Information-based branching schemes for binary linear mixed integer problems
Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by ex...
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| Veröffentlicht in: | Mathematical programming computation Jg. 1; H. 4; S. 249 - 293 |
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01.12.2009
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| ISSN: | 1867-2949, 1867-2957 |
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| Abstract | Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from an incomplete branch-and-bound tree. In particular, we use this information to define new branching rules that reduce the risk of incurring inappropriate branchings. We provide computational results that demonstrate the effectiveness of the new branching rules on various benchmark instances. |
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| AbstractList | Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from an incomplete branch-and-bound tree. In particular, we use this information to define new branching rules that reduce the risk of incurring inappropriate branchings. We provide computational results that demonstrate the effectiveness of the new branching rules on various benchmark instances. |
| Author | Savelsbergh, Martin W. P. Kılınç Karzan, Fatma Nemhauser, George L. |
| Author_xml | – sequence: 1 givenname: Fatma surname: Kılınç Karzan fullname: Kılınç Karzan, Fatma email: fkilinc@gatech.edu organization: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology – sequence: 2 givenname: George L. surname: Nemhauser fullname: Nemhauser, George L. organization: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology – sequence: 3 givenname: Martin W. P. surname: Savelsbergh fullname: Savelsbergh, Martin W. P. organization: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology |
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| Cites_doi | 10.1287/ijoc.14.4.373.2823 10.1109/12.769433 10.1016/j.disopt.2006.10.006 10.1017/S0269888900001041 10.1016/0004-3702(77)90029-7 10.1287/opre.1070.0397 10.1016/j.orl.2004.04.002 10.1287/ijoc.11.2.173 10.1007/s10107-002-0363-5 10.1007/s12532-008-0001-1 10.1007/s10107-006-0009-0 10.1016/S0166-218X(96)00003-0 10.1007/s101070100263 10.1023/A:1011207119557 10.1007/BF01584074 10.1016/j.orl.2005.07.009 10.1287/mnsc.20.5.736 10.4171/dms/1-3/62 10.1145/1160633.1160732 10.1145/378239.379017 10.1287/ijoc.2.1.61 10.1002/9781118033036 10.1016/S1574-6526(07)03002-7 |
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| Keywords | 90B40 Search theory Branch-and-bound 90C11 Mixed integer programming Computational algorithms 90-04 Explicit machine computation and programs (not the theory of computation or programming) 90-08 Computational methods Variable selection |
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| Title | Information-based branching schemes for binary linear mixed integer problems |
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