Polygon decomposition for efficient construction of Minkowski sums

Agarwal, Pankaj K.; Flato, Eyal; Halperin, Dan

doi:10.1016/s0925-7721(01)00041-4

Cited by 95 publications

(6 citation statements)

References 11 publications

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“…Frontiers in Mechanical Engineering frontiersin.org Milenkovic et al (Milenkovic et al, 1992). Other methodologies to generate NFP can be found in publications of relevant scholars (Agarwal et al, 2002;Dean et al, 2006;Huyao et al, 2007;Burke et al, 2010).…”

Section: Geometric Approachmentioning

confidence: 99%

Two-dimensional irregular packing problems: A review

Guo

et al. 2022

Front. Mech. Eng.

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Two-dimensional (2D) irregular packing problems are widespread in manufacturing industries such as shipbuilding, metalworking, automotive production, aerospace, clothing and furniture manufacturing. Research on 2D irregular packing problems is essential for improving material utilization and industrial automation. Much research has been conducted on this problem with significant research results and certain algorithms. The work has made important contributions to solving practical problems. This paper reviews recent advances in the domain of 2D irregular packing problems based on a variety of research papers. We first introduce the basic concept and research background of 2D irregular packing problems and then summarize algorithms and strategies that have been proposed for the problems in recent years. Conclusion summarize development trends and research hotspots of typical 2D irregular shape packing problems. We hope that this review could provide guidance for researchers in the field of 2D irregular packing.

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Section: Geometric Approachmentioning

confidence: 99%

Two-dimensional irregular packing problems: A review

Guo

et al. 2022

Front. Mech. Eng.

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“…Although the decomposition method can tackle non-convex polygons, it also creates two further issues: efficient decomposition and robust recombination of the sub-NFPs. Agarwal et al [20] conducted an extensive investigation into different decomposition and recombination operations with respect to constructing Minkowski sums of non-convex polygons. There are further challenges in the recombination operations.…”

Section: Decomposition and Phi-functionmentioning

confidence: 99%

Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem

Luo

Rao

2022

Mathematics

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This paper introduces an efficient and robust sliding algorithm for the creation of no-fit polygons. The improved algorithm can cope with complex cases and is given an implementation in detail. The proposed concept of a touching group can simplify the judging process when recognizing the potential translation vector for an orbital polygon. In addition, the generation of the no-fit polygon only involves three main steps based on the proposed concept. The proposed algorithm has a mechanism that searches other start positions to generate a complete no-fit polygon for handling complex cases. To improve the efficiency, many acceleration strategies have been proposed, such as point exclusion strategy and point inclusion test. The robust and efficient performance of the algorithm is tested by well-known benchmark instances and degenerate and complex cases, such as holes, interlocking concavities and jigsaw-type pieces. Experimental results show that the proposed algorithm can produce complete no-fit polygons for complex cases, and acceleration strategies can reduce the creation time of no-fit polygon on benchmark instances by more than sixteen percent on average.

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“…Since then, many researchers have continued to develop and improve NFP. Although different methods of solving the NFP problems have been proposed, they can be summarized into three general methods: (a) Minkowski sums ( [28][29][30][31]), (b) the decomposition algorithm ( [32][33][34]), and (c) the orbiting algorithm ( [35,36]).…”

Section: A No-fit Polygonmentioning

confidence: 99%

Sequence Transfer-Based Particle Swarm Optimization Algorithm for Irregular Packing Problems

et al. 2021

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The two-dimensional (2D) irregular packing problem is a classical optimization problem with NP-hard characteristics and has high computational complexity. To date, packing problems have generally been solved by artificial experience and heuristic algorithms. However, these algorithms are not highly efficient and the excellent cases cannot be preserved, which both time and economic costs are high. Inspired by transfer learning and considering the characteristics of 2D irregular packing problems, we propose a sequence transfer-based particle swarm optimization algorithm (ST-PSO) to solve the multi-constraint packing problem. A piece-matching strategy based on an improved shape context algorithm, and a piece-sequencing generation strategy for transferring the packing sequence are developed for particle swarm optimization(PSO) initialization. In the process of PSO, an adaptive adjustment strategy is used with an improved positioning strategy to adjust the packing position of the pieces. The results indicate that this method can robustly, quickly, and efficiently achieve packing of 2D irregular pieces. Compared with the data prior to transfer, the ST-PSO can inherit and transfer the historical packing sequence in less time and retain or exceed the actual packing data of the samples. This algorithm could be applied to industrial applications to reduce waste, packing time, and production costs.INDEX TERMS irregular pieces, multiple constraints, particle swarm optimization algorithm, sequence transfer, two-dimensional packing optimization.

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Polygon decomposition for efficient construction of Minkowski sums

Cited by 95 publications

References 11 publications

Two-dimensional irregular packing problems: A review

Two-dimensional irregular packing problems: A review

Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem

Sequence Transfer-Based Particle Swarm Optimization Algorithm for Irregular Packing Problems

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