Integer programming for urban design

Abstract

We present an integer program (IP) for urban design that (1) maximizes the floor area; (2) fills building volume with room templates; (3) encodes translational symmetry in urban layout; and (4) constructs economical urban routes. Regardless that integer programming is intensively studied in operational research (OR), its role in solving geometrical and topological problems in urban design was overlooked. Based on a regular grid, our 0–1 IP formulates the sunlight-gain rules, which give urban sites their shapes, especially for residential projects. With predefined plot templates, the gross floor area (volume) within a given site can be maximized under various sunlight requirements. Subsequently, the IP fills each building volume with 2D/3D room templates. Finally, an IP-based algorithm constructs routes that connect all plots and the site’s entrances to public transportation. Both the classical Steiner tree model and the latest coverage network model are extended to create reasonable routes. In addition, this work extends the concept of special ordered sets (SOS) to encode translational symmetry in urban layouts. Encoding layout symmetry can benefit from the solvers’ SOS2 mechanism in the Branch-and-Bound search algorithm. The results indicate that traditional decision making for cities could be partially automated by IP and an abundance of valid solutions are available for designers.