In Pursuit of the Optimal City: Evaluation of Procedurally Generated City Layouts

With the world population increasing, new living areas must be created to accommodate the increased number of people. The designs of most existing cities have a series of well-documented limitations. For example, some cities have serious traffic congestion problems, while others are unsafe. There is a lot of research on methods of improving parts of existing cities, and in many cases the improvement of a city is a constant and ongoing process. However, this research is limited by a few key factors: it is applied to the designs of current cities; it typically focuses on specific, localised issues; and they typically aim to fulfil a single objective, rather than optimise all aspects of a city at once.Recently, cities such as the {\em The Line} (Neom) project in Saudi Arabia, and Brasilia and Canberra before it, have been designed and built from scratch. These projects often make bold claims that their designs are ``optimal" in some regard.To directly compare how different city structures influence the efficiency of a city, we take a principled approach by procedurally generating a series of cities of different structure using {\em CitySprout}, a novel and open-source road network generator. We generate cities and then then compare them in the context of three key metrics: road density, to quantify space efficiency; living structure, to quantify 'liveability'; and mean circuity, to quantify travel distance efficiency.We discuss the limitations of attempting to optimise cities in this way, and then conclude that the optimal city structure depends on which metric is considered most important. A Grid structure can fit the most people in a given area; an Organic structure is highly liveable; and a Line structure allows for almost direct travel across the city, with only small detours required.