Abstract
Dual-feasible functions have been used to compute fast lower bounds and valid inequalities for integer linear optimization problems. However, almost all the functions proposed in the literature are defined only for positive arguments, which restricts considerably their applicability. The characteristics and properties of dual-feasible functions with general domains remain mostly unknown. In this paper, we show that extending these functions to negative arguments raises many issues. We explore these functions in depth with a focus on maximal functions, i.e. the family of non-dominated functions. The knowledge of these properties is fundamental to derive good families of general maximal dual-feasible functions that might lead to strong cuts for integer linear optimization problems and strong lower bounds for combinatorial optimization problems with knapsack constraints.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alves, C., de Carvalho, J., Clautiaux, F., Rietz, J.: Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem. Eur. J. Oper. Res. 233, 43–63 (2014)
Carlier, J., Néron, E.: Computing redundant resources for the resource constrained project scheduling problem. Eur. J. Oper. Res. 176, 1452–1463 (2007)
Clautiaux, F., Alves, C., de Carvalho, J.: A survey of dual-feasible and superadditive functions. An. Oper. Res. 179, 317–342 (2010)
Johnson, D.: Near optimal bin packing algorithms. Dissertation. Massachussetts Institute of Technology, Cambridge, Massachussetts (1973)
Nemhauser, G., Wolsey, L.: Integer and combinatorial optimization. Wiley-Interscience (1998)
Rietz, J., Alves, C., de Carvalho, J.: Theoretical investigations on maximal dual feasible functions. Oper. Res. Let. 38, 174–178 (2010)
Rietz, J., Alves, C., de Carvalho, J.: Worst-case analysis of maximal dual feasible functions. Opt. Let. 6, 1687–1705 (2012)
Rietz, J., Alves, C., de Carvalho, J.: On the extremality of maximal dual feasible functions. Oper. Res. Let. 40, 25–30 (2012)
Rietz, J., Alves, C., de Carvalho, J., Clautiaux, F.: Computing valid inequalities for general integer programs using an extension of maximal dual-feasible functions to negative arguments. In: 1st International Conference on Operations Research and Enterprise Systems, Vilamoura (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Rietz, J., Alves, C., de Carvalho, J.M.V., Clautiaux, F. (2014). On the Properties of General Dual-Feasible Functions. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8580. Springer, Cham. https://doi.org/10.1007/978-3-319-09129-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-09129-7_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09128-0
Online ISBN: 978-3-319-09129-7
eBook Packages: Computer ScienceComputer Science (R0)