Abstract
Every day optimization problems arise in our life and industry. Many of them require huge amount of calculations and need special type of algorithms to be solved. An important industrial problem is cutting stock problem (CSP). Cutting with less possible waste is significant in some industries. The aim of this work is to cut 2D items from rectangular stock, minimizing the waste. Even the simplified version of the problem, when the items are rectangular is NP hard. When the number of items increases, the computational time increases exponentially. It is impossible to find the optimal solution for a reasonable time. Only for very small problems the exact algorithms and traditional numerical methods can be applied. We propose a stochastic algorithm which solves the problem, when the items are irregular polygons.
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 Discret. Math. 47, 133–140 (2015)
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. Discret. Appl. Math. 123, 379–396 (2002)
Acknowledgment
Work presented here is partially supported by the Bulgarian National Scientific Fund under Grants DFNI I02/20 “Efficient Parallel Algorithms for Large Scale Computational Problems” and DFNI DN 02/10 “New Instruments for Data Mining and their Modeling”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Evtimov, G., Fidanova, S. (2018). Heuristic Algorithm for 2D Cutting Stock Problem. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_37
Download citation
DOI: https://doi.org/10.1007/978-3-319-73441-5_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73440-8
Online ISBN: 978-3-319-73441-5
eBook Packages: Computer ScienceComputer Science (R0)