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A Hybrid Method for the Modelling and Optimisation of Constrained Search Problems

Author

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  • Sitek Pawel
  • Wikarek Jaroslaw

    (Faculty of Electrical Engineering, Automatics and Computer Science Kielce University of Technology, Kielce, Poland)

Abstract

The paper presents a concept and the outline of the implementation of a hybrid approach to modelling and solving constrained problems. Two environments of mathematical programming (in particular, integer programming) and declarative programming (in particular, constraint logic programming) were integrated. The strengths of integer programming and constraint logic programming, in which constraints are treated in a different way and different methods are implemented, were combined to use the strengths of both. The hybrid method is not worse than either of its components used independently. The proposed approach is particularly important for the decision models with an objective function and many discrete decision variables added up in multiple constraints. To validate the proposed approach, two illustrative examples are presented and solved. The first example is the authors’ original model of cost optimisation in the supply chain with multimodal transportation. The second one is the two-echelon variant of the well-known capacitated vehicle routing problem.

Suggested Citation

  • Sitek Pawel & Wikarek Jaroslaw, 2014. "A Hybrid Method for the Modelling and Optimisation of Constrained Search Problems," Foundations of Management, Sciendo, vol. 5(3), pages 1-16, August.
    • Handle: RePEc:vrs:founma:v:5:y:2014:i:3:p:16:n:1
    DOI: 10.2478/fman-2014-0016
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    References listed on IDEAS

    as
    1. Michela Milano & Mark Wallace, 2010. "Integrating Operations Research in Constraint Programming," Annals of Operations Research, Springer, vol. 175(1), pages 37-76, March.
    2. 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.
    3. Guido Perboli & Roberto Tadei & Daniele Vigo, 2011. "The Two-Echelon Capacitated Vehicle Routing Problem: Models and Math-Based Heuristics," Transportation Science, INFORMS, vol. 45(3), pages 364-380, August.
    4. J. Christian Lang, 2010. "Production and Operations Management: Models and Algorithms," Lecture Notes in Economics and Mathematical Systems, in: Production and Inventory Management with Substitutions, chapter 0, pages 9-79, Springer.
    5. Pawel Sitek, 2011. "The Declarative Framework Approach to Decision Support for Constrained Search Problems," Chapters, in: Chiang Jao (ed.), Efficient Decision Support Systems - Practice and Challenges From Current to Future, IntechOpen.
    6. J. Christian Lang, 2010. "Production and Inventory Management with Substitutions," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-04247-8, December.
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