A Hybrid Genetic Algorithm for the Two - Dimensional Guillotine Cutting Problem

In this article an algorithm to solve the two-dimensional guillotine cutting problem is proposed. This problem considers the cut of a number of rectangular pieces from a single large rectangular plate. Two restrictions are considered: all cuts must be of guillotine type and, the number of time a piece can be cut from the plate has an upper bound. The aim is to generate a cutting pattern with minimum trim loss. The algorithm is based on the enumeration of parts of the problem domain by using ideas from the genetic algorithms. A cutting pattern is represented by means of a string which is obtained from a syntactic binary tree associated with the pattern. Reproduction and crossover operators are adequately defined in order to guarantee that all newly generated strings correspond to feasible solutions. The successive generation of string populations permit to obtain better strings that correspond to cutting pattern with smaller trim losses. The encoding used not only optimizes the memory required to solve the problem but simplifies the process of pattern generation. In order to evaluate the performance of this method a set of numerical experiments is performed. It is shown that this method can manage instances greater than those the algorithm of Oliveira and Ferreira can handle, considering the same computational resources. Furthermore, even considering the problem with pieces rotation, the quality of the obtained solutions is improved in terms of trim loss, when compared to the modified Wang’s algorithm.