A Markovian Framing of WaveFunctionCollapse for Procedurally Generating Aesthetically Complex Environments
This work addresses procedural content generation for game developers and designers, representing an incremental improvement by applying existing optimization frameworks to a known bottleneck.
The paper tackles the challenge of jointly optimizing designer objectives and adjacency constraints in procedural content generation by reformulating WaveFunctionCollapse as a Markov Decision Process, enabling separate optimization of constraints and objectives. The results show that this decoupled approach consistently outperforms traditional joint optimization methods across multiple domains as task complexity increases.
Procedural content generation often requires satisfying both designer-specified objectives and adjacency constraints implicitly imposed by the underlying tile set. To address the challenges of jointly optimizing both constraints and objectives, we reformulate WaveFunctionCollapse (WFC) as a Markov Decision Process (MDP), enabling external optimization algorithms to focus exclusively on objective maximization while leveraging WFC's propagation mechanism to enforce constraint satisfaction. We empirically compare optimizing this MDP to traditional evolutionary approaches that jointly optimize global metrics and local tile placement. Across multiple domains with various difficulties, we find that joint optimization not only struggles as task complexity increases, but consistently underperforms relative to optimization over the WFC-MDP, underscoring the advantages of decoupling local constraint satisfaction from global objective optimization.