Abstract
The linear programming duality is well understood and the reduced cost of a column is frequently used in various algorithms. On the other hand, for integer programs it is not clear how to define a dual function even though the subadditive dual theory was developed a long time ago. In this work we propose a family of computationally tractable subadditive dual functions for integer programs. We develop a solution methodology that computes an optimal primal solution and an optimal subadditive dual function. We report computational results for set partitioning instances. To the best of our knowledge these are the first computational experiments on computing the optimal subadditive dual function.
Keywords
- Valid Inequality
- Dual Objective
- Complementary Slackness
- Greedy Estimate
- Complementary Slackness Condition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
Anbil, R., Johnson, E., and Tanga, R. (1992). A global approach to crew pairing optimization. IBM Systems Journal, 31, 71–78.
Balas, E. and Carrera, M. (1996). A dynamic subgradient-based branch-and-bound procedure for set covering. Operations Research, 44, 875–890.
Borndorfer, R. (1998). A spects of Set Packing, Partitioning, and Covering. Ph.D. thesis, Technical University of Berlin.
Burdet, C. and Johnson, E. (1977). A subadditive approach to solve integer programs. Annals of Discrete Mathematics, 1, 117–144.
CPLEX Optimization (1999). Using the CPLEX Callable Library. ILOG Inc., 6.5 edition.
Eso, M. (1999). Parallel Branch and Cut for Set Partitioning. Ph.D. thesis, Cornell University.
Hoffman, K. and Padberg, M. (1993). Solving airline crew scheduling problems by branch-and-cut. Management Science, 39, 657–682.
Johnson, E. (1973). Cyclic groups, cutting planes and shortest path. In T. Hu and S. Robinson, editors, Mathematical Programming, pages 185–211. Academic Press.
Klabjan, D. (2001a). A new subadditive approach to integer programming: Implementation and computational results. Technical report, University of Illinois at Urbana-Champaign. Available from http://www.staff.uiuc.edu/~klabjan/professional.html.
Klabjan, D. (2001b). A new subadditive approach to integer programming: Theory and algorithms. Technical report, University of Illinois at Urbana-Champaign. Available from http://www.staff.uiuc.edu/~klabjan/professional.html.
Llewellyn, D. and Ryan, J. (1993). A primal dual integer programming algorithm. Discrete Applied Mathematics, 45, 261–275.
Nemhauser, G. and Wolsey, L. (1988). Integer and combinatorial optimization. John Wiley & Sons.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Klabjan, D. (2002). A New Subadditive Approach to Integer Programming. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_27
Download citation
DOI: https://doi.org/10.1007/3-540-47867-1_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43676-8
Online ISBN: 978-3-540-47867-6
eBook Packages: Springer Book Archive