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A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes

In: Operations Research Proceedings 2018

Author

Listed:
  • Lovis Anderson

    (Zuse Institute)

  • Benjamin Hiller

    (Zuse Institute)

Abstract

Optimization models often feature disjunctions of polytopes as submodels. Such a disjunctive set is initially (at best) relaxed to its convex hull, which is then refined by branching. To measure the error of the convex relaxation, the (relative) difference between the volume of the convex hull and the volume of the disjunctive set may be used. This requires a method to compute the volume of the disjunctive set. We propose a revised variant of an old algorithm by Bieri and Nef (Linear Algebra Appl 52:69–97, 1983) for this purpose. The algorithm uses a sweep-plane to incrementally calculate the volume of the disjunctive set as a function of the offset parameter of the sweep-plane.

Suggested Citation

  • Lovis Anderson & Benjamin Hiller, 2019. "A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes," Operations Research Proceedings, in: Bernard Fortz & Martine Labbé (ed.), Operations Research Proceedings 2018, pages 87-93, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-18500-8_12
    DOI: 10.1007/978-3-030-18500-8_12
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