Annals of Operations Research

, Volume 81, Issue 0, pp 467–496 | Cite as

Modelling discrete optimisation problems inconstraint logic programming

  • Peter Barth
  • Alexander Bockmayr
Article

Abstract

Constraint logic programming has become a promising new technology for solving complexcombinatorial problems. In this paper, we investigate how (constraint) logic programmingcan support the modelling part when solving discrete optimisation problems. First, we showthat the basic functionality of algebraic modelling languages can be realised very easily ina pure logic programming system like PROLOG and that, even without using constraints,various additional features are available. Then we focus on the constraint-solving facilitiesoffered by constraint logic programming systems. In particular, we explain how the constraintsolver of the constraint logic programming language CLP(PB) can be used in modelling0 - 1 problems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Aggoun and N. Beldiceanu, Extending CHIP in order to solve complex scheduling and placement problems, Math. Comput. Modelling 17(7)(1993)57–73.CrossRefGoogle Scholar
  2. [2]
    A. Aggoun, D. Chan, P. Dufresne, E. Falvey, H. Grant, A. Herold, G. Macartney, M. Meier, D. Miller, B. Perez, E. van Rossum, J. Schimpf, P.A. Tsahageas and D.H. de Villeneuve, ECLIPSE 3.4, ECRC Common Logic Programming System, Technical report, ECRC, Munich, July 1994.Google Scholar
  3. [3]
    E. Balas and J.B. Mazzola, Nonlinear 0–1 programming: II. Dominance relations and algorithms, Mathematical Programming 30(1984)22–45.Google Scholar
  4. [4]
    P. Barth, Short Guide to CLP(PB), Max-Planck-Institut für Informatik, 1994. System available: ftp:yyftp.mpi-sb.mpg.deypubytoolsyCLPPByclppb.html.Google Scholar
  5. [5]
    P. Barth, A Davis–Putnam based enumeration algorithm for linear pseudo-Boolean optimization, Technical Report MPI-I-95-2-003, Max-Planck-Institut für Informatik, Saarbrücken, January 1995. System available: http:yywww.mpi-sb.mpg.dey~barthyopbdpyopbdp.html.Google Scholar
  6. [6]
    P. Barth, Logic-Based 0 –1 Constraint Programming, Operations Research/Computer Science Interfaces Series, Kluwer, 1996.Google Scholar
  7. [7]
    P. Barth and A. Bockmayr, Modelling 0 –1 problems in CLP(PB), in: Practical Application of Constraint Technology, PACT '96, Conference and Exhibition, London, 1996.Google Scholar
  8. [8]
    P. Barth and A. Bockmayr, PLAM: ProLog and Algebraic Modelling, in: Practical Application of Prolog, PAP '97, Conference and Exhibition, London, April 1997.Google Scholar
  9. [9]
    G. Baues, P. Kay and P. Charlier, Constraint based resource allocation for airline crew scheduling, ATTIS '94, Paris, 1994.Google Scholar
  10. [10]
    N. Beldiceanu and E. Contejean, Introducing global constraints in CHIP, Math. Comput. Modelling 20(12)(1994)97–123.CrossRefGoogle Scholar
  11. [11]
    F. Benhamou, D. McAllester and P. van Hentenryck, CLP(Intervals) revisited, in: Logic Programming, Proceedings of the 1994 International Symposium, ILPS '94, 1994.Google Scholar
  12. [12]
    A. Bockmayr, Logic programming with pseudo-Boolean constraints, in: Constraint Logic Programming. Selected Research, eds. F. Benhamou and A. Colmerauer, MIT Press, 1993, chapter 18, pp. 327–350.Google Scholar
  13. [13]
    W.F. Clocksin and C.S. Mellish, Programming in Prolog, Springer, 1981.Google Scholar
  14. [14]
    P. Codognet and D. Diaz, Compiling constraints in CLP(FD), Journal of Logic Programming 27(1996)185–226.CrossRefGoogle Scholar
  15. [15]
    A. Colmerauer, Introduction to PROLOG III, in: 4th Annual ESPRIT Conference, Bruxelles, North-Holland, 1987.Google Scholar
  16. [16]
    M. Dincbas, P. van Hentenryck, H. Simonis, A. Aggoun and T. Graf, The constraint logic programming language CHIP, in: Fifth Generation Computer Systems, Tokyo, 1988, Springer, 1988.Google Scholar
  17. [17]
    R. Fourer, Modeling languages versus matrix generators for linear programming, ACM Trans. Math. Software 9(1983)143–183.CrossRefGoogle Scholar
  18. [18]
    R. Fourer, D. Gay and B.W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, The Scientific Press, San Francisco, 1993. http://www.ampl.com/cm/cs/what/ampl/.Google Scholar
  19. [19]
    M. Grötschel, Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme, volume 36 of Mathematical Systems in Economics, Verlag Anton Hain, Meisenheim am Glan, 1977.Google Scholar
  20. [20]
    J. Jaffar and J.-L. Lassez, Constraint logic programming, in: Proc. 14th ACM Symp. on Principles of Programming Languages, Munich, 1987.Google Scholar
  21. [21]
    J. Jaffar and M.J. Maher, Constraint logic programming: A survey, Journal of Logic Programming 19/20(1994)503–581.CrossRefGoogle Scholar
  22. [22]
    J. Jaffar, S. Michaylov, P.J. Stuckey and R.H.C. Yap, The CLP(R) language and system, ACM Transactions on Programming Languages and Systems 14(1992)339–395.CrossRefGoogle Scholar
  23. [23]
    LINDO Systems, Inc., Chicago, LINGO Optimization Modeling Language, 1994. http://www.lindo.com/.Google Scholar
  24. [24]
    K.I.M. McKinnon and H.P. Williams, Constructing integer programming models by the predicate calculus, Annals of Operations Research 21(1989)227–246.CrossRefGoogle Scholar
  25. [25]
    A. Meeraus and A. Brooke, GAMS: A User's Guide, Boyd and Fraser, 1993. http://www.gams.com/.Google Scholar
  26. [26]
    G. Mitra, C. Lucas, S. Moody and E. Hadjiconstantinou, Tools for reformulating logical forms into zero–one mixed integer programs, Eur. J. Oper. Res. 72(1994)262–276.CrossRefGoogle Scholar
  27. [27]
    J.J. Moré and S.J. Wright, Optimization Software Guide, SIAM, 1993.Google Scholar
  28. [28]
    W. Older and F. Benhamou, Programming in CLP(BNR), in: Principles and Practice of Constraint Programming PPCP '93, Newport, RI, 1993.Google Scholar
  29. [29]
    F. Puget, A C++ implementation of CLP, Technical Report, ILOG S.A., 1994. http://www.ilog.com.Google Scholar
  30. [30]
    R. Sharda, Linear and Discrete Optimization and Modeling Software, UNICOM, 1993.Google Scholar
  31. [31]
    G. Smolka, The OZ programming model, in: Computer Science Today: Recent Trends and Developments, ed. J. van Leeuwen, Springer, LNCS 1000, 1995.Google Scholar
  32. [32]
    L. Sterling and E. Shapiro, The Art of Prolog, MIT Press, 1986.Google Scholar
  33. [33]
    P. van Hentenryck, Constraint Satisfaction in Logic Programming, MIT Press, 1989.Google Scholar
  34. [34]
    P. van Hentenryck and Y. Deville, The cardinality operator: A new logical connective for constraint logic programming, in: Constraint Logic Programming. Selected Research, eds. F. Benhamou and A. Colmerauer, MIT Press, 1993, chapter 20, pp. 383–403.Google Scholar
  35. [35]
    M. Wallace, Practical applications of constraint programming, Constraints 1(1996) 139–168.CrossRefGoogle Scholar
  36. [36]
    H.P. Williams, Model Building in Mathematical Programming, Wiley, 3rd revised edition, 1993.Google Scholar
  37. [37]
    H.P. Williams, Model Solving in Mathematical Programming, Wiley, 1993.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Peter Barth
  • Alexander Bockmayr

There are no affiliations available

Personalised recommendations