A stochastic method for the generation of optimized building layouts respecting urban regulations

The development in an urban area normally has to obey planning regulations. In France, such regulations are specified in local urban planning schemes (LUPS or PLU in French) defining the right to build at municipal or inter-municipal level. Many aspects are concerned in a PLU. We address to the spatial aspect defining the rules for building development. Since these rules are stated in technical documents, it’s not easy to comprehend or to assess their impacts. Driven by such issues, we propose to generate 3D building layouts that comply with the rules and have optimized indicators (e.g. floor area ratio), which is optional but useful. A building layout is a configuration of a number of buildings with various shapes (simplified as 3D boxes in this work). Thus, it can be seen as a realization of a marked point process (MPP) of 3D boxes, whose probability distribution can be defined through Gibbs energy with regard to a reference process. Its energy component reflects the compliance with the PLU rules in our problem. By maximizing this probability the optimal building layout can be found. The optimization task is realized by trans-dimensional simulated annealing (TDSA) coupled with a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler. Several common types of the French PLU rules are studied and modeled into energy terms, and a case study is conducted to validate our approach.