. Such a placement is performed on the basis of the importance and the category of the proposed service in the tiles. Moreover, we suggest two approximate approaches: a heuristic based on shelf strategy and a memetic algorithm. The exact resolution of the proposed multi-objective mathematical model gives an optimal solution only for small and medium instances. For the other instances, it is difficult to reach the optimal value in a short running time, which shows the practical interest of the proposed approaches.