1,694 research outputs found
Branching Bisimilarity with Explicit Divergence
We consider the relational characterisation of branching bisimilarity with
explicit divergence. We prove that it is an equivalence and that it coincides
with the original definition of branching bisimilarity with explicit divergence
in terms of coloured traces. We also establish a correspondence with several
variants of an action-based modal logic with until- and divergence modalities
Branching via Cutting Plane Selection: Improving Hybrid Branching
Cutting planes and branching are two of the most important algorithms for
solving mixed-integer linear programs. For both algorithms, disjunctions play
an important role, being used both as branching candidates and as the
foundation for some cutting planes. We relate branching decisions and cutting
planes to each other through the underlying disjunctions that they are based
on, with a focus on Gomory mixed-integer cuts and their corresponding split
disjunctions. We show that selecting branching decisions based on quality
measures of Gomory mixed-integer cuts leads to relatively small
branch-and-bound trees, and that the result improves when using cuts that more
accurately represent the branching decisions. Finally, we show how the history
of previously computed Gomory mixed-integer cuts can be used to improve the
performance of the state-of-the-art hybrid branching rule of SCIP. Our results
show a 4\% decrease in solve time, and an 8\% decrease in number of nodes over
affected instances of MIPLIB 2017
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