Budget-Aware Sequential Brick Assembly with Efficient Constraint Satisfaction
Abstract: We tackle the problem of \emph{sequential brick assembly} with LEGO bricks to create combinatorial 3D structures. This problem is challenging since this brick assembly task encompasses the characteristics of combinatorial optimization problems. In particular, the number of assemblable structures increases exponentially as the number of bricks used increases. To solve this problem, we propose a new method to predict the scores of the next brick position by employing a U-shaped sparse 3D convolutional neural network. Along with the 3D convolutional network, a \emph{one-initialized brick-sized} convolution filter is used to efficiently validate physical constraints between bricks without training itself. By the nature of this one-initialized convolution filter, we can readily consider several different brick types by benefiting from modern implementation of convolution operations. To generate a novel structure, we devise a sampling strategy to determine the next brick position considering the satisfaction of physical constraints. Moreover, our method is designed for either \emph{budget-free} or \emph{budget-aware} scenario where a budget may confine the number of bricks and their types. We demonstrate that our method successfully generates a variety of brick structures and outperforms existing methods with Bayesian optimization, deep graph generative model, and reinforcement learning.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Laurent_Charlin1
Submission Number: 2695
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