Abstract
We investigate a complex stacking problem that stems from storage planning of steel slabs in integrated steel production. Besides the practical importance of such stacking tasks, they are appealing from a theoretical point of view. We show that already a simple version of our stacking problem is PSPACE-complete. Thus, fast algorithms for computing provably good solutions as they are required for practical purposes raise various algorithmic challenges. We describe an algorithm that computes solutions within 5/4 of optimality for all our real-world test instances. The basic idea is a search in an exponential state space that is guided by a state-valuation function. The algorithm is extremely fast and solves practical instances within a few seconds. We assess the quality of our solutions by computing instance-dependent lower bounds from a combinatorial relaxation formulated as mixed integer program. To the best of our knowledge, this is the first approach that provides quality guarantees for such problems.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-Dynamic Programming. Athena Scientific (1996)
Bertsekas, D.P., Tsitsiklis, J.N., Wu, C.: Rollout algorithms for combinatorial optimization. Journal of Heuristics 3(3), 245–262 (1997)
Bonet, B., Loerincs, G., Geffner, H.: A robust and fast action selection mechanism for planning. In: Proceedings of the 14th National Conference on AI, pp. 714–719 (1997)
Cull, P., Ecklund, E.F.: Towers of hanoi and analysis of algorithms. The American Mathematical Monthly 90, 407–420 (1985)
Dekker, R., Voogd, P., van Asperen, E.: Advanced methods for container stacking. OR Spectrum 28, 563–586 (2006)
Fox, M., Long, D.: Progress in AI planning research and application. CEPIS 3, 10–25 (2002)
Hansen, J., Clausen, J.: Crane scheduling for a plate storage. Technical Report 1, Informatics and Mathematical Modelling, Technical University of Denmark (2002)
Hearn, R.A., Demaine, E.D.: PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation. Theoretical Computer Science 343(1–2), 72–96 (2005)
Jansen, K.: The mutual exclusion scheduling problem for permutation and comparability graphs. Information and Computation 180, 71–81 (2003)
McDermott, D.: A heuristic estimator for means ends analysis in planning. In: Proceedings of the 3rd International Conference on Artificial Intelligence Planning Systems, pp. 142–149 (1996)
Savitch, W.J.: Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences 4(2), 177–192 (1970)
Steenken, D., Voß, S., Stahlbock, R.: Container terminal operation and operations research - a classification and literature review. OR Spectrum 26, 3–49 (2004)
Tang, L., Liu, J., Rong, A., Yang, Z.: Modelling and a genetic algorithm solution to the slab stack shuffling problem in implementing steel rolling schedulings. International Journal of Production Research 40(7), 1583–1595 (2002)
Walsh, T.: The towers of hanoi revisited, moving the rings by counting the moves. Information Processing Letters 15(2), 64–67 (1982)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
König, F.G., Lübbecke, M., Möhring, R., Schäfer, G., Spenke, I. (2007). Solutions to Real-World Instances of PSPACE-Complete Stacking . In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_64
Download citation
DOI: https://doi.org/10.1007/978-3-540-75520-3_64
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75519-7
Online ISBN: 978-3-540-75520-3
eBook Packages: Computer ScienceComputer Science (R0)