Automated Drawing of Railway Schematics Using Numerical Optimization in SAT.

Schematic drawings showing railway tracks and equipment are commonly used to visualize railway operations and to communicate system specifications and construction blueprints. Recent advances in on-line collaboration and modeling tools have raised the expectations for quickly making changes to models, resulting in frequent changes to layouts, text, and/or symbols in schematic drawings. Automating the creation of high-quality schematic views from geographical and topological models can help engineers produce and update drawings efficiently. This paper describes three methods for automatically producing schematic railway drawings with increasing level of quality and control over the result. The final method, implemented in the tool that we present, can use any combination of the following optimization criteria, which have different priorities in different use cases: width and height of the drawing, the diagonal line lengths, and the number of bends. We show how to encode schematic railway drawings as an optimization problem over Boolean and numerical domains, using combinations of unary number encoding, lazy difference constraints, and numerical optimization into an incremental SAT formulation.