Solutions to real-world instances of PSPACE-complete stacking

Authors:
Felix G. König;Macro Lübbecke;Rolf Möhring;Guido Schäfer;Ines Spenke
Affiliations:
Technische Universität Berlin, Institut für Mathematik, Berlin, Germany;Technische Universität Berlin, Institut für Mathematik, Berlin, Germany;Technische Universität Berlin, Institut für Mathematik, Berlin, Germany;Technische Universität Berlin, Institut für Mathematik, Berlin, Germany;Technische Universität Berlin, Institut für Mathematik, Berlin, Germany
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

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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.