Automated generation of concentric circles metro maps using mixed-integer optimization

Abstract

The concentric circles (CC) map design is an alternative approach for schematically representing metro systems. Compared with traditional octo-linear maps, CC maps can effectively simplify the perception of a network by visually accenting circular line patterns. This design offers new insights into the schematic drawing of metro systems that can improve map readability and engagement. Automated mapping studies in the literature have mostly applied the traditional octo-linear design using optimization methods, where design criteria are modeled as constraints and/or objective functions in a constrained mixed-integer optimization program, whereas the automated CC map drawing approach has received less attention. In this article, we develop an automatic CC map drawing method by adopting map design criteria as a mixed-integer programming problem. Numerical experiments are conducted using (a) a simple network to illustrate the model procedure in detail, (b) two real-world metro networks in Vienna and Montréal to analyze the effects of the selected map center and parameter settings and (c) the Beijing subway to analyze the applicability of the proposed approach to large-scale metro networks.