Nonlinear cutting stock problem model to minimize the number of different patterns and objects

In this article we solve a nonlinear cutting stock problem which represents a cutting stock problem that considers the minimization of, both, the number of objects used and setup. We use a linearization of the nonlinear objective function to make possible the generation of good columns with the Gilmore and Gomory procedure. Each time a new column is added to the problem, we solve the original nonlinear problem by an Augmented Lagrangian method. This process is repeated until no more profitable columns is generated by Gilmore and Gomory technique. Finally, we apply a simple heuristic to obtain an integral solution for the original nonlinear integer problem.617

A genetic symbiotic algorithm applied to the one-dimensional cutting stock problem

This work presents a genetic symbiotic algorithm to minimize the number of objects and the setup in a one-dimensional cutting stock problem. The algorithm implemented can generate combinations of ordered lengths of stock (the cutting pattern) and, at the same time, the frequency of the cutting patterns, through a symbiotic process between two distinct populations, solutions and cutting patterns. Working with two objectives in the fitness function and with a symbiotic relationship between the two populations, we obtained positive results when compared with other methods described in the literature.<br>Neste trabalho desenvolvemos um algoritmo genético simbiótico com objetivo de minimizar o número de objetos processados e o setup num problema de corte unidimensional. Nosso algoritmo genético gera seus próprios padrões em conjunto com soluções para o problema, através de um processo simbiótico entre duas populações distintas, a de soluções e a de padrões. Trabalhando com os dois objetivos na função de aptidão e com a relação simbiótica entre as duas populações, obtivemos resultados competitivos em relação aos métodos descritos na literatura