Solving the Packing Problem with Genetic Algorithms

The aim of this article is to apply the methodology of genetic algorithms to the packing problem encountered in a sticker company. Owing to the nature of the packing operation in this company the problem is not easily solved with exact integer linear programming algorithms (Gilmore and Gomory, 1963). Industrial applications of packing methodology can be found in (Dyson and Gregory, 1974), (Farley, 1988), (Haessler and Talbot, 1983), (Madsen, 1979), (Sculli, 1981) and more recently in (Spieksma, 1994), all of whom use integer linear models. Several reasons led us to decide to use genetic algorithms as an alternative tool to solve the complex problems of cutting, and highly acceptable results were obtained. The article describes the steps necessary for the implementation genetic algorithms: codification, evaluation function, selection, reproduction, crossover and mutation for the problem of situating rectangles on a surface.