Procedural Puzzle Generation: A Survey
Tags: #gaming #ai #design #procedural content generation #algorithms
Authors: Barbara De Kegel, Mads Haahr
Overview
My paper, “Procedural Puzzle Generation: A Survey”, explores the exciting and growing field of procedural content generation (PCG) for puzzles in games. While PCG has been widely used to create game worlds, characters, and narratives, its application to puzzles has been relatively limited, despite puzzles being a popular game element. My co-author, Mads Haahr, and I address this gap by providing a comprehensive overview of existing research in PCG for puzzles.
Our work is targeted at game developers and researchers in the field of artificial intelligence, particularly those interested in PCG and its application to game design. We believe our findings are especially relevant in light of the increasing demand for engaging and replayable game experiences, which procedurally generated puzzles can help deliver.
We organize our survey around eleven different categories of puzzles, each with its unique characteristics and challenges for procedural generation. We analyze each category in detail, reviewing existing research and highlighting both successful approaches and open problems. We also discuss the advantages and disadvantages of different generation techniques, such as constructive vs. generate-and-test, direct vs. simulation-based evaluation, and online vs. offline generation.
Our analysis reveals that while there has been significant progress in procedural puzzle generation, there are still many exciting challenges and opportunities for future research. We identify several key areas where further work is needed, including developing techniques for generating puzzles with specific difficulty levels, creating adaptive puzzles that respond to player actions, and improving the aesthetic quality of procedurally generated content. We believe that addressing these challenges will lead to more engaging and innovative puzzle games in the future.
Book Outline
1. I. INTRODUCTION
Puzzles present a unique opportunity for PCG in games, as they are popular with players but the replay value of individual puzzles is typically low. Procedurally generating puzzles addresses this limitation by allowing for the creation of many interesting puzzles that improve gameplay without needing designers to hand-craft them all.
Key concept: “Procedural content generation (PCG) for games has existed since the 1980s and is becoming increasingly important for creating game worlds, backstory, and characters across many genres, in particular, open-world games, such as Minecraft (2011) and No Man’s Sky (2016).”
PCG offers exciting potential to reduce content production costs and scale content almost infinitely, while also allowing for greater adaptivity and variety in gameplay.
1. I. INTRODUCTION
The benefits of using PCG to create puzzles extend beyond simply increasing replayability. Puzzles can be used to enhance storytelling, improve adaptiveness to player actions, and drive designer creativity by offloading the creation of individual puzzle instances to an algorithm.
Key concept: “We define puzzles as problems to which the player can find a solution based on previous knowledge (from in or outside the game) and/or by exploring the solution space [4].”
Puzzles are not limited to dedicated puzzle games and can be incorporated into a wide variety of genres to enhance gameplay by offering players unique challenges.
1. I. INTRODUCTION
Rather than providing a general overview of PCG in games, we focus specifically on PCG for puzzles. To facilitate this analysis, we present 11 categories of puzzles that have been subject to PCG, based on our survey of the literature, ranging from Sokoban-type puzzles to word puzzles and riddles.
Key concept: Figure 1: Map of puzzle categories.
We group puzzles into 11 categories based on their core mechanics and characteristics relevant to procedural generation. These categories are not strict, as puzzles can often overlap, and are intended to provide a framework for understanding how different puzzle types lend themselves to different generation techniques.
1. I. INTRODUCTION
We identify eight key characteristics of PCG methods that are important in the context of puzzle generation, including constructive vs. generate-and-test, direct vs. simulation-based evaluation, online vs. offline generation, degree and dimension of control, automatic generation vs. mixed authorship, generic vs. adaptive generation, and quality considerations. These characteristics help analyze the different approaches to puzzle generation and identify areas for future research.
Key concept: “The outcome of applying PCG is usually unpredictable, which can be a deterrent, but also a benefit, especially insofar that it can aid designer creativity.”
The unpredictable nature of PCG can help designers explore new and novel puzzle designs, leading to more creative and engaging puzzles.
2. II. SURVEY OF PROCEDURAL PUZZLE GENERATION
Sokoban-type puzzles, with their simple rules but complex solutions, have been a popular target for research in procedural generation. Early approaches focused on generate-and-test methods that involved using BFS to ensure solvability. These methods were often limited by the computational cost of BFS, which struggles with puzzles that require long solution sequences.
Key concept: “One of the earliest forays into puzzle generation was by Murase et al. [17] who developed a program to create Sokoban problems in three stages; generation, checking, and evaluation.”
This is an early example of a generate-and-test approach, where potential levels are created and then tested for solvability, using a breadth-first search (BFS) algorithm. This approach, while simple, can be computationally expensive, especially for complex puzzles.
2. II. SURVEY OF PROCEDURAL PUZZLE GENERATION
More recently, Monte Carlo Tree Search (MCTS) has proven to be a promising approach for generating Sokoban-type puzzles, as it can handle large branching factors and guarantees solvability. MCTS also lends itself well to generating puzzles of varying difficulty by tuning its evaluation function, either through domain-specific metrics or data-driven approaches that leverage player feedback.
Key concept: “MCTS requires an evaluation function to guide the search.”
Evaluating the quality and difficulty of procedurally generated puzzles is a key challenge. Different approaches have been explored, including using domain-specific metrics, data-driven methods based on player feedback, and AI-based evaluation using search algorithms.
3. II. SURVEY OF PROCEDURAL PUZZLE GENERATION
Sliding puzzles, while similar to Sokoban-type puzzles, present their own challenges for generation. The lack of a player character and the free movement of tiles in any direction mean that simple backward generation from a solution may not result in interesting or challenging puzzles.
Key concept: “Block-sliding puzzles can conceivably be generated by starting from the end configuration and working backward, in a similar fashion to some of the generation methods described in Section II-A.”
This highlights a common theme in puzzle generation; working backward from a solution can be a useful strategy for ensuring solvability. However, the quality of the resulting puzzle is dependent on the specific mechanics of the puzzle and how the backward generation is implemented.
4. II. SURVEY OF PROCEDURAL PUZZLE GENERATION
Tile-matching puzzles, especially match-three games, are often randomly generated, making procedural generation a trivial task. However, more complex tile-matching games, such as Fruit Dating, which blends elements from Sokoban and sliding puzzles, demonstrate the potential for applying PCG to create more intricate tile-matching puzzles.
Key concept: “As is characteristic for the Sokoban and sliding puzzle types, Fruit Dating requires the puzzler to rearrange items while anticipating the outcome of each move to prevent dead ends.”
Many puzzle types, especially those involving moving objects in a constrained space, require the player to think several moves ahead to avoid getting stuck in an unsolvable state. This makes brute-force approaches unfeasible and presents a challenge for automatic puzzle solvers.
5. II. SURVEY OF PROCEDURAL PUZZLE GENERATION
Assembly puzzles, while not extensively explored in PCG research, offer potential for exploring new generation techniques, especially in the 3-D domain. Research on generating interlocking puzzles, such as those that can be locked by a single key piece, demonstrates the possibility of creating complex 3-D assembly puzzles using procedural generation.
Key concept: “There is no formal research into the generation of 2-D assembly puzzles, likely because they are relatively uncomplicated to create.”
Some puzzle types, while popular, have not received much attention in the field of PCG, as generating them is often straightforward. This highlights the importance of focusing on puzzle types that present unique challenges for procedural generation.
6. II. SURVEY OF PROCEDURAL PUZZLE GENERATION
Mazes are a classic example of procedurally generated content in games. While traditional maze generation algorithms have focused on creating level structures, more recent research has explored using evolutionary algorithms and answer set programming (ASP) to generate stand-alone maze puzzles with specific properties, such as difficulty and aesthetics.
Key concept: “Constructive maze generation is an old topic in computer science, mainly popularized in the context of dungeon and/or level generation.”
Maze generation techniques, particularly those used in dungeon and level generation, are well-established in the field of PCG. However, generating stand-alone maze puzzles, rather than level structures, requires a different approach, focused on ensuring solvability and creating interesting challenges for the player.
Essential Questions
1. Why is Procedural Content Generation (PCG) particularly relevant for puzzles in games?
Procedural Content Generation (PCG) offers a way to automatically create engaging and varied game content, including puzzles. This is particularly beneficial for puzzles as their replay value is often low, and hand-crafting numerous unique puzzles is a time-consuming task for developers. PCG can reduce design costs, enhance replayability, and introduce adaptive challenges tailored to individual players. This survey argues for the significance of PCG in puzzle design, highlighting its potential to not only improve gameplay but also contribute to a deeper understanding of puzzle mechanics and player engagement.
2. How are puzzles categorized in the context of PCG, and why is this categorization important?
The paper identifies eleven distinct categories of puzzles commonly found in games, ranging from the well-known Sokoban-type puzzles to more complex narrative and physics-based puzzles. This categorization is based on the puzzles’ core mechanics and characteristics relevant to procedural generation, acknowledging that overlaps exist. The authors utilize this categorization to systematically analyze the existing research in PCG for each puzzle type, allowing for a deeper understanding of the challenges and opportunities associated with generating different kinds of puzzles.
3. What factors influence the quality of procedurally generated puzzles, and what are the challenges in ensuring high-quality output?
Generating solvable puzzles is only the first step in PCG for games. The quality of the generated puzzles is crucial, and several factors contribute to it. Difficulty, variety, freshness, and aesthetics are all important considerations. However, evaluating and controlling these aspects in a procedural generation system is challenging. Different approaches, such as domain-specific metrics, player feedback analysis, and AI-based evaluation, are discussed in the paper, highlighting the ongoing research in this area.
4. What are the differences between online and offline puzzle generation, and what are the implications for future research?
The paper highlights a trend towards offline generation methods in PCG for puzzles. This means that the puzzles are created before the game starts, rather than during gameplay. While offline methods offer more control and reliability in ensuring quality, they limit the potential for adaptive and dynamic puzzle generation. Online PCG, which creates puzzles on-the-fly during gameplay, is a promising but challenging area for future research, offering opportunities for personalized and unpredictable puzzle experiences.
5. What are the challenges in developing generalizable PCG techniques that can be applied to a wide range of puzzle types?
The survey underscores the lack of a unified approach to procedural puzzle generation. Most existing methods are tailored to specific puzzle types, limiting their generalizability. Developing more general PCG techniques that can be applied across different puzzle categories, while maintaining the ability to produce novel and interesting puzzles, is a significant challenge. The paper suggests that exploring constraint-based techniques, like Answer Set Programming (ASP), might offer a path towards more generalizable puzzle generation.
Key Takeaways
1. Evaluating and Controlling Puzzle Difficulty
One of the biggest challenges in PCG for puzzles is ensuring the generated content is challenging yet solvable. The paper explores various approaches to evaluating and controlling difficulty, including using domain-specific metrics, analyzing player data to identify difficulty-related features, and employing AI-based solvers to estimate puzzle complexity. It emphasizes the need for further research in this area, as creating puzzles with predictable and desirable difficulty levels is crucial for player engagement.
Practical Application:
A game developer working on a puzzle game could analyze player data, such as the time taken to solve different puzzles, the number of attempts, and common mistakes, to identify features that correlate with difficulty. This information can then be used to fine-tune the parameters of their puzzle generator and create puzzles that are more consistently challenging and engaging for players.
2. Simulation-Based Evaluation
Many PCG approaches rely on simulation-based evaluation to assess the quality and solvability of generated puzzles, especially for puzzles with dynamic elements like physics-based puzzles. This involves using AI agents to solve the generated puzzles, providing insights into their difficulty, potential solutions, and unforeseen shortcuts. The paper highlights the usefulness of this approach but also emphasizes the need for developing more sophisticated and human-like AI agents to better reflect actual player behavior.
Practical Application:
A level designer for a platformer game could use an AI agent to simulate different jump trajectories and landing positions, allowing them to identify potential pitfalls or unintended shortcuts in their level design. This information can then be used to refine the level layout and ensure it provides a challenging and enjoyable experience for players.
3. Constraint-Based Generation
While many PCG techniques are based on random generation or heuristic search, the paper highlights the potential of constraint-based approaches, like ASP, for creating puzzles with specific desired properties. These methods allow designers to explicitly define constraints, such as the required solution steps or the presence of certain elements, ensuring the generated puzzles meet specific criteria. This provides a higher degree of control over the generated content, making it particularly useful for educational games and puzzles with well-defined learning objectives.
Practical Application:
An educational game designer could use a constraint-based puzzle generator like Answer Set Programming (ASP) to create puzzles that teach specific programming concepts. The designer can specify constraints that ensure the generated puzzles require the player to apply those concepts to find the solution, creating a tailored learning experience.
Suggested Deep Dive
Chapter: II. SURVEY OF PROCEDURAL PUZZLE GENERATION
This section provides a detailed overview of various PCG methods applied to different puzzle categories. A deep dive into this chapter will expose the reader to the nuances of each puzzle type and how various generation techniques are adapted to address their specific challenges. This is crucial for understanding the practical application of PCG in puzzle design.
Memorable Quotes
I. INTRODUCTION. 21
A particular challenge faced by such games is that the content and/or gameplay may become repetitive. Puzzles constitute an effective technique for improving gameplay by offering players interesting problems to solve…
I. INTRODUCTION. 23
Procedural generation of puzzles comes with similar challenges as procedural generation of other game elements. A barrier for mainstream adoption of generated puzzles, compared to other types of content, may be the strict solvability constraint.
II. SURVEY OF PROCEDURAL PUZZLE GENERATION. 24
Despite the simplicity of the rules, Sokoban puzzles can be challenging to solve [15], for both human and machine players. Past research has determined that solving generalized Sokoban puzzles, i.e., on an n×n board, is PSPACE-complete [16].
II. SURVEY OF PROCEDURAL PUZZLE GENERATION. 27
One “gap” is formed by the lack of application of techniques that can execute in an online environment. Decreasing the generation time while maintaining quality and solvability is an important challenge to overcome in the face of integration of procedurally generated puzzles into commercial games.
III. ANALYSIS. 39
Aesthetic quality in itself poses the fourth challenge. We observed that procedural generation techniques for puzzles struggle to create designs that are as aesthetically pleasing as human designs.
Comparative Analysis
This survey stands out by focusing specifically on PCG for puzzles, a niche often overlooked in broader PCG surveys. While works like Shaker, Togelius, and Nelson’s Procedural Content Generation in Games offer a comprehensive overview of PCG, they only touch briefly on puzzles. Our work delves deeper, categorizing puzzles and analyzing the suitability of various PCG methods for each type. This detailed analysis, combined with the identification of open challenges and future directions, makes our work a valuable resource for researchers and developers interested in enriching game experiences through procedural puzzle generation. It aligns with other notable works in emphasizing the importance of quality considerations, evaluation metrics, and designer control in PCG, but specifically tailors these concepts to the unique constraints and possibilities of puzzle generation.
Reflection
This survey of procedural puzzle generation provides a valuable foundation for understanding the current state of the field and its potential for enhancing game experiences. While the paper acknowledges the significant progress made in generating various types of puzzles, it rightly emphasizes the need for addressing key challenges, such as difficulty control, quality evaluation, and generalizability of PCG methods. The focus on offline generation, while understandable in a research context, highlights the need for further exploration of online techniques to enable dynamic and adaptive puzzles in games. The authors’ proposition that constraint-based methods like ASP could lead to more generalizable PCG techniques is particularly insightful. This survey, however, primarily focuses on the technical aspects of puzzle generation and less on the player experience. Further research is needed to understand how players perceive and engage with procedurally generated puzzles, especially concerning their perceived difficulty, novelty, and enjoyment. Additionally, exploring the potential of combining PCG with other game design approaches, such as player modeling and narrative design, could lead to even more engaging and personalized puzzle experiences.
Flashcards
What is backward generation in the context of puzzle generation?
A technique where puzzles are created by starting with a solved state and working backward, often used in sliding puzzles and Sokoban.
What’s the difference between direct and simulation-based puzzle evaluation?
Direct evaluation assesses a puzzle based on its inherent features, while simulation-based evaluation uses an AI agent to solve the puzzle and measure its difficulty.
What is a successful method for generating Sokoban-type puzzles?
Monte Carlo Tree Search (MCTS), a search technique that explores the puzzle generation space by simulating gameplay, has shown promise in generating Sokoban-type puzzles with varying difficulty.
What is Answer Set Programming (ASP) and how is it used in puzzle generation?
Answer Set Programming (ASP), a declarative logic programming approach, allows for specifying constraints and generating puzzles that satisfy those constraints, making it suitable for puzzles like chromatic mazes and path-building puzzles.
What are the unique challenges of generating narrative puzzles?
Narrative puzzles, often found in adventure games, involve exploration and logical thinking within a narrative context. Generating them procedurally involves challenges like ensuring logical progression, replayability, and a satisfying solution that fits the narrative.
What are the two types of difficulty discussed in the context of physics puzzles?
Dexterity difficulty, relevant in physics puzzles, focuses on the player’s execution of a solution, requiring precise timing and control, while strategic difficulty relates to the process of finding the solution through logic and exploration.
What is the puzzle-dice system, and what is its main advantage?
The puzzle-dice system, developed by MIT Media Lab Singapore, allows for generating narrative puzzles with guaranteed solvability by using a grammar-based approach that combines puzzle patterns and designer-created game items.
What are Smart terrain causality chains (STCCs) and how are they used in puzzle generation?
Smart terrain causality chains (STCCs) use the concept of smart terrain items, with their associated actions and properties, to generate narrative puzzle solutions based on causality relationships between items in the game world.