TY - GEN
T1 - Sequential-merge facets for two-dimensional group problems
AU - Dey, Santanu S.
AU - Richard, Jean Philippe P.
PY - 2007
Y1 - 2007
N2 - In this paper, we show how to generate strong cuts for unstructured mixed integer programs through the study of high-dimensional group problems. We present a new operation that generates facet-defining inequalities for two-dimensional group problems by combining two facet-defining inequalities of one-dimensional group problems. Because the procedure allows the use of a large variety of one-dimensional constituent inequalities, it yields large families of new cutting planes for MIPs that we call sequentialmerge inequalities. We show that sequential-merge inequalities can be used to generate inequalities whose continuous variable coefficients are stronger than those of one-dimensional cuts and can be used to derive the three-gradient facet-defining inequality introduced by Dey and Richard [4].
AB - In this paper, we show how to generate strong cuts for unstructured mixed integer programs through the study of high-dimensional group problems. We present a new operation that generates facet-defining inequalities for two-dimensional group problems by combining two facet-defining inequalities of one-dimensional group problems. Because the procedure allows the use of a large variety of one-dimensional constituent inequalities, it yields large families of new cutting planes for MIPs that we call sequentialmerge inequalities. We show that sequential-merge inequalities can be used to generate inequalities whose continuous variable coefficients are stronger than those of one-dimensional cuts and can be used to derive the three-gradient facet-defining inequality introduced by Dey and Richard [4].
UR - http://www.scopus.com/inward/record.url?scp=38049042276&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38049042276&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-72792-7_3
DO - 10.1007/978-3-540-72792-7_3
M3 - Conference contribution
AN - SCOPUS:38049042276
SN - 9783540727910
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 30
EP - 42
BT - Integer Programming and Combinatorial Optimization - 12th International IPCO Conference, Proceedings
PB - Springer Verlag
T2 - 12th International Conference on Integer Programming and Combinatorial Optimization, IPCO XII
Y2 - 25 June 2007 through 27 June 2007
ER -