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A new approach to integrating mixed integer programming and constraint logicprogramming

Author

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  • R. Rodosek
  • M.G. Wallace
  • M.T. Hajian

Abstract

This paper represents an integration of Mixed Integer Programming (MIP) and ConstraintLogic Programming (CLP) which, like MIP, tightens bounds rather than adding constraintsduring search. The integrated system combines components of the CLP system ECLiPSe[7] and the MIP system CPLEX [5], in which constraints can be handled by either one orboth components. Our approach is introduced in three stages. Firstly, we present an automatictransformation which maps CLP programs onto such CLP programs that any disjunction iseliminated in favour of auxiliary binary variables. Secondly, we present improvements ofthis mapping by using a committed choice operator and translations of pre‐defined non‐linearconstraints. Thirdly, we introduce a new hybrid algorithm which reduces the solutionspace of the problem progressively by calling finite domain propagation of ECLiPSe aswell as dual simplex of CPLEX. The advantages of this integration are illustrated by efficientlysolving difficult optimisation problems like the Hoist Scheduling Problem [23]and the Progressive Party Problem [27]. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • R. Rodosek & M.G. Wallace & M.T. Hajian, 1999. "A new approach to integrating mixed integer programming and constraint logicprogramming," Annals of Operations Research, Springer, vol. 86(0), pages 63-87, January.
    • Handle: RePEc:spr:annopr:v:86:y:1999:i:0:p:63-87:10.1023/a:1018904229454
    DOI: 10.1023/A:1018904229454
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    Cited by:

    1. Michela Milano & Greger Ottosson & Philippe Refalo & Erlendur S. Thorsteinsson, 2002. "The Role of Integer Programming Techniques in Constraint Programming's Global Constraints," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 387-402, November.
    2. Russell, Robert A. & Urban, Timothy L., 2010. "Multicriteria models for planning power-networking events," European Journal of Operational Research, Elsevier, vol. 207(1), pages 83-91, November.
    3. Gedik, Ridvan & Rainwater, Chase & Nachtmann, Heather & Pohl, Ed A., 2016. "Analysis of a parallel machine scheduling problem with sequence dependent setup times and job availability intervals," European Journal of Operational Research, Elsevier, vol. 251(2), pages 640-650.
    4. Sourd, Francis & Rogerie, Jerome, 2005. "Continuous filling and emptying of storage systems in constraint-based scheduling," European Journal of Operational Research, Elsevier, vol. 165(2), pages 510-524, September.
    5. Feng, Jianguang & Che, Ada & Chu, Chengbin & Levner, Eugene & Kats, Vladimir, 2024. "Scheduling robotic cells with fixed processing times or time windows: Classification, solution approaches, polynomial algorithms and complexity," European Journal of Operational Research, Elsevier, vol. 319(2), pages 468-483.
    6. Tallys Yunes & Ionuţ D. Aron & J. N. Hooker, 2010. "An Integrated Solver for Optimization Problems," Operations Research, INFORMS, vol. 58(2), pages 342-356, April.
    7. Vipul Jain & Ignacio E. Grossmann, 2001. "Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 258-276, November.
    8. G Zhu & J F Bard & G Yu, 2005. "Disruption management for resource-constrained project scheduling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 365-381, April.
    9. Yannis Pavlis & Will Recker, 2009. "A Mathematical Logic Approach for the Transformation of the Linear Conditional Piecewise Functions of Dispersion-and-Store and Cell Transmission Traffic Flow Models into Linear Mixed-Integer Form," Transportation Science, INFORMS, vol. 43(1), pages 98-116, February.

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