An Object-Based Evolutionary Algorithm for Solving Rectangular Piece Nesting Problems

Nesting problems have been tackled by researchers using a vast number of algorithms in the past. Most of the algorithms, however, need to perform on a one-dimensional space. Therefore, the problem must be transformed into a one-dimensional space problem similar to the travelling salesman problem. Consequently, loss of solutions due to the dimensional reduction may occur. In this study, an object-based evolutionary algorithm for rectangular piece nesting problems is proposed. This methodology is created on truly two-dimensional space, allowing new mechanisms (i.e., individual representation, initialization, etc.) and new object-based genetic operators (i.e., hill-climbing, mutation, and recombination operators) to perform effectively on the space. Since no dimensional reduction is used, therefore, no solution losses during the searching. Simulation/animation of the layouts shows the continual improvement by using this method over generations. Experimental results are promising

An Object-Based Evolutionary Algorithm: The Nesting Solution

The nesting problems have received considerable attention and have been addressed by a variety of algorithms. Recently, evolutionary algorithms have been adopted for solutions. Most of these algorithms, however, require a search in one-dimensional space; thus a transformation of the problem to a single dimension, as in the sequencing problems, is needed. Unfortunately, this restricts the search space. In this study an object-based evolutionary algorithm for the nesting problems is proposed. The methodology is created in a true two-dimensional space, allowing object-based mechanisms and object-based evolutionary operators to perform effectively on the space without restricting search alternatives. Implementation of the algorithm is conducted using grid representation where no overlapping is allowed. Layout simulation/animation over generations shows the continual improvement by this method. Experimental results of packing density on rectangular and irregular versions of the nesting problem are up to 94.41% and 82.34%, respectively. For industrial-size data, five hundred and forty-three pieces are tested. The final packing density is 74.89

Genetic algorithms for the scheduling in additive manufacturing

[EN] Genetic Algorithms (GAs) are introduced to tackle the packing problem. The scheduling in Additive Manufacturing (AM) is also dealt with to set up a managed market, called “Lonja3D”. This will enable to determine an alternative tool through the combinatorial auctions, wherein the customers will be able to purchase the products at the best prices from the manufacturers. Moreover, the manufacturers will be able to optimize the production capacity and to decrease the operating costs in each case.This research has been partially financed by the project: “Lonja de Impresión 3D para la Industria 4.0 y la Empresa Digital (LONJA3D)” funded by the Regional Government of Castile and Leon and the European Regional Development Fund (ERDF, FEDER) with grant VA049P17Castillo-Rivera, S.; De Antón, J.; Del Olmo, R.; Pajares, J.; López-Paredes, A. (2020). Genetic algorithms for the scheduling in additive manufacturing. International Journal of Production Management and Engineering. 8(2):59-63. https://doi.org/10.4995/ijpme.2020.12173OJS596382Ahsan, A., Habib, A., Khoda, B. (2015). Resource based process planning for additive manufacturing. Computer-Aided Design, 69, 112-125. https://doi.org/10.1016/j.cad.2015.03.006Araújo, L., Özcan, E., Atkin, J., Baumers, M., Tuck, C., Hague, R. (2015). Toward better build volume packing in additive manufacturing: classification of existing problems and benchmarks. 26th Annual International Solid Freeform Fabrication Symposium - an Additive Manufacturing Conference, 401-410.Berman, B. (2012). 3-D printing: The new industrial revolution. Business Horizons, 55: 155-162. https://doi.org/10.1016/j.bushor.2011.11.003Canellidis, V., Dedoussis, V., Mantzouratos, N., Sofianopoulou, S. (2006). Preprocessing methodology for optimizing stereolithography apparatus build performance. Computers in Industry, 57, 424-436. https://doi.org/10.1016/j.compind.2006.02.004Chergui, A., Hadj-Hamoub, K., Vignata, F. (2018). Production scheduling and nesting in additive manufacturing. Computers & Industrial Engineering, 126, 292-301. https://doi.org/10.1016/j.cie.2018.09.048Demirel, E., Özelkan, E.C., Lim, C. (2018). Aggregate planning with flexibility requirements profile. International Journal of Production Economics, 202, 45-58. https://doi.org/10.1016/j.ijpe.2018.05.001Fera, M., Fruggiero, F., Lambiase, A., Macchiaroli, R., Todisco, V. (2018). A modified genetic algorithm for time and cost optimization of an additive manufacturing single-machine scheduling. International Journal of Industrial Engineering Computations, 9, 423-438. https://doi.org/10.5267/j.ijiec.2018.1.001Hopper, E., Turton, B. (1997). Application of genetic algorithms to packing problems - A Review. Proceedings of the 2nd Online World Conference on Soft Computing in Engineering Design and Manufacturing, Springer Verlag, London, 279-288. https://doi.org/10.1007/978-1-4471-0427-8_30Ikonen, I., Biles, W.E., Kumar, A., Wissel, J.C., Ragade, R.K. (1997). A genetic algorithm for packing three-dimensional non-convex objects having cavities and holes. ICGA, 591-598.Kim, K.H., Egbelu, P.J. (1999). Scheduling in a production environment with multiple process plans per job. International Journal of Production Research, 37, 2725-2753. https://doi.org/10.1080/002075499190491Lawrynowicz, A. (2011). Genetic algorithms for solving scheduling problems in manufacturing systems. Foundations of Management, 3(2), 7-26. https://doi.org/10.2478/v10238-012-0039-2Li, Q., Kucukkoc, I., Zhang, D. (2017). Production planning in additive manufacturing and 3D printing. Computers and Operations Research, 83, 157-172. https://doi.org/10.1016/j.cor.2017.01.013Milošević, M., Lukić, D., Đurđev, M., Vukman, J., Antić, A. (2016). Genetic Algorithms in Integrated Process Planning and Scheduling-A State of The Art Review. Proceedings in Manufacturing Systems, 11(2), 83-88.Pour, M.A., Zanardini, M., Bacchetti, A., Zanoni, S. (2016). Additive manufacturing impacts on productions and logistics systems. IFAC, 49(12), 1679-1684. https://doi.org/10.1016/j.ifacol.2016.07.822Wilhelm, W.E., Shin, H.M. (1985). Effectiveness of Alternate Operations in a Flexible Manufacturing System. International Journal of Production Research, 23(1), 65-79. https://doi.org/10.1080/00207548508904691Xirouchakis, P., Kiritsis, D., Persson, J.G. (1998). A Petri net Technique for Process Planning Cost Estimation. Annals of the CIRP, 47(1), 427-430. https://doi.org/10.1016/S0007-8506(07)62867-4Zhang, Y., Bernard, A., Gupta, R.K., Harik, R. (2014). Evaluating the design for additive manufacturing: a process planning perspective. Procedia CIRP, 21, 144-150. https://doi.org/10.1016/j.procir.2014.03.17

A scanline-based algorithm for the 2D free-form bin packing problem

Abstract This paper describes a heuristic algorithm for the two-dimensional free-form bin packing (2D-FBP) problem, which is also called the irregular cutting and packing, or nesting problem. Given a set of 2D free-form bins, which in practice may be plate materials, and a set of 2D free-form items, which in practice may be plate parts to be cut out of the materials, the 2D-FBP problem is to lay out items inside one or more bins in such a way that the number of bins used is minimized, and for each bin, the yield is maximized. The proposed algorithm handles the problem as a variant of the one-dimensional bin-packing problem; i.e., items and bins are approximated as sets of scanlines, and scanlines are packed. The details of the algorithm are given, and its application to a nesting problem in a shipbuilding company is reported. The proposed algorithm consists of the basic and the group placement algorithms. The basic placement algorithm is a variant of the first-fit decreasing algorithm which is simply extended from the one-dimensional case to the two-dimensional case by a novel scanline approximation. The group placement algorithm is an extension of the basic placement algorithm with recombination of input items. A numerical study with real instances shows that the basic placement algorithm has sufficient performance for most of the instances, however, the group placement algorithm is required when items must be aligned in columns. The qualities of the resulting layouts are good enough for practical use, and the processing times required for both algorithms are much faster than those by manual nesting. 1

A general genetic algorithm for one and two dimensional cutting and packing problems

Cutting and packing problems are combinatorial optimisation problems. The major interest in these problems is their practical significance, in manufacturing and other business sectors. In most manufacturing situations a raw material usually in some standard size has to be divided or be cut into smaller items to complete the production of some product. Since the cost of this raw material usually forms a significant portion of the input costs, it is therefore desirable that this resource be used efficiently. A hybrid general genetic algorithm is presented in this work to solve one and two dimensional problems of this nature. The novelties with this algorithm are: A novel placement heuristic hybridised with a Genetic Algorithm is introduced and a general solution encoding scheme which is used to encode one dimensional and two dimensional problems is also introduced

Quantization with Knowledge Base Applied to Geometrical Nesting Problem

Nesting algorithms deal with placing two-dimensional shapes on the given canvas. In this paper a binary way of solving the nesting problem is proposed. Geometric shapes are quantized into binary form, which is used to operate on them. After finishing nesting they are converted back into original geometrical form. Investigations showed, that there is a big influence of quantization accuracy for the nesting effect. However, greater accuracy results with longer time of computation. The proposed knowledge base system is able to strongly reduce the computational time

Analysis of irregular three-dimensional packing problems in additive manufacturing: a new taxonomy and dataset

© 2018 Informa UK Limited, trading as Taylor & Francis Group. With most Additive Manufacturing (AM) technology variants, build processes take place inside an internal enclosed build container, referred to as a ‘build volume’. It has been demonstrated that the effectiveness with which this volume is filled with product geometries forms an important determinant of overall process efficiency in AM. For effective operations management, it is important to understand not only the problem faced, but also which methods have proved effective (or ineffective) for problems with these characteristics in the past. This research aims to facilitate this increased understanding. The build volume packing task can be formulated as a three-dimensional irregular packing (3DIP) problem, which is a combinatorial optimisation problem requiring the configuration of a set of arbitrary volumetric items. This paper reviews existing general cutting and packing taxonomies and provides a new specification which is more appropriate for classifying the problems encountered in AM. This comprises a clear-cut problem definition, a set of precise categorisation criteria for objectives and problem instances, and a simple notation. Furthermore, the paper establishes an improved terminology with terms that are familiar to, but not limited to, researchers and practitioners in the field of AM. Finally, this paper describes a new dataset to be used in the evaluation of existing and proposed computational solution methods for 3DIP problems encountered in AM and discusses the importance of this research for further underpinning work