Abstract: We present a novel Markov chain Monte Carlo (MCMC) algorithm that generates samples from transdimensional distributions encoding complex constraints. We use factor graphs, a type of graphical model, to encode constraints as factors. Our proposed MCMC method, called locally annealed reversible jump MCMC, exploits knowledge of how dimension changes affect the structure of the factor graph. We employ a sequence of annealed distributions during the sampling process, allowing us to explore the state space across different dimensionalities more freely. This approach is motivated by the application of layout synthesis where relationships between objects are characterized as constraints. In particular, our method addresses the challenge of synthesizing open world layouts where the number of objects are not fixed and optimal configurations for different numbers of objects may be drastically different. We demonstrate the applicability of our approach on two open world layout synthesis problems: coffee shops and golf courses.