Solutions to Real-World Instances of PSPACE-Complete Stacking

  • Felix G. König
  • Macro Lübbecke
  • Rolf Möhring
  • Guido Schäfer
  • Ines Spenke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4698)


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.


State Graph Valuation Function Permutation Graph Quantify Boolean Formula False Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Felix G. König
    • 1
  • Macro Lübbecke
    • 1
  • Rolf Möhring
    • 1
  • Guido Schäfer
    • 1
  • Ines Spenke
    • 1
  1. 1.Technische Universität Berlin, Institut für Mathematik, MA 6-1, Straße des 17. Juni 136, 10623 BerlinGermany

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