research-article

Finding an Optimal LEGO® Brick Layout of Voxelized 3D Object Using a Genetic Algorithm

Authors:

Byung-Ro MoonAuthors Info & Claims

GECCO '15: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

Pages 1215 - 1222

https://doi.org/10.1145/2739480.2754667

Published: 11 July 2015 Publication History

Abstract

In this paper, we propose a genetic algorithm for a LEGO(R) brick layout problem. The task is to build a given 3D object with LEGO(R) bricks. A brick layout is modeled as a solution to a combinatorial optimization problem, through intermediate voxelization, which tries to maximize the connectivity and then minimize the number of used bricks. We attack the problem in the context of genetic search. The proposed randomized greedy algorithm produces initial solutions, and the solutions are effectively improved by an evolutionary process. New domain-specific methods are proposed as well, which include a random boundary mutation and a thickening approach. We tested our algorithm on various objects collected from the web. Experimental results showed that the algorithm produces efficient, and mostly optimal solutions for benchmark models. Unlike some previous works, our algorithm is not limited to assemble few specific objects, but it can deal with diverse kind of objects. To the best of our knowledge, this is the most extensive empirical study on the problem.

References

[1]

M. Ayers and R. Zeleznik. The LEGO interface toolkit. In Proceedings of the 9th Annual ACM Symposium on User Interface Software and Technology, pages 97--98, 1996.

Digital Library

[2]

D. Cohen-Or and A. Kaufman. Fundamentals of surface voxelization. Graphical models and image processing, 57(6):453--461, 1995.

Digital Library

[3]

R. Gower, A. Heydtmann, and H. Petersen. LEGO: Automated model construction. 32nd European Study Group with Industry - Final Report, pages 81--94, 1998.

[4]

L. Jensen, B. Kristensen, and Y. Demazeau. Flip: a platform to integrate embodied agent technology. In Intelligent Agent Technology, 2003. IAT 2003. IEEE/WIC International Conference on, pages 103--110, 2003.

Digital Library

[5]

A. B. Kahng and B. R. Moon. Toward more powerful recombinations. In Proceedings of the 6th International Conference on Genetic Algorithms, pages 96--103, 1995.

Digital Library

[6]

S. Mueller, T. Mohr, K. Guenther, J. Frohnhofen, and P. Baudisch. fabrickation: fast 3d printing of functional objects by integrating construction kit building blocks. In Proceedings of the 32nd annual ACM conference on Human factors in computing systems, pages 3827--3834, 2014.

Digital Library

[7]

F. S. Nooruddin and G. Turk. Simplification and repair of polygonal models using volumetric techniques. IEEE Transactions on Visualization and Computer Graphics, 9(2):191--205, 2003.

Digital Library

[8]

P. Petrovic. Solving LEGO brick layout problem using evolutionary algorithms. In Proceedings to Norwegian Conference on Computer Science, 2001.

[9]

M. Peysakhov, V. Galinskaya, and W. C. Regli. Using graph grammars and genetic algorithms to represent and evolve LEGO assemblies. In D. Whitley, editor, Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pages 269--276, 2000.

[10]

M. Peysakhov and W. C. Regli. Using assembly representations to enable evolutionary design of LEGO structures. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 17(2):155--168, 2003.

Digital Library

[11]

E. Smal. Automated brick sculpture construction. PhD thesis, Stellenbosch: Stellenbosch University, 2008.

[12]

R. Testuz, Y. Schwartzburg, and M. Pauly. Automatic generation of constructable brick sculptures. In Proc. Eurographics, volume 13, 2013.

[13]

O. Timcenko. LEGO: How to build with LEGO. 32nd European Study Group with Industry - Final Report, pages xix--xxi, 1998.

[14]

L. van Zijl and E. Smal. Cellular automata with cell clustering. In Automata-2008: Theory and Applications of Cellular Automata, pages 425--441, 2008.

[15]

M. Zhang, J. Mitani, Y. Kanamori, and Y. Fukui. Blocklizer: Interactive design of stable mini block artwork. In ACM SIGGRAPH 2014 Posters, SIGGRAPH '14, pages 18:1--18:1, 2014.

Digital Library

Cited By

Walsman AZhang MFishman AFarhadi AFox D(2024)Learning to Build by Building Your Own InstructionsComputer Vision – ECCV 202410.1007/978-3-031-73024-5_16(261-278)Online publication date: 24-Nov-2024
https://doi.org/10.1007/978-3-031-73024-5_16
Guo MLi CZhao YLee G(2024)TreeSBA: Tree-Transformer for Self-supervised Sequential Brick AssemblyComputer Vision – ECCV 202410.1007/978-3-031-73016-0_3(35-51)Online publication date: 26-Oct-2024
https://doi.org/10.1007/978-3-031-73016-0_3
Zhou MGe JXu HFu C(2023)Computational Design of LEGO® Sketch ArtACM Transactions on Graphics10.1145/361830642:6(1-15)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618306
Show More Cited By

Index Terms

Finding an Optimal LEGO® Brick Layout of Voxelized 3D Object Using a Genetic Algorithm
1. Computing methodologies
  1. Artificial intelligence
    1. Control methods
    2. Search methodologies
2. Theory of computation
  1. Design and analysis of algorithms
    1. Algorithm design techniques
      1. Dynamic programming

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cover image ACM Conferences

GECCO '15: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

July 2015

1496 pages

ISBN:9781450334723

DOI:10.1145/2739480

Editor:
Sara Silva
Universidade de Lisboa, Portugal
,
General Chair:
Anna I. Esparcia-Alcázar
Universitat Politècnica de València, Spain

Copyright © 2015 ACM.

Publication rights licensed to ACM. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 July 2015

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Funding Sources

Korea Ministry of Science ICT & Future Planning(MSIP) / National Research Foundation of Korea(NRF)
Ministry of Culture Sports and Tourism(MCST) and Korea Creative Content Agency(KOCCA) in the Culture Technology(CT) Research

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GECCO '15

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SIGEVO

GECCO '15: Genetic and Evolutionary Computation Conference

July 11 - 15, 2015

Madrid, Spain

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GECCO '15 Paper Acceptance Rate 182 of 505 submissions, 36%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

Walsman AZhang MFishman AFarhadi AFox D(2024)Learning to Build by Building Your Own InstructionsComputer Vision – ECCV 202410.1007/978-3-031-73024-5_16(261-278)Online publication date: 24-Nov-2024
https://doi.org/10.1007/978-3-031-73024-5_16
Guo MLi CZhao YLee G(2024)TreeSBA: Tree-Transformer for Self-supervised Sequential Brick AssemblyComputer Vision – ECCV 202410.1007/978-3-031-73016-0_3(35-51)Online publication date: 26-Oct-2024
https://doi.org/10.1007/978-3-031-73016-0_3
Zhou MGe JXu HFu C(2023)Computational Design of LEGO® Sketch ArtACM Transactions on Graphics10.1145/361830642:6(1-15)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618306
Walsman AZhang MKotar KDesingh KFarhadi AFox D(2022)Break and Make: Interactive Structural Understanding Using LEGO BricksComputer Vision – ECCV 202210.1007/978-3-031-19815-1_6(90-107)Online publication date: 23-Oct-2022
https://dl.acm.org/doi/10.1007/978-3-031-19815-1_6
Zhou JChen XXu Y(2019)Automatic Generation of Vivid LEGO Architectural SculpturesComputer Graphics Forum10.1111/cgf.1360338:6(31-42)Online publication date: 14-Feb-2019
https://doi.org/10.1111/cgf.13603
Lee SKim JMyung H(2018)Split-and-Merge-Based Genetic Algorithm (SM-GA) for LEGO Brick Sculpture OptimizationIEEE Access10.1109/ACCESS.2018.28590396(40429-40438)Online publication date: 2018
https://doi.org/10.1109/ACCESS.2018.2859039
Yun GPark CYang HMin KMao XThalmann DGavrilova M(2017)Legorization with multi-height bricks from silhouette-fitted voxelizationProceedings of the Computer Graphics International Conference10.1145/3095140.3095180(1-6)Online publication date: 27-Jun-2017
https://dl.acm.org/doi/10.1145/3095140.3095180

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