Irregular packing overlap minimization using discrete Voronoi mountain

Abstract

Cutting and packing problems are of great importance in a myriad of industries such as: wood, textile, glass and shipbuilding. The irregular strip packing problem considers a container with infinite length where irregular items must be inserted into. A group of solutions in the literature solves the problem by allowing overlap between items and then applying a method which minimizes the total overlap value of the layout. The best results in the literature were obtained using overlap minimization techniques and it is the strategy adopted in this work. Fast overlap evaluation is obtained by the employment of the Voronoi mountain concept. It is used to pre-evaluate the overlap value for two items by adopting a raster representation, which is stored prior to the execution of the algorithm. Tests performed using a benchmark case showed that, even with reduced precision, competitive layouts can be obtained using the proposed approach.