Abstract
The Cutting Path Problem (CPP) is a complex continuous and combinatorial optimization problem that is about finding an optimal tool path for CNC technologies equipment. The problem has many valuable industrial applications arising from the Industry 4.0 strategy, such as those, related to tool path routing for the sheet metal cutting machines. The CPP is strongly NP-hard enclosing variants of the well-known Traveling Salesman Problem (TSP) as sub-problems. In this paper, we for the first time propose an open access library of sample instances (CPPLib) for the CPP to facilitate the benchmarking of optimization algorithms, most of them are heuristics or metaheuristics. Each instance is obtained as an image of a finite set of mutually nested industrial parts on a metal sheet and is presented in the DXF vector format that is induced by a solution result of the well-known 2D nesting problem. For the first time we propose geometric and quantitative principles for constructing different groups (classes) of such image instances. Along with continuous CPP settings, the library contains their discrete counterparts presented in the form of instances of the Precedence Constraints Generalized Traveling Salesman Problem (PCGTSP), since the solution processes for the CPP mostly based on discretizing boundary contours of parts. In addition, the paper presents examples of testing some optimization algorithms for solving the cutting path problem on test instances from the developed CPPLib library.
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
Dewil, R., Vansteenwegen, P., Cattrysse, D.: A review of cutting path algorithms for laser cutters. Int. J. Adv. Manuf. Technol. 87(5–8), 1865–1884 (2016). https://doi.org/10.1007/s00170-016-8609-1
Petunin, A.: General Model of Tool Path Problem for the CNC Sheet Cutting Machines. IFAC-PapersOnLine 52(13), 2662–2667 (2019). https://doi.org/10.1016/j.ifacol.2019.11.609
Oliveira J.F.C., Ferreira J.A.S.: Algorithms for nesting problems. In: Vidal R.V.V. (eds) Applied Simulated Annealing. Lecture Notes in Economics and Mathematical Systems, vol 396. Springer, Berlin, Heidelberg (1993). https://doi.org/https://doi.org/10.1007/978-3-642-46787-5_13
Chentsov, A.G., Khachai, M.Yu., Khachai, D.M.: An exact algorithm with linear complexity for a problem of visiting megalopolises. Proc. Steklov Inst. Math. 295(1), 38–46 (2016). https://doi.org/10.1134/S0081543816090054
Chentsov, A.G., Khachay, M.Yu., Khachay, D.M.: Linear time algorithm for precedence constrained asymmetric Generalized Traveling Salesman Problem. IFAC-PapersOnLine 49(12), 651–655 (2016). https://doi.org/https://doi.org/10.1016/j.ifacol.2016.07.767. 8th IFAC Conference on Manufacturing Modelling, Management and Control MIM 2016
Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds.): OPTA 2018. CCIS, vol. 871. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93800-4
Khachay, M., Neznakhina, K.: Complexity and approximability of the Euclidean generalized traveling salesman problem in grid clusters. Ann. Math. Artif. Intell. 88(1–3), 53–69 (2019). https://doi.org/10.1007/s10472-019-09626-w
Chentsov, A.G., Chentsov, P.A., Petunin, A.A., Sesekin, A.N.: Model of megalopolises in the tool path optimisation for CNC plate cutting machines. Int. J. Prod. Res. 56(14), 4819–4830 (2018)
TSPLIB Homepage. https://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsplib.html. Accessed 01 Nov 2020
GTSPLIB Homepage. https://www.cs.nott.ac.uk/~pszdk/gtsp.html. Accessed 01 Nov 2020
PCGTSPLIB Homepage. https://www.fcc.chalmers.se/external/PCGTSPLIB/. Accessed 01 Nov 2020
Petunin, A.A.: Modeling of tool path for the CNC sheet cutting machines. In: Pasheva, B., Popivanov, N., Venkov, G. (eds.) 41st International Conference "Applications of Mathematics in Engineering and Economics", AMEE 2015, 1690. [060002] (AIP Conference Proceedings; 1690. American Institute of Physics Publising LLC (2015). https://doi.org/10.1063/1.4936740
Tavaeva, A.F., Petunin, A.A., Polishchuk, E.G.: Methods of Cutting Cost Minimizing in Problem of Tool Route Optimization for CNC Laser Machines. In: Radionov, A.A., Kravchenko, O.A., Guzeev, V.I., Rozhdestvenskiy, Y.V. (eds.) ICIE 2019. LNME, pp. 447–455. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-22063-1_48
CCPLIB Homepage, https://drive.google.com/drive/folders/1e95DUVXq0XAX7UI15wUaNpAY0exbXc8T?usp=sharing. Accessed 01 Nov 2020
Petunin, A.A., Polishchuk, E.G., Ukolov, S.S.: On the new Algorithm for Solving Continuous Cutting Problem. IFAC-PapersOnLine 52(13), 2320–2325 (2019). https://doi.org/10.1016/j.ifacol.2019.11.552
Khachay, M., Kudriavtsev, A., Petunin, A.: PCGLNS: A Heuristic Solver for the Precedence Constrained Generalized Traveling Salesman Problem. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds.) OPTIMA 2020. LNCS, vol. 12422, pp. 196–208. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-62867-3_15
Acknowledgements
This research was performed as part of research conducted in the Ural Mathematical Center and funded by the Russian Foundation for Basic Research, grants no. 19-01-00573 and no. 20-08-00873.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Petunin, A. et al. (2021). Library of Sample Image Instances for the Cutting Path Problem. In: Del Bimbo, A., et al. Pattern Recognition. ICPR International Workshops and Challenges. ICPR 2021. Lecture Notes in Computer Science(), vol 12665. Springer, Cham. https://doi.org/10.1007/978-3-030-68821-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-68821-9_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-68820-2
Online ISBN: 978-3-030-68821-9
eBook Packages: Computer ScienceComputer Science (R0)
