NDLI: Optimizing over the first Chvátal closure

Content Provider	Springer Nature Link
Author	Fischetti, Matteo Lodi, Andrea
Copyright Year	2006
Abstract	How difficult is, in practice, to optimize exactly over the first Chvátal closure of a generic ILP? Which fraction of the integrality gap can be closed this way, e.g., for some hard problems in the MIPLIB library? Can the first-closure optimization be useful as a research (off-line) tool to guess the structure of some relevant classes of inequalities, when a specific combinatorial problem is addressed? In this paper we give answers to the above questions, based on an extensive computational analysis. Our approach is to model the rank-1 Chvátal-Gomory separation problem, which is known to be NP-hard, through a MIP model, which is then solved through a general-purpose MIP solver. As far as we know, this approach was never implemented and evaluated computationally by previous authors, though it gives a very useful separation tool for general ILP problems. We report the optimal value over the first Chvátal closure for a set of ILP problems from MIPLIB 3.0 and 2003. We also report, for the first time, the optimal solution of a very hard instance from MIPLIB 2003, namely nsrand-ipx, obtained by using our cut separation procedure to preprocess the original ILP model. Finally, we describe a new class of ATSP facets found with the help of our separation procedure.
Starting Page	3
Ending Page	20
Page Count	18
File Format	PDF
ISSN	00255610
Journal	Mathematical Programming
Volume Number	110
Issue Number	1
e-ISSN	14364646
Language	English
Publisher	Springer-Verlag
Publisher Date	2006-12-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Integer programs Separation problems Chvátal–Gomory cuts Computational analysis Mathematical Methods in Physics Mathematical and Computational Physics Combinatorics Numerical Analysis Mathematics of Computing Calculus of Variations and Optimal Control; Optimization
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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