A Hierarchical Method for Large-Scale Two-Dimensional Layout

The optimal layout problem of allocating different types of rectangular shapes to a large rectangular sheet (also referred to as the two-dimensional knapsack problem) is tackled by a hierarchical approach using the concepts of quad-cut, guillotine-cut, and edge-cut with variable window sizes. The method can handle sheet defects and also allows for the specification of important pieces at a fixed or variable location. In addition, the hierarchical approach has the flexibility of generating different layout patterns with little computational effort once the knapsack function for the largest window has been obtained. Although the method is suboptimal in the sense that it may not achieve the best possible result with minimum waste, extensive simulation indicates that it always gives good alternative solutions at reasonable computational cost; this is in contrast with the optimal solution for large-scale problems which often requires excessive computational effort beyond practical consideration.