Abstract
Cutting Stock Problem (CSP) is an important industrial problem. In this paper we focus on the variant arising in building construction, where a set of plates needs to be cut from rectangular stock, minimizing the waste. The CSP is known to be NP-hard combinatorial problem. The goal of this work is to propose an efficient way for subtracting of two polygons with some matching vertices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alvarez-Valdes, R., Parajon, A., Tamarit, J.M.: A computational study of heuristic algorithms for two-dimensional cutting stock problems. In: 4th Metaheuristics International Conference (MIC 2001), pp. 16–20 (2001)
Alvarez-Valdes, R., Parreno, F., Tamarit, J.M.: A Tabu Search algorithm for two dimensional non-guillotine cutting problems. Eur. J. Oper. Res. 183(3), 1167–1182 (2007)
Cintra, G., Miyazawa, F., Wakabayashi, Y., Xavier, E.: Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation. Eur. J. Oper. Res. 191, 61–85 (2008)
Dusberger, F., Raidl, G.R.: A variable neighborhood search using very large neighborhood structures for the 3-staged 2-dimensional cutting stock problem. In: Blesa, M.J., Blum, C., Voß, S. (eds.) HM 2014. LNCS, vol. 8457, pp. 85–99. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07644-7_7
Dusberger, F., Raidl, G.R.: Solving the 3-staged 2-dimensional cutting stock problem by dynamic programming and variable neighborhood search. Electron. Notes Discrete Math. 47, 133–140 (2015)
Evtimov, G., Fidanova, S.: Heuristic algorithm for 2D cutting stock problem. In: Lirkov, I., Margenov, S. (eds.) LSSC 2017. LNCS, vol. 10665, pp. 350–357. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73441-5_37
Gonçalves, J.F.: A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem. Eur. J. Oper. Res. 183(3), 1212–1229 (2007)
Parmar, K., Prajapati, H., Dabhi, V.: Cutting stock problem: a survey of evolutionary computing based solution. In: Proceedings of Green Computing Communication and Electrical Engineering (2014). https://doi.org/10.1109/ICGCCEE.2014.6921411
Lodi, A., Martello, S., Vigo, D.: Recent advances on two-dimensional bin packing problems. Discrete Appl. Math. 123, 379–396 (2002)
Lin, Z., Li, Y.: An efficient algorithm for intersection, union and difference between two polygons. In: Proceedings of Computer Network and Multimedia Technology, Wuhan, China, pp. 1–4 (2009)
Acknowledgment
The work presented here is partially supported by the Bulgarian National Research Fund under Grants DFNI DN 12/5 and DFNI DN 02/10.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Evtimov, G., Fidanova, S. (2019). Subtraction of Two 2D Polygons with Some Matching Vertices. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-10692-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10691-1
Online ISBN: 978-3-030-10692-8
eBook Packages: Computer ScienceComputer Science (R0)