Split-and-Merge-Based Genetic Algorithm (SM-GA) for LEGO Brick Sculpture Optimization

This paper proposes a split-and-merge-based genetic algorithm (SM-GA) for converting a given 3-D voxel model into an LEGO brick sculpture using a minimal number of bricks. The proposed SM-GA is designed to always generate a feasible brick layout in accordance with a given voxel model considering the stability and connectivity between layouts. A novel split-and-merge operator to find the optimal layout is also proposed. To evaluate the effectiveness of the proposed approach, computational and physical experiments are performed. In the computational experiments, the performance of the proposed approach is compared with that of the most recent conventional GA approach. Also, the result of a 3-D physical sculpture made of real LEGO bricks is presented. Compared with the conventional GA-based approach, it is shown that the proposed SM-GA is more effective in finding the near optimal solution to the LEGO brick layout problem.