1. A Case Study ofExpressively ConstrainableLevel Design Automation Toolsfor a Puzzle GameAdam M. Smith (presenter), Erik Andersen, Michael Mateas, ZoranPopovidexpressiveintelligencestudio centerforgamescience UC Santa Cruz University of Washingtonamsmith@soe.ucsc.eduFDG 2012 Raleigh, USA

2. Refraction (deployed game) Over 495,000 plays on Kongregate.expressiveintelligencestudio UC Santa Cruz

3. Towards Infinite Refraction Automatically designed levels & progressions Customization for individual players Educational soundnessexpressiveintelligencestudio UC Santa Cruz

4. Requirements for Design Automation Solves hard combinatorial search problems in reasonable amounts of time Small amount of code Trustable output Hard constraints Global optimizationexpressiveintelligencestudio UC Santa Cruz

5. Refraction gameplayexpressiveintelligencestudio UC Santa Cruz

6. Roadmap Design automation problems Original solutions Introduction to answer set programming (ASP) New solutions Comparisons: size, speed, style Lessons learnedexpressiveintelligencestudio UC Santa Cruz

7. Three Design Automation Problems Synthesis Mission Generation Grid Embedding Analysis Puzzle Solvingexpressiveintelligencestudio UC Santa Cruz

8. Problem: Mission Generation Expressions: ((1/2)/2), (1/2)+(1/4), (1/4)+(1/4), Parameters: 24 blockers, 7 benders, 7 distractorsexpressiveintelligencestudio UC Santa Cruz

9. Problem: Grid Embedding Mission Spaceexpressiveintelligencestudio UC Santa Cruz

10. Example: Puzzle Solving S2 B x S2 S2 x x x x x x x S2 Tgt B x x x x x 3/4 B B x x E2 B x C2 Tgt Src S2 1/2 1/4 C2 S2 x S2 Src B x x x x 1/1 B B x x x Puzzle Solutionexpressiveintelligencestudio UC Santa Cruz

11. Six Design Automation Tools Problem Original Approach New Approach Mission Generation Custom, feed-forward ASP (AnsProlog + Lua) algorithm (Java) Grid Embedding Depth-first search (Java) ASP (AnsProlog) Puzzle Solving Depth-first search (Java) ASP (AnsProlog + Lua) S2 B x S2 S2 x x x x x x x S2 Tgt B x x x x x 3/4 B B x x E2 B x C2 Tgt Src S2 1/2 1/4 C2 S2 x S2 Src B x x x x 1/1 B B x x xexpressiveintelligencestudio UC Santa Cruz

12. Original Mission Generator Custom feed-forward algorithm: Several stages that iteratively expand graph Expression translation Opportunistic connection Target completion Note: Common PCG strategy Output meets requirements by constructionexpressiveintelligencestudio UC Santa Cruz

13. Original Grid Embedder Depth-first search: Transfer pieces from mission to spots on grid one- by-one Notes: This is a tough combinatorial search problem! DFS is complete on finite problems. A* would be faster, but more complex. We want to maintain less code!expressiveintelligencestudio UC Santa Cruz

14. Original Puzzle Solver Depth-first search: Place pieces from tray one-by-one Note: Harder: math not resolved, no solution template A* ... we really want more control over solutions!expressiveintelligencestudio UC Santa Cruz

15. Brief intro to ASP (not Prolog!) ASP (answer set programming) is a declarative logic programming paradigm focused on complex (NP and NPNP) combinatorial search an optimization problems. Overview: Designer defines problem (in AnsProlog syntax). Grounder transforms problem into SAT-like. High-performance solver enumerates solutions.expressiveintelligencestudio UC Santa Cruz

16. Answer Set Program Design Guess a solution so that none of its deduced properties are forbidden, optionally optimizing a metric.expressiveintelligencestudio UC Santa Cruz

17. Answer Set Program Design Which two numbers that multiply to 42 have the smallest sum? % guess two numbers 2 { picked(1..42) } 2. % deduce if they multiply to 42 product_ok :- picked(A), picked(B), 42==A*B. % forbid lack of proper product :- not product_ok. % optimize (weighted) sum #minimize [ picked(A)=A ].expressiveintelligencestudio UC Santa Cruz

18. New Grid Embedder Answer Set Program: Guess: Absolute positions for pieces (x;y) Directions for laser ports (n;e;w;s) Deduce: Relative positions from absolute positions Free paths from relative positions Beam production from free paths Expression instantiation from beams Forbid: Overlapping pieces Lack of embedding for mission edges Illegal port configurations Notes: How do I place and configure the pieces so that the apparent mission subsumes the required mission? This tool involves 75 lines of code.expressiveintelligencestudio UC Santa Cruz

19. New Mission Generator Answer Set Program: Guess node and edge descriptions so that required expressions and piece counts are satisfied. Notes: What vs. How clarifies problem Now easy to drop in additional constraints without redesign. Concatenate this with embedder to make monolithic generator!expressiveintelligencestudio UC Santa Cruz

20. New Puzzle Solver Answer Set Program: Guess placement of player pieces so that all targets are powered correctly. Notes: 100% faithful model of game How many pieces are used in the simplest solution that does not cross any beams or use an expander?expressiveintelligencestudio UC Santa Cruz

21. Code Size Comparison Problem Original Solution New Solution Mission Generation 1,145 Java 194 AnsProlog + 38 Lua Grid Embedding 987 Java 75 AnsProlog + 0 Lua Puzzle Solving 988 Java 83 AnsProlog + 61 Lua Improvements: - Much smaller than even simple custom algorithms - No procedural commitments - Freely include extra constraints in inputexpressiveintelligencestudio UC Santa Cruz

22. Search Time Comparison Problem Java Search ASP Search Mission Generation < 1 ms. < 1 ms. Grid Embedding 650 ms.* 110 ms. Puzzle Solving No solutions within 350 ms. one hour* * Including an advanced feature borrowed from the answer set solver. Problems derived from running example: (representative of late-stage gameplay)expressiveintelligencestudio UC Santa Cruz

23. Embedding Style Examplesexpressiveintelligencestudio UC Santa Cruz

24. Lessons Learned We rebuilt our design automation tools for a real, deployed game on a substrate that natively understood hard constraints and global optimization and they were smaller and went a bit faster. and they transformed the way were designing our new game.expressiveintelligencestudio UC Santa Cruz

25. Design Process Impact Got out of the search algorithm design business Got into the expressive authoring business We clarified our design automation problems Found new uses for tools: Mission Gen. + Grid Embed. = Unified Puzzle Synthesizer Solver = Puzzle Analysis Power Tool Discovered new constraints: Stylistic Educational Gained rapid prototyping toolsexpressiveintelligencestudio UC Santa Cruz

26. Thanks!Presenter:Adam M. Smithamsmith@soe.ucsc.eduexpressiveintelligencestudio UC Santa Cruz