5382
eng
reportzib
0
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2015-03-09
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Branching on multi-aggregated variables
In mixed-integer programming, the branching rule is a key component to a fast convergence of the branch-and-bound algorithm. The most common strategy is to branch on simple disjunctions that split the domain of a single integer variable into two disjoint intervals. Multi-aggregation is a presolving step that replaces variables by an affine linear sum of other variables, thereby reducing the problem size. While this simplification typically improves the performance of MIP solvers, it also restricts the degree of freedom in variable-based branching rules.
We present a novel branching scheme that tries to overcome the above drawback by considering general disjunctions defined by multi-aggregated variables in addition to the standard disjunctions based on single variables. This natural idea results in a hybrid between variable- and constraint-based branching rules. Our implementation within the constraint integer programming framework SCIP incorporates this into a full strong branching rule and reduces the number of branch-and-bound nodes on a general test set of publicly available benchmark instances. For a specific class of problems, we show that the solving time decreases significantly.
1438-0064
urn:nbn:de:0297-zib-53829
10.1007/978-3-319-18008-3_10
urn:nbn:de:0297-zib-53829
Integration of AI and OR Techniques in Constraint Programming
Gerald Gamrath
Gerald Gamrath
Anna Melchiori
Timo Berthold
Ambros Gleixner
Domenico Salvagnin
ZIB-Report
15-10
eng
uncontrolled
mixed-integer programming, branch-and-bound, branching rule, strong branching
Integer programming
Mixed integer programming
Polyhedral combinatorics, branch-and-bound, branch-and-cut
Mathematical Optimization
Mathematical Optimization Methods
Berthold, Timo
Gamrath, Gerald
Gleixner, Ambros
ASTfSCM
MIP-ZIBOPT
MODAL-SynLab
Siemens
MODAL-Gesamt
https://opus4.kobv.de/opus4-zib/files/5382/ZR-15-10.pdf