Abstract
Sheet metal cutting using lasers is ubiquitous in the industry, and is used to produce everything from home decorations to excavator scoops. Metal waste is costly for the industry, both in terms of money, but also in terms of an increased environmental footprint. Tomologic develops a unique optimisation system that can reduce this waste drastically. This paper presents a CP approach to the Laser Cutting Path Planning Problem (LCPPP), a very hard important sub problem within the Tomologic optimisation system. A solution to the LCPPP is, given a packing of some details on a metal sheet, an ordering of the cuts necessary to separate the details from the sheet. The problem is complicated by physical factors such as heat from the laser beam, or details moving or flexing. In the paper, we explain the problem in detail and present our CP approach that we developed for solving the problem. The possibility (in CP) of custom search heuristics turned out to be crucial to be able to solve the problem efficiently, as these could be made to guide the search to good first solutions.
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References
Tomologic AB. Market Survey (2010)
Bennell, J.A., Oliveira, J.F.: A tutorial in irregular shape packing problems. Journal of the Operational Research Society 60(S1), S93–S105 (2009)
Beldiceanu, N., Carlsson, M., Rampon, J.X.: Global constraint catalog, working version as of April 24 (2013), http://www.emn.fr/z-info/sdemasse/gccat/
Stuckey, P.J., Tack, G.: Minizinc with functions. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 268–283. Springer, Heidelberg (2013)
Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M.J., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998)
Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: de Mántaras, R.L., Saitta, L. (eds.) ECAI, pp. 146–150. IOS Press (2004)
Michel, L., Van Hentenryck, P.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 228–243. Springer, Heidelberg (2012)
Baatar, D., Boland, N., Brand, S., Stuckey, P.J.: CP and IP approaches to cancer radiotherapy delivery optimization. Constraints 16(2), 173–194 (2011)
Schrijvers, T., Tack, G., Wuille, P., Samulowitz, H., Stuckey, P.J.: Search combinators. Constraints 18(2), 269–305 (2013)
Gecode team: Gecode, the generic constraint development environment (2012), http://www.gecode.org/
Schulte, C., Tack, G., Lagerkvist, M.Z.: Modeling and Programming with Gecode (2012), Corresponds to Gecode 3.7.3
López-Ortiz, A., Quimper, C.G., Tromp, J., van Beek, P.: A fast and simple algorithm for bounds consistency of the alldifferent constraint. In: Gottlob, G., Walsh, T. (eds.) IJCAI, pp. 245–250. Morgan Kaufmann (2003)
Schulte, C.: Programming branchers. In: Schulte, C., Tack, G., Lagerkvist, M.Z. (eds.) Modeling and Programming with Gecode (2012), Corresponds to Gecode 3.7.3
Schulte, C.: Oz explorer: A visual constraint programming tool. In: Kuchen, H., Swierstra, S.D. (eds.) PLILP 1996. LNCS, vol. 1140, pp. 477–478. Springer, Heidelberg (1996)
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Lagerkvist, M.Z., Nordkvist, M., Rattfeldt, M. (2013). Laser Cutting Path Planning Using CP. In: Schulte, C. (eds) Principles and Practice of Constraint Programming. CP 2013. Lecture Notes in Computer Science, vol 8124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40627-0_58
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DOI: https://doi.org/10.1007/978-3-642-40627-0_58
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