Here you can find the abstracts of my publications as well as links to the respective full texts.
Publications
E. G. Birgin, R. D. Lobato and R. Morabito. Generating unconstrained two-dimensional non-guillotine cutting patterns by a recursive partitioning algorithm. Journal of the Operational Research Society (2012) 63, 183–200.
Abstract: In this study, a dynamic programming approach to deal with the unconstrained twodimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. Since a counterexample for which the approach fails to find known optimal solutions was not found, it is conjectured that it always finds an optimal unconstrained non-guillotine cutting. The method is able to find the optimal cutting pattern of a large number of problem instances of moderate sizes known in the literature. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method.
Keywords: Cutting and packing, two-dimensional non-guillotine cutting pattern, dynamic programming, recursive approach, distributor's pallet loading problem.
DOI: 10.1057/jors.2011.6
Web site: http://lagrange.ime.usp.br/~lobato/utdc/.
E. G. Birgin and R. D. Lobato. Orthogonal packing of identical rectangles within isotropic convex regions. Computers & Industrial Engineering (2010) 59, 595–602.
Abstract: A mixed integer continuous nonlinear model and a solution method for the problem of orthogonally packing identical rectangles within an arbitrary convex region are introduced in the present work. The convex region is assumed to be made of an isotropic material in such a way that arbitrary rotations of the items, preserving the orthogonality constraint, are allowed. The solution method is based on a combination of branch and bound and active-set strategies for bound-constrained minimization of smooth functions. Numerical results show the reliability of the presented approach.
Keywords: Packing and cutting of rectangles, orthogonal packing, isotropic convex regions, feasibility problems, nonlinear programming, models.
DOI: 10.1016/j.cie.2010.07.004
Web site and source code: http://lagrange.ime.usp.br/~lobato/igenpack/.
E. G. Birgin, R. D. Lobato and R. Morabito. An effective recursive partitioning approach for the packing of identical rectangles in a rectangle. Journal of the Operational Research Society (2010) 61, 306–320.
Abstract: In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an $L$-approach for packing rectangles into larger rectangles and $L$-shaped pieces. The combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50000 instances). It is also effective for solving the instances of problem set Cover III (almost 100000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. The computer implementation and the data sets are available for benchmarking purposes.
Keywords: Cutting and packing, manufacturer's pallet loading problem, woodpulp stowage problem, non-guillotine cutting pattern, dynamic programming, raster points.
Web site and source code: http://lagrange.ime.usp.br/~lobato/packing/.
