NDLI: On the exact separation of mixed integer knapsack cuts

Content Provider	Springer Nature Link
Author	Fukasawa, Ricardo Goycoolea, Marcos
Copyright Year	2009
Abstract	During the last decades, much research has been conducted on deriving classes of valid inequalities for mixed integer knapsack sets, which we call knapsack cuts. Bixby et al. (The sharpest cut: the impact of Manfred Padberg and his work. MPS/SIAM Series on Optimization, pp. 309–326, 2004) empirically observe that, within the context of branch-and-cut algorithms to solve mixed integer programming problems, the most important inequalities are knapsack cuts derived by the mixed integer rounding (MIR) procedure. In this work we analyze this empirical observation by developing an algorithm to separate over the convex hull of a mixed integer knapsack set. The main feature of this algorithm is a specialized subroutine for optimizing over a mixed integer knapsack set which exploits dominance relationships. The exact separation of knapsack cuts allows us to establish natural benchmarks by which to evaluate specific classes of them. Using these benchmarks on MIPLIB 3.0 and MIPLIB 2003 instances we analyze the performance of MIR inequalities. Our computations, which are performed in exact arithmetic, are surprising: In the vast majority of the instances in which knapsack cuts yield bound improvements, MIR cuts alone achieve over 87% of the observed gain.
Ending Page	41
Page Count	23
Starting Page	19
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	128
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-06-06
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Integer programming Cutting plane algorithms Mathematical Methods in Physics Mixed integer knapsack problem Mathematics of Computing Calculus of Variations and Optimal Control; Optimization Numerical Analysis Theoretical, Mathematical and Computational Physics Mixed integer programming Combinatorics Polyhedral combinatorics, branch-and-bound, branch-and-cut
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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