Genetic Algorithms for the Single-Sheet and Multi-Sheet Non-convex Cutting Stock Problem

The two-dimensional cutting stock problem is the problem of cutting two-dimensional parts from a sheet such that the cutting requirements are met and no cuts overlap. This paper presents a genetic algorithm for the cutting-stock problem which handles non-convex, irregularly shaped parts and regular sheets. The objective is to maximize the utilization of the sheet for a given bill of materials. The salient features of this algorithm are the way in which layouts are described, and the way in which the e ciency function is computed. We create 'pseudo-layout' of the parts on the sheet , which are easier to be manipulated by the genetic algorithm. Also pseudo layout can be changed into unique actual layouts in a simple manner. The proposed algorithm can handle placement of highly irregular parts with ease as no simplifying assumptions are made about the shape of the parts to be placed. The algorithm was tested with part requirements resembling those from an actual leather industry stock cut need. Several runs were made with di erent bill of materials and varying sheet dimensions. The e ciency of placement ranged from 65-75%.