New extesions of the scalarizations techiques in the multiobjective one-dimensional cutting stock problem

The present work deals with the Multiobjective One-Dimensional Cutting Stock Problem (MODCSP). This problem has an enormous practical importance, and the multiobjective approach has been little reported in the literature. The bi-objective model considered aims to minimize the sum of the frequency of cutting patterns to meet minimal demand and the number of different cutting patterns to be used (setup), being these objectives conflicting. In this case, the MODCSP has a non-unitary set of solutions, said \textit{efficient solutions}, equally important for the problem. The generation of each efficient solution requires the optimization of an Integer Linear Problem. So, the complete enumeration of these solutions can be an expensive task, especially when cutting patterns are not provided by the user. In this thesis, we applied seven different methods that transform the MODCSP on scalar optimization problems, where each problem provide an efficient solution. Six scalarization methods were adapted from literature and one was unprecedentedly developed. In the case of the cutting patterns be provided a priori, we used a relaxation strategy (heuristic) to accelerate obtaining of the set efficient solutions. In this approach, we relaxed the integrality condition of the variables and each efficient solution was rounded by a specially developed heuristic. The extensive results in Chapter 8 validated that this idea was adequate and effective. Furthermore, the new scalarization technique proved to be very competitive with other established in the literature, enabling growth and advancement in the area of the Cutting Problems and in Multiobjective Combinatorial Optimization (AU)