Paper Info
Title
A survey of dual-feasible and superadditive functions
Abstract
Dual-feasible functions are valuable tools that can be used to compute both lower bounds for different combinatorial problems and valid inequalities for integer programs. Several families of functions have been used in the literature. Some of them were defined explicitly, and others not. One of the main objectives of this paper is to survey these functions, and to state results concerning their quality. We clearly identify dominant subsets of functions, i.e. those which may lead to better bounds or stronger cuts. We also describe different frameworks that can be used to create dual-feasible functions. With these frameworks, one can get a dominant function based on other ones. Two new families of dual-feasible functions obtained by applying these methods are proposed in this paper. We also performed a computational comparison on the relative strength of the functions presented in this paper for deriving lower bounds for the bin-packing problem and valid cutting planes for the pattern minimization problem. Extensive experiments on instances generated using methods described in the literature are reported. In many cases, the lower bounds are improved, and the linear relaxations are strengthened.
Year
DOI
Venue
2010
10.1007/s10479-008-0453-8
Annals OR
Keywords
Field
DocType
Maximal Function,Valid Inequality,Integer Hull,Superadditive Function,Strong Valid Inequality
Integer,Superadditivity,Discrete mathematics,Mathematical optimization,Maximal function,Mathematics
Journal
Volume
Issue
ISSN
179
1
0254-5330
Citations 
PageRank 
References 
29
1.01
18
Authors
3
Name
Order
Citations
PageRank
François Clautiaux124817.16
Cláudio Alves218416.29
José M. Valério De Carvalho316814.06