TY - GEN
A1 - Anderson, Lovis
A1 - Hiller, Benjamin
T1 - A Sweep-Plane Algorithm for the Computation of the Volume of a Union of Polytopes
N2 - 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. Naively, this can be done via
inclusion/exclusion and leveraging the existing code for the volume
of polytopes. However, this is often inefficient.
We propose a revised variant of an old algorithm by Bieri and Nef
(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.
T3 - ZIB-Report - 18-37
KW - Disjunctive Programming
KW - Volume Algorithm
KW - Union of Polytopes
Y1 - 2018
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6948
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-69489
SN - 1438-0064
ER -