Evolutionary Wave Function Collapse

Constraint-based game content generators that learn local constraints from existing content, such as Wave Function Collapse (WFC), can generate visually satisfying game levels but face challenges in guaranteeing global properties, such as playability. On the other hand, reinforcement-learning trained generators can guarantee global properties -- because such properties can easily be included in reward functions -- but the results can be visually dissatisfying. In this paper, we explore ways to combine these methods. Specifically, we constrain the action space of a PCGRL generator with constraints learned by WFC, effectively allowing the PCGRL generator to achieve global properties while forced to adhere to local constraints. To better analyze how this hybrid content generation method operates, we vary the number and type of inputs, and we test whether to randomly collapse the starting state and exclude rare patterns. While the method is sensitive to hyperparameter tuning, the best of our trained generators produce visually satisfying and playable puzzle-platform game levels -- such as Lode Runner levels -- with desired global properties.

Video games are a dynamic medium experienced over time. While there are many Procedural Content Generation (PCG) approaches for generating video game levels, they often use representations that abstract away this dynamic nature. In this paper, we introduce a novel, domain-independent ``cake'' representation for game levels over time which implicitly encodes dynamic information. We present a novel level generation approach Playtrace Reconstructive Partitioning (PRP) specifically developed for this cake representation. We compare against six state-of-the-art PCG approaches in the game domain of \textit{Sokoban}, and find that our approach can generate valid levels without sacrificing solution diversity. We believe our cake representation more neatly encodes the implicit dynamic nature of games compared to existing representations, which allows for our domain-agnostic level generation algorithm PRP.

LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems. The standard approach is to evolve a monolithic program that directly outputs a candidate solution. We present ImprovEvolve, an algorithmic alternative that drastically reduces cognitive load on the LLM. Instead of prompting the model for an end-to-end optimizer, we evolve a program with three specialized operators of initialization, local improvement, and perturbation. We then approach the optimum by iteratively applying local improvements and intensity-scheduled perturbations, effectively driving a basin-hopping search with LLM-evolved subroutines. For hexagon in hexagon packing, ImprovEvolve discovers new state-of-the-art packings of 11, 12, 15, and 16 hexagons, and additionally for 14, 17, and 23 hexagons after minimal expert tuning of the generated code. For the second autocorrelation inequality, the evolved and human-scaled program pushes the lower bound from 0.96102 to 0.96258. For spherical codes, the ImprovEvolve program lowers the best-known maximum cosine for the majority of 90 randomly chosen diverse state-of-the-art spherical codes, achieving relative improvements of up to 2.4%.