7814
eng
reportzib
0
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2020-04-03
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Estimating the Size of Branch-And-Bound Trees
This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the gap, and propose a new measure, which we call leaf frequency.
We study two simple ways to transform these progress measures into B&B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model.
In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP.
1438-0064
urn:nbn:de:0297-zib-78144
Gregor Hendel
Gregor Hendel
Daniel Anderson
Pierre Le Bodic
Marc Pfetsch
ZIB-Report
20-02
eng
uncontrolled
mixed integer programming
eng
uncontrolled
machine learning
eng
uncontrolled
branch and bound
eng
uncontrolled
forecasting
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Mathematical Optimization
Hendel, Gregor
ASTfSCM
MODAL-SynLab
Siemens
MODAL-Gesamt
https://opus4.kobv.de/opus4-zib/files/7814/zibreportestimatingSearchTreeSize.pdf