Abstract
Dynamic Programming (DP) can solve many complex problems in polynomial or pseudo-polynomial time, and it is widely used in Constraint Programming (CP) to implement powerful global constraints. Implementing such constraints is a nontrivial task beyond the capability of most CP users, who must rely on their CP solver to provide an appropriate global constraint library. This also limits the usefulness of generic CP languages, some or all of whose solvers might not provide the required constraints. A technique was recently introduced for directly modelling DP in CP, which provides a way around this problem. However, no comparison of the technique with other approaches was made, and it was missing a clear formalisation. In this paper we formalise the approach and compare it with existing techniques on MiniZinc benchmark problems, including the flow formulation of DP in Integer Programming. We further show how it can be improved by state reduction methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beldiceanu, N., Carlsson, M., Rampon, J.X.: Global constraint catalog, (revision a) (2012)
Bellman, R.: The theory of dynamic programming. Technical report, RAND Corp Santa Monica CA (1954)
Bergman, D., Cire, A.A., van Hoeve, W.J., Hooker, J.N.: Discrete optimization with decision diagrams. INFORMS J. Comput. 28(1), 47–66 (2016)
Bradley, S.P., Hax, A.C., Magnanti, T.L.: Applied Mathematical Programming. Addison Wesley (1977)
Chu, G., Stuckey, P.J.: Minimizing the maximum number of open stacks by customer search. In: International Conference on Principles and Practice of Constraint Programming, pp. 242–257. Springer (2009)
Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)
Eppen, G.D., Martin, R.K.: Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35(6), 832–848 (1987)
Focacci, F., Milano, M.: Connections and integrations of dynamic programming and constraint programming. In: CPAIOR 2001 (2001)
Freuder, E.C.: Progress towards the holy grail. Constraints 23(2), 158–171 (2018)
Malitsky, Y., Sellmann, M., van Hoeve, W.J.: Length-lex bounds consistency for knapsack constraints. In: International Conference on Principles and Practice of Constraint Programming, pp. 266–281. Springer (2008)
Martello, S.: Knapsack Problems: Algorithms and Computer Implementations. Wiley-Interscience Series in Discrete Mathematics and Optimization (1990)
Martello, S., Pisinger, D., Toth, P.: New trends in exact algorithms for the 0–1 knapsack problem. Eur. J. Oper. Res. 123(2), 325–332 (2000)
Martin, R.K.: Generating alternative mixed-integer programming models using variable redefinition. Oper. Res. 35(6), 820–831 (1987)
Pisinger, D.: A minimal algorithm for the 0–1 knapsack problem. Oper. Res. 45(5), 758–767 (1997)
Plateau, G., Nagih, A.: 0–1 knapsack problems. In: Paradigms of Combinatorial Optimization: Problems and New Approaches, vol. 2, pp. 215–242 (2013)
Prestwich, S.D., Rossi, R., Tarim, S.A., Visentin, A.: Towards a closer integration of dynamic programming and constraint programming. In: 4th Global Conference on Artificial Intelligence (2018)
Quimper, C.G., Walsh, T.: Global grammar constraints. In: International Conference on Principles and Practice of Constraint Programming, pp. 751–755. Springer (2006)
Stuckey, P.J., Feydy, T., Schutt, A., Tack, G., Fischer, J.: The minizinc challenge 2008–2013. AI Mag. 35(2), 55–60 (2014)
Zhou, N.F., Kjellerstrand, H., Fruhman, J.: Constraint Solving and Planning with Picat. Springer (2015)
Acknowledgments
This publication has emanated from research supported in part by a research grant from Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289 which is co-funded under the European Regional Development Fund.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Visentin, A., Prestwich, S.D., Rossi, R., Tarim, A. (2020). Modelling Dynamic Programming-Based Global Constraints in Constraint Programming. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_42
Download citation
DOI: https://doi.org/10.1007/978-3-030-21803-4_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21802-7
Online ISBN: 978-3-030-21803-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)