Efficient automated schematic map drawing using multiobjective mixed integer programming

We present an efficient multiobjective mixed binary linear program that automates schematic mapping for network visualization and navigation. Schematic mapping has broad applications in representing transit networks, circuits, disease pathways, project tasks, organograms, and taxonomies. Good schematic maps employ distortion while preserving topology to facilitate access to physical or virtual networks. Automation is critical to saving time and costs, while encouraging adoption. We build upon previous work, particularly that of Nöllenburg and Wolff, improving upon the computational efficiency of their model by relaxing integrality constraints and reducing the number of objectives from three to two. We also employ an efficient augmented ϵ-constraint method to assist in obtaining all Pareto optimal solutions, both supported and unsupported, for a given network. Through the Vienna Underground network and a cancer pathway, along with three numerical examples, we demonstrate the applications of our methods. Finally, we discuss future directions for research in this area.