Advertisement

Annals of Operations Research

, Volume 81, Issue 0, pp 421–433 | Cite as

Towards a closer integration of finite domainpropagation and simplex-based algorithms

  • Mozafar T. Hajian
  • Hani El-Sakkout
  • Mark Wallace
  • Jonathan M. Lever
  • Barry Richards
Article

Abstract

This paper describes our experience in implementing an industrial application using thefinite domain solver of the ECL i PS e constraint logic programming (CLP) system, inconjunction with the mathematical programming (MP) system, FortMP. In this technique,the ECL i PS e system generates a feasible solution that is adapted to construct a starting point(basic solution) for the MP solver. The basic solution is then used as an input to the FortMPsystem to warm-start the simplex (SX) algorithm, hastening the solution of the linearprogramming relaxation, (LPR). SX proceeds as normal to find the optimal integer solution.Preliminary results indicate that the integration of the two environments is suitable for thisapplication in particular, and may generally yield significant benefits. We describe adaptationsrequired in the hybrid method, and report encouraging experimental results for thisproblem.

Keywords

Feasible Solution Linear Programming Relaxation Close Integration Finite Domain Plane Type 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R.J. Dakin, A tree search algorithm for mixed integer programming problems, The Computer Journal 8((1965)250–255CrossRefGoogle Scholar
  2. [2]
    E. Davis, Constraint propagation with interval labels, Artificial Intelligence 32(1987) 281–331CrossRefGoogle Scholar
  3. [3]
    H. El-Sakkout, Modelling fleet assignment in a flexible environment, Proceedings of the 2nd International Conference on the Practical Application of Constraint Technology, The Practical Application Company Ltd, 1996, pp. 27–39.Google Scholar
  4. [4]
    E.F.D. Ellison et al., FortMP, User Guide and Reference Manual, Nag Ltd, Oxford, UK, 1995.Google Scholar
  5. [5]
    H. Gallaire, Logic programming: Further developments, in: IEEE Symposium on Logic Programming, Boston, MA, July 1985.Google Scholar
  6. [6]
    M.T. Hajian, Computational methods for discrete programming problems, Ph.D. Thesis, Mathematics and Statistics Department, Brunel, University of West London, 1992.Google Scholar
  7. [7]
    R.M. Haralick and G.L. Elliot, Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence 14(1980)263–314.CrossRefGoogle Scholar
  8. [8]
    J. Jaffar and J.-L. Lassez, Constraint Logic Programming, in: POPL-87, Munich, Germany, January 1987.Google Scholar
  9. [9]
    H.W. Kuhn and A.W. Tucker, Linear Inequalities and Related Systems, Princeton University Press, Princeton, NJ, 1956.Google Scholar
  10. [10]
    A. Land and A.W. Tucker, An automatic method for solving discrete programming problems, Econometrica 28(1960)497–520.CrossRefGoogle Scholar
  11. [11]
    A.K. Mackworth, Consistency in networks of relations, Artificial Intelligence 8(1977) 99–118.CrossRefGoogle Scholar
  12. [12]
    G. Mitra, Theory and Application of Mathematical Programming, Academic Press, London, 1976.Google Scholar
  13. [13]
    U. U. Montanari, Networks of constraints: Fundamental properties and applications to picture processing, Information Science 7(1974)95–132.CrossRefGoogle Scholar
  14. [14]
    G.L. Nemhauser and E.R. Wolsey, Integer and Combinatorial Optimisation, Wiley, New York, 1988.Google Scholar
  15. [15]
    G.J. Sussman and G.L. Steele, CONSTRAINTS: A language for expressing almost-hierarchical descriptions, Artificial Intelligence 14(1980)1–39.CrossRefGoogle Scholar
  16. [16]
    M. Tamiz, Design implementation and testing of a general linear programming system exploiting sparsity, Ph.D. Thesis, Mathematics and Statistics Department, Brunel, University of West London, 1986.Google Scholar
  17. [17]
    P. Van Hentenryck, Constraint Satisfaction in Logic Programming, Logic Programming Series, The MIT Press, 1989.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Mozafar T. Hajian
  • Hani El-Sakkout
  • Mark Wallace
  • Jonathan M. Lever
  • Barry Richards

There are no affiliations available

Personalised recommendations