# Expanding Horizons of Level Diversity via Multi-objective Evolutionary Learning

arXiv: https://arxiv.org/abs/2509.24341 · HTML: https://mlsanity.com/paper/2509.24341/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 76 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 29 of 29)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Procedural Content Generation via Machine Learning (PCGML)](https://mlsanity.com/paper/1702.00539/) (2017)
- [PCGRL: Procedural Content Generation via Reinforcement Learning](https://mlsanity.com/paper/2001.09212/) (2020)
- [Evolving Mario Levels in the Latent Space of a Deep Convolutional Generative Adversarial Network](https://mlsanity.com/paper/1805.00728/) (2018)
- [Deep Learning for Procedural Content Generation](https://mlsanity.com/paper/2010.04548/) (2020)
- [MarioGPT: Open-Ended Text2Level Generation through Large Language Models](https://mlsanity.com/paper/2302.05981/) (2023)
- [Illuminating Mario Scenes in the Latent Space of a Generative Adversarial Network](https://mlsanity.com/paper/2007.05674/) (2020)
- [Procedural Content Generation through Quality Diversity](https://mlsanity.com/paper/1907.04053/) (2019)
- [Evolutionary Generative Adversarial Networks](https://mlsanity.com/paper/1803.00657/) (2018)
- [Learning Controllable Content Generators](https://mlsanity.com/paper/2105.02993/) (2021)
- [Bootstrapping Conditional GANs for Video Game Level Generation](https://mlsanity.com/paper/1910.01603/) (2019)
- [Experience-Driven PCG via Reinforcement Learning: A Super Mario Bros Study](https://mlsanity.com/paper/2106.15877/) (2021)
- [TOAD-GAN: Coherent Style Level Generation from a Single Example](https://mlsanity.com/paper/2008.01531/) (2020)
- [Learning to Generate Levels From Nothing](https://mlsanity.com/paper/2002.05259/) (2020)
- [Tile Pattern KL-Divergence for Analysing and Evolving Game Levels](https://mlsanity.com/paper/1905.05077/) (2019)
- [Games for Artificial Intelligence Research: A Review and Perspectives](https://mlsanity.com/paper/2304.13269/) (2023)
- [Multi-Domain Level Generation and Blending with Sketches via Example-Driven BSP and Variational Autoencoders](https://mlsanity.com/paper/2006.09807/) (2020)
- [Affective Game Computing: A Survey](https://mlsanity.com/paper/2309.14104/) (2023)
- [Multi-Objective level generator generation with Marahel](https://mlsanity.com/paper/2005.08368/) (2020)
- [Procedural Content Generation using Neuroevolution and Novelty Search for Diverse Video Game Levels](https://mlsanity.com/paper/2204.06934/) (2022)
- [Mitigating Unfairness via Evolutionary Multi-objective Ensemble Learning](https://mlsanity.com/paper/2210.16754/) (2022)
- [Does Preference Always Help? A Holistic Study on Preference-Based Evolutionary Multi-Objective Optimisation Using Reference Points](https://mlsanity.com/paper/1909.13567/) (2019)
- [The Right Variety: Improving Expressive Range Analysis with Metric Selection Methods](https://mlsanity.com/paper/2304.02366/) (2023)
- [Measuring Diversity of Game Scenarios](https://mlsanity.com/paper/2404.15192/) (2024)
- [Evolving Flying Machines in Minecraft Using Quality Diversity](https://mlsanity.com/paper/2302.00782/) (2023)
- [Generating Game Levels of Diverse Behaviour Engagement](https://mlsanity.com/paper/2207.02100/) (2022)
- [Procedural Content Generation via Knowledge Transformation (PCG-KT)](https://mlsanity.com/paper/2305.00644/) (2023)
- [Interpreting Multi-objective Evolutionary Algorithms via Sokoban Level Generation](https://mlsanity.com/paper/2406.10663/) (2024)

## Abstract (arXiv)

In recent years, the generation of diverse game levels has gained increasing interest, contributing to a richer and more engaging gaming experience. A number of level diversity metrics have been proposed in literature, which are naturally multi-dimensional, leading to conflicted, complementary, or both relationships among these dimensions. However, existing level generation approaches often fail to comprehensively assess diversity across those dimensions. This paper aims to expand horizons of level diversity by considering multi-dimensional diversity when training generative models. We formulate the model training as a multi-objective learning problem, where each diversity metric is treated as a distinct objective. Furthermore, a multi-objective evolutionary learning framework that optimises multiple diversity metrics simultaneously throughout the model training process is proposed. Our case study on the commonly used benchmark Super Mario Bros. demonstrates that our proposed framework can enhance multi-dimensional diversity and identify a Pareto front of generative models, which provides a range of tradeoffs among playability and two representative diversity metrics, including a content-based one and a player-centered one. Such capability enables decision-makers to make informed choices when selecting generators accommodating a variety of scenarios and the diverse needs of players and designers.