This paper describes a neuro-based optimization algorithm for three dimensional (3-D) rectangular puzzles which are the problems to arrange the irregular-shaped blocks so that they perfectly fit into a fixed three dimensional rectangular shape. First, the fitting function of the 3-D block, which means the fitting degree of each irregular block to the neighboring block and the rectangular configuration, is described. Next, the energy function for the 3-D rectangular puzzles is proposed, where the horizontal rotation of the block is also considered. Finally, our optimization method is applied to several examples using the 3-D analog neural array and it is shown that our algorithm is useful for solving 3-D rectangular puzzles.

This paper describes a neuro-based optimization algorithm for three dimensional (3-D) cylindric puzzles which are problems to arrange the irregular-shaped slices so that they perfectly fit into a fixed three dimensional cylindric shape. First, the idea to expand the 2-dimensional tiling technique to 3-dimensional puzzles is described. Next, to energy function with the fitting function of each polyomino is introduced, which is available for 3-D cylindric puzzles. Furthermore our algorithm is applied to several examples using the analog neural array. Finally, it is shown that our algorithm is useful for solving 3-D cylindric puzzles.