NDLI: Coordinated cutting plane generation via multi-objective separation

Content Provider	Springer Nature Link
Author	Coniglio, Stefa Gualandi, Stefa Amaldi, Edoardo
Copyright Year	2012
Abstract	In cutting plane methods, the question of how to generate the “best possible” set of cuts is both central and crucial. We propose a lexicographic multi-objective cutting plane generation scheme that generates, among all the maximally violated valid inequalities of a given family, an inequality that is undominated and maximally diverse w.r.t. the cuts that were previously found. By optimizing a diversity measure, we introduce a form of coordination between successive cuts. Our focus is on valid inequalities with 0–1 coefficients in the left-hand side and a constant right-hand side, which encompasses several families of valid inequalities. As cut diversity measure, we consider an aggregate of the 1-norm distances w.r.t. the normal vectors of the previous cuts. In this case, our lexicographic multi-objective separation problem reduces to the standard separation problem with different values for the objective function coefficients. The impact of our coordinated cutting plane generation scheme is assessed in a pure cutting plane setting when separating stable set and cut set inequalities for, respectively, the max clique and min Steiner tree problems. Compared to the standard separation of undominated maximally violated cuts, we close the same fraction of the duality gap in a considerably smaller number of rounds and cuts. The potential of our scheme is also indicated by the results obtained in a cut-and-branch setting for max clique, where cut coordination allows for a substantial reduction, on average, of the number of branch-and-bound nodes.
Ending Page	110
Page Count	24
Starting Page	87
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	143
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2012-10-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Integer programming Cutting plane methods Mathematical Methods in Physics Multi-objective separation Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Theoretical, Mathematical and Computational Physics Coordinated cutting plane generation Multi-objective and goal programming Combinatorics Polyhedral combinatorics, branch-and-bound, branch-and-cut
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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