Abstract
Benders Decomposition is a form of hybridisation that allows linear programming to be combined with other kinds of algorithms. It extracts new constraints for one subproblem from the dual values of the other subproblem. This paper describes an implementation of Benders Decomposition, in the ECLiPSe language, that enables it to be used within a constraint programming framework. The programmer is spared from having to write down the dual form of any subproblem, because it is derived by the system. Examples are used to show how problem constraints can be modelled in an undecomposed form. The programmer need only specify which variables belong to which subproblems, and the Benders Decomposition is extracted automatically. A class of minimal perturbation problems is used to illustrate how different kinds of algorithms can be used for the different subproblems. The implementation is tested on a set of minimal perturbation benchmarks, and the results are analysed.
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References
H. H. El Sakkout. Improving Backtrack Search: Three Case Studies of Localized Dynamic Hybridization. PhD thesis, Imperial College, London University, 1999.
N. Beldiceanu and E. Contjean. Introducing global constraints in CHIP. Mathematical and Computer Modelling, 12:97–123, 1994.
R. E. Gomory. An algorithm for integer solutions to linear programs. In R. L. Graves and P. Wolfe, editors, Recent Advances in Mathematical Programming, pages 269–302. McGraw-Hill, 1963.
H. H. El Sakkout and M. G. Wallace. Probe backtrack search for minimal perturbation in dynamic scheduling. Constraints, 5(4):359–388, 2000.
L. H. Appelgren. A column generation algorithm for a ship scheduling problem. Transportation Science, 3:53–68, 1969.
U. Junker, S. E. Karisch, N. Kohl, B. Vaaben, T. Fahle, and M. Sellmann. A framework for constraint programming based column generation. In Proceedings ofthe 5th International Conference on Principles and Practice ofConstr aint Programming-LNCS 1713, pages 261–274. Springer-Verlag, 1999.
T. H. Yunes, A. V. Moura, and C. C. de Souza. A hybrid approach for solving large scale crew scheduling problems. In Proceedings ofthe Second International Workshop on Practical Aspects of De clarative Languages (PADL’00), pages 293–307, Boston, MA, USA, 2000.
M. Sellmann and T. Fahle. Cp-based lagrangian relaxation for a multimedia application. In [17], 2001.
T. Benoist, F. Laburthe, and B. Rottembourg. Lagrange relaxation and constraint programming collaborative schemes for travelling tournament problems. In [17], 2001.
F. Focacci, A. Lodi, and M. Milano. Embedding relaxations in global constraints for solving TSP and its time constrained variant. Annals of Mathematics and Artificial Intelligence, Special issue on Large Scale Combinatorial Optimization, 2001.
G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, 1963.
J. F. Benders. Partitioning procedures for solving mixed variables programming problems. Numerische Mathematik, 4:238–252, 1962.
J. N. Hooker and G. Ottosson. Logic-based benders decomposition. http://ba.gsia.cmu.edu/jnh/papers.html, 1999.
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Eremin, A., Wallace, M. (2001). Hybrid Benders Decomposition Algorithms in Constraint Logic Programming. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_1
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DOI: https://doi.org/10.1007/3-540-45578-7_1
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