Concepts of neighbourhood and universal compact yield towards achieving best pattern layouts

Clustering of a given set of patterns or nesting onto a stock is a typical and mingled issue in cutting stock problems. The traditional methods seem to be not intelligent enough to solve the problem due to the possibility of having combinations. A compact neighbourhood algorithm (CNA) that relates the number of neighbours and the sharing space between them is proposed. Based on the results of CNA, we can now define a universal compact yield of stock for a specific pattern or cluster on a scientific basis. It also provides necessary geometrical hints of the subsequent nesting process with the consideration of various types of layout.