Vanessa Volz

Vanessa Volz, Boris Naujoks, Pascal Kerschke et al.

The term Procedural Content Generation (PCG) refers to the (semi-)automatic generation of game content by algorithmic means, and its methods are becoming increasingly popular in game-oriented research and industry. A special class of these methods, which is commonly known as search-based PCG, treats the given task as an optimisation problem. Such problems are predominantly tackled by evolutionary algorithms. We will demonstrate in this paper that obtaining more information about the defined optimisation problem can substantially improve our understanding of how to approach the generation of content. To do so, we present and discuss three efficient analysis tools, namely diagonal walks, the estimation of high-level properties, as well as problem similarity measures. We discuss the purpose of each of the considered methods in the context of PCG and provide guidelines for the interpretation of the results received. This way we aim to provide methods for the comparison of PCG approaches and eventually, increase the quality and practicality of generated content in industry.

Jacob Schrum, Benjamin Capps, Kirby Steckel et al.

Generative Adversarial Networks (GANs) are a powerful indirect genotype-to-phenotype mapping for evolutionary search. Much previous work applying GANs to level generation focuses on fixed-size segments combined into a whole level, but individual segments may not fit together cohesively. In contrast, segments in human designed levels are often repeated, directly or with variation, and organized into patterns (the symmetric eagle in Level 1 of The Legend of Zelda, or repeated pipe motifs in Super Mario Bros). Such patterns can be produced with Compositional Pattern Producing Networks (CPPNs). CPPNs define latent vector GAN inputs as a function of geometry, organizing segments output by a GAN into complete levels. However, collections of latent vectors can also be evolved directly, producing more chaotic levels. We propose a hybrid approach that evolves CPPNs first, but allows latent vectors to evolve later, combining the benefits of both approaches. These approaches are evaluated in Super Mario Bros. and The Legend of Zelda. We previously demonstrated via a Quality-Diversity algorithm that CPPNs better cover the space of possible levels than directly evolved levels. Here, we show that the hybrid approach (1) covers areas that neither of the other methods can, and (2) achieves comparable or superior QD scores.

Koen van der Blom, Timo M. Deist, Vanessa Volz et al.

Optimisation algorithms are commonly compared on benchmarks to get insight into performance differences. However, it is not clear how closely benchmarks match the properties of real-world problems because these properties are largely unknown. This work investigates the properties of real-world problems through a questionnaire to enable the design of future benchmark problems that more closely resemble those found in the real world. The results, while not representative as they are based on only 45 responses, indicate that many problems possess at least one of the following properties: they are constrained, deterministic, have only continuous variables, require substantial computation times for both the objectives and the constraints, or allow a limited number of evaluations. Properties like known optimal solutions and analytical gradients are rarely available, limiting the options in guiding the optimisation process. These are all important aspects to consider when designing realistic benchmark problems. At the same time, the design of realistic benchmarks is difficult, because objective functions are often reported to be black-box and many problem properties are unknown. To further improve the understanding of real-world problems, readers working on a real-world optimisation problem are encouraged to fill out the questionnaire: https://tinyurl.com/opt-survey

Thomas Bartz-Beielstein, Carola Doerr, Daan van den Berg et al.

This survey compiles ideas and recommendations from more than a dozen researchers with different backgrounds and from different institutes around the world. Promoting best practice in benchmarking is its main goal. The article discusses eight essential topics in benchmarking: clearly stated goals, well-specified problems, suitable algorithms, adequate performance measures, thoughtful analysis, effective and efficient designs, comprehensible presentations, and guaranteed reproducibility. The final goal is to provide well-accepted guidelines (rules) that might be useful for authors and reviewers. As benchmarking in optimization is an active and evolving field of research this manuscript is meant to co-evolve over time by means of periodic updates.

Vanessa Volz, Boris Naujoks

While games have been used extensively as milestones to evaluate game-playing AI, there exists no standardised framework for reporting the obtained observations. As a result, it remains difficult to draw general conclusions about the strengths and weaknesses of different game-playing AI algorithms. In this paper, we propose reporting guidelines for AI game-playing performance that, if followed, provide information suitable for unbiased comparisons between different AI approaches. The vision we describe is to build benchmarks and competitions based on such guidelines in order to be able to draw more general conclusions about the behaviour of different AI algorithms, as well as the types of challenges different games pose.

Vanessa Volz, Niels Justesen, Sam Snodgrass et al.

Recent procedural content generation via machine learning (PCGML) methods allow learning from existing content to produce similar content automatically. While these approaches are able to generate content for different games (e.g. Super Mario Bros., DOOM, Zelda, and Kid Icarus), it is an open questions how well these approaches can capture large-scale visual patterns such as symmetry. In this paper, we propose match-three games as a domain to test PCGML algorithms regarding their ability to generate suitable patterns. We demonstrate that popular algorithm such as Generative Adversarial Networks struggle in this domain and propose adaptations to improve their performance. In particular we augment the neighborhood of a Markov Random Fields approach to not only take local but also symmetric positional information into account. We conduct several empirical tests including a user study that show the improvements achieved by the proposed modifications, and obtain promising results.

Koen van der Blom, Timo M. Deist, Tea Tušar et al.

Benchmarks are a useful tool for empirical performance comparisons. However, one of the main shortcomings of existing benchmarks is that it remains largely unclear how they relate to real-world problems. What does an algorithm's performance on a benchmark say about its potential on a specific real-world problem? This work aims to identify properties of real-world problems through a questionnaire on real-world single-, multi-, and many-objective optimization problems. Based on initial responses, a few challenges that have to be considered in the design of realistic benchmarks can already be identified. A key point for future work is to gather more responses to the questionnaire to allow an analysis of common combinations of properties. In turn, such common combinations can then be included in improved benchmark suites. To gather more data, the reader is invited to participate in the questionnaire at: https://tinyurl.com/opt-survey

Jacob Schrum, Vanessa Volz, Sebastian Risi

Generative Adversarial Networks (GANs) are proving to be a powerful indirect genotype-to-phenotype mapping for evolutionary search, but they have limitations. In particular, GAN output does not scale to arbitrary dimensions, and there is no obvious way of combining multiple GAN outputs into a cohesive whole, which would be useful in many areas, such as the generation of video game levels. Game levels often consist of several segments, sometimes repeated directly or with variation, organized into an engaging pattern. Such patterns can be produced with Compositional Pattern Producing Networks (CPPNs). Specifically, a CPPN can define latent vector GAN inputs as a function of geometry, which provides a way to organize level segments output by a GAN into a complete level. This new CPPN2GAN approach is validated in both Super Mario Bros. and The Legend of Zelda. Specifically, divergent search via MAP-Elites demonstrates that CPPN2GAN can better cover the space of possible levels. The layouts of the resulting levels are also more cohesive and aesthetically consistent.

Jacob Schrum, Jake Gutierrez, Vanessa Volz et al.

Generative Adversarial Networks (GANs) are an emerging form of indirect encoding. The GAN is trained to induce a latent space on training data, and a real-valued evolutionary algorithm can search that latent space. Such Latent Variable Evolution (LVE) has recently been applied to game levels. However, it is hard for objective scores to capture level features that are appealing to players. Therefore, this paper introduces a tool for interactive LVE of tile-based levels for games. The tool also allows for direct exploration of the latent dimensions, and allows users to play discovered levels. The tool works for a variety of GAN models trained for both Super Mario Bros. and The Legend of Zelda, and is easily generalizable to other games. A user study shows that both the evolution and latent space exploration features are appreciated, with a slight preference for direct exploration, but combining these features allows users to discover even better levels. User feedback also indicates how this system could eventually grow into a commercial design tool, with the addition of a few enhancements.

Alexander Dockhorn, Simon M. Lucas, Vanessa Volz et al.

This paper examines learning approaches for forward models based on local cell transition functions. We provide a formal definition of local forward models for which we propose two basic learning approaches. Our analysis is based on the game Sokoban, where a wrong action can lead to an unsolvable game state. Therefore, an accurate prediction of an action's resulting state is necessary to avoid this scenario. In contrast to learning the complete state transition function, local forward models allow extracting multiple training examples from a single state transition. In this way, the Hash Set model, as well as the Decision Tree model, quickly learn to predict upcoming state transitions of both the training and the test set. Applying the model using a statistical forward planner showed that the best models can be used to satisfying degree even in cases in which the test levels have not yet been seen. Our evaluation includes an analysis of various local neighbourhood patterns and sizes to test the learners' capabilities in case too few or too many attributes are extracted, of which the latter has shown do degrade the performance of the model learner.

Simon M. Lucas, Vanessa Volz

This paper provides a detailed investigation of using the Kullback-Leibler (KL) Divergence as a way to compare and analyse game-levels, and hence to use the measure as the objective function of an evolutionary algorithm to evolve new levels. We describe the benefits of its asymmetry for level analysis and demonstrate how (not surprisingly) the quality of the results depends on the features used. Here we use tile-patterns of various sizes as features. When using the measure for evolution-based level generation, we demonstrate that the choice of variation operator is critical in order to provide an efficient search process, and introduce a novel convolutional mutation operator to facilitate this. We compare the results with alternative generators, including evolving in the latent space of generative adversarial networks, and Wave Function Collapse. The results clearly show the proposed method to provide competitive performance, providing reasonable quality results with very fast training and reasonably fast generation.

Simon M. Lucas, Alexander Dockhorn, Vanessa Volz et al.

This paper investigates the effect of learning a forward model on the performance of a statistical forward planning agent. We transform Conway's Game of Life simulation into a single-player game where the objective can be either to preserve as much life as possible or to extinguish all life as quickly as possible. In order to learn the forward model of the game, we formulate the problem in a novel way that learns the local cell transition function by creating a set of supervised training data and predicting the next state of each cell in the grid based on its current state and immediate neighbours. Using this method we are able to harvest sufficient data to learn perfect forward models by observing only a few complete state transitions, using either a look-up table, a decision tree or a neural network. In contrast, learning the complete state transition function is a much harder task and our initial efforts to do this using deep convolutional auto-encoders were less successful. We also investigate the effects of imperfect learned models on prediction errors and game-playing performance, and show that even models with significant errors can provide good performance.

Simon M. Lucas, Jialin Liu, Ivan Bravi et al.

This paper introduces a simple and fast variant of Planet Wars as a test-bed for statistical planning based Game AI agents, and for noisy hyper-parameter optimisation. Planet Wars is a real-time strategy game with simple rules but complex game-play. The variant introduced in this paper is designed for speed to enable efficient experimentation, and also for a fixed action space to enable practical inter-operability with General Video Game AI agents. If we treat the game as a win-loss game (which is standard), then this leads to challenging noisy optimisation problems both in tuning agents to play the game, and in tuning game parameters. Here we focus on the problem of tuning an agent, and report results using the recently developed N-Tuple Bandit Evolutionary Algorithm and a number of other optimisers, including Sequential Model-based Algorithm Configuration (SMAC). Results indicate that the N-Tuple Bandit Evolutionary offers competitive performance as well as insight into the effects of combinations of parameter choices.

Vanessa Volz, Jacob Schrum, Jialin Liu et al.

Generative Adversarial Networks (GANs) are a machine learning approach capable of generating novel example outputs across a space of provided training examples. Procedural Content Generation (PCG) of levels for video games could benefit from such models, especially for games where there is a pre-existing corpus of levels to emulate. This paper trains a GAN to generate levels for Super Mario Bros using a level from the Video Game Level Corpus. The approach successfully generates a variety of levels similar to one in the original corpus, but is further improved by application of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Specifically, various fitness functions are used to discover levels within the latent space of the GAN that maximize desired properties. Simple static properties are optimized, such as a given distribution of tile types. Additionally, the champion A* agent from the 2009 Mario AI competition is used to assess whether a level is playable, and how many jumping actions are required to beat it. These fitness functions allow for the discovery of levels that exist within the space of examples designed by experts, and also guide the search towards levels that fulfill one or more specified objectives.

Vanessa Volz, Günter Rudolph, Boris Naujoks

In this paper, we propose a novel approach (SAPEO) to support the survival selection process in multi-objective evolutionary algorithms with surrogate models - it dynamically chooses individuals to evaluate exactly based on the model uncertainty and the distinctness of the population. We introduce variants that differ in terms of the risk they allow when doing survival selection. Here, the anytime performance of different SAPEO variants is evaluated in conjunction with an SMS-EMOA using the BBOB bi-objective benchmark. We compare the obtained results with the performance of the regular SMS-EMOA, as well as another surrogate-assisted approach. The results open up general questions about the applicability and required conditions for surrogate-assisted multi-objective evolutionary algorithms to be tackled in the future.

Vanessa Volz, Günter Rudolph, Boris Naujoks

Game balancing is an important part of the (computer) game design process, in which designers adapt a game prototype so that the resulting gameplay is as entertaining as possible. In industry, the evaluation of a game is often based on costly playtests with human players. It suggests itself to automate this process using surrogate models for the prediction of gameplay and outcome. In this paper, the feasibility of automatic balancing using simulation- and deck-based objectives is investigated for the card game top trumps. Additionally, the necessity of a multi-objective approach is asserted by a comparison with the only known (single-objective) method. We apply a multi-objective evolutionary algorithm to obtain decks that optimise objectives, e.g. win rate and average number of tricks, developed to express the fairness and the excitement of a game of top trumps. The results are compared with decks from published top trumps decks using simulation-based objectives. The possibility to generate decks better or at least as good as decks from published top trumps decks in terms of these objectives is demonstrated. Our results indicate that automatic balancing with the presented approach is feasible even for more complex games such as real-time strategy games.