Budget-Aware Sequential Brick Assembly with Efficient Constraint Satisfaction

TL;DR

This paper introduces a novel neural network-based method for sequential LEGO brick assembly that efficiently predicts placement scores and respects constraints, enabling the generation of diverse 3D structures within budget limitations.

Contribution

The paper presents a new approach combining a U-shaped sparse 3D CNN and a constraint validation filter for efficient, budget-aware brick assembly, outperforming existing methods.

Findings

Successfully generates diverse 3D brick structures

Outperforms Bayesian optimization, graph models, and reinforcement learning

Handles budget constraints effectively

Abstract

We tackle the problem of 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 one-initialized brick-sized convolution filter is used to efficiently validate assembly 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 assembly constraints. Moreover, our method is designed for either budget-free or 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.