5750
2015
eng
141
156
9075
conferenceobject
0
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2015-04-16
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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.
Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2015
10.1007/978-3-319-18008-3_10
Lecture Notes in Computer Science
yes
urn:nbn:de:0297-zib-53829
Gerald Gamrath
Gerald Gamrath
Anna Melchiori
Timo Berthold
Ambros Gleixner
Domenico Salvagnin
Mathematical Optimization
Mathematical Optimization Methods
Berthold, Timo
Gamrath, Gerald
Gleixner, Ambros
ASTfSCM
MIP-ZIBOPT
MODAL-SynLab
Siemens
MODAL-Gesamt