Advertisement

Operations-Research-Spektrum

, Volume 16, Issue 3, pp 193–202 | Cite as

Modellbasierte Inferenz in CHARME

  • Erwin Pesch
  • Andreas Drexl
  • Antoon Kolen
Article
  • 39 Downloads

Zusammenfassung

Constraint-basierte Logikprogrammierung ist ein neues und auch für das Operations Research vielversprechendes Gebiet der Künstlichen Intelligenz. Eine logikorientierte Programmiersprache generiert zulässige Lösungen eines Constraint-Satisfaction-Problems, dessen Beschreibung auf einer Menge logischer Aussagen und einer Anzahl von Nebenbedingungen basiert. Ein Constraint-Satisfaction-Problem besteht aus einer Menge von Variablen sowie einer Menge von Nebenbedingungen über diesen Variablen. Gesucht ist eine zulässige Wertezuweisung der Variablen, als Teilmenge des cartesischen Produkts der Variablenwertebereiche, die allen Nebenbedingungen genügt. Traditionelle Lösungsverfahren basieren auf einer Suche mittels Backtracking. Konsistenzprüfungen von Variablenwertzuweisungen können dabei die Effizienz des Suchverfahrens wesentlich erhöhen, da neues, implizit vorhandenes Wissen über den Suchraum aus der Menge der Nebenbedingungen erschlossen und genutzt wird. Constraint-basierte Logiksprachen reduzieren während der Lösungssuche die Variablenwertebereiche automatisch, so daß nur noch node- und arc-konsistente Relationen betrachtet werden. CHARME [7, 8] ist eine derartige Programmiersprache, in der modellnahe Implementierungen parametergesteuerte Suchstrategien zulassen, die u. U. Probleme der Kombinatorischen Optimierung effizient lösbar machen.

Schlüsselwörter

CSP Logik-orientierte Programmiersprachen Constraint Propagation Backtracking Arc-Konsistenz Path-Konsistenz 

Abstract

Constraint logic programming is a relatively new area of research in Artficial Intelligence that holds an immense promise for Operations Researchers. The idea is to provide a logic programming language that accepts a series of logic statements and (arithmetic) constraints and then is capable to generate a feasible solution to the underlying constraint satisfaction problem. Informally, a constraint satisfaction problem is posed as follows. Given a set of variables and a set of constraints, each specifying a relation on a particular subset of the variables, find the relation on the set of all variables which satisfies all the given constraints. The required solution relation is a subset of the cartesian product of the variable domains. Traditionally, backtrack search is used to solve constraint satisfaction problems. In order to overcome the inefficiency of a simple backtrack search consistency checks among variable value assignments were incorporated introducing new knowledge by constraint based reasoning to reduce the search space and discover failures earlier. Most common are node- and arc-consistency checks the only ones which are also implicity introduced in recent constraint based logic programming languages. CHARME [7, 8] is such a programming language, a general modeling language and problem solver that allows to find model-based implementations and provides guided backtrack search which can lead to efficient and competitive search strategies for certain problems in combinatorial optimization.

Key words

CSP logic programming constraint propagation Backtracking Arc-Consistency Path-Consistency 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. 1.
    Van Beek P (1992) Reasoning about qualitative information. Artif Intell 58:297–326CrossRefGoogle Scholar
  2. 2.
    Berge C (1973) Graphs and Hypergraphs. North Holland, AmsterdamGoogle Scholar
  3. 3.
    Bibel W (1987) Automated Theorem Proving. 2. Auflage. Vieweg, BraunschweigCrossRefGoogle Scholar
  4. 4.
    Bitner JR, Reingold EM (1975) Backtrack programming techniques. Communications ACM 18:651–656CrossRefGoogle Scholar
  5. 5.
    Borning AH (1981) The propramming language aspects of ThingLab. A constraint-oriented simulation laboratory. ACM TOPLAS 3:353–397CrossRefGoogle Scholar
  6. 6.
    Bruynooghe M (1981) Solving combinatorial search problems by intelligent backtracking. Inf Proc Lett 12:36–39CrossRefGoogle Scholar
  7. 7.
    Bull (1990a) Artificial Intelligence, Charme V1, Users Guide. Bull S. A., Cedoc-DilogGoogle Scholar
  8. 8.
    Bull (1990b) Artificial Intelligence, Charme V1, Reference Manual. Bull S. A., Cedoc-DilogGoogle Scholar
  9. 9.
    Clocksin WF, Mellish CS (1984) Programming in Prolog. Springer, Berlin Heidelberg New YorkCrossRefGoogle Scholar
  10. 10.
    Cohen J (1990) Constraint logic programming languages. Communications ACM 33:52–68CrossRefGoogle Scholar
  11. 11.
    Colmerauer A (1987) Opening the PROLOG III universe. Byte 12:177–182Google Scholar
  12. 12.
    Colmerauer A (1990) An introduction to PROLOG III. Communications ACM: 69–90Google Scholar
  13. 13.
    Cooper MC (1989/90) An optimalk-consistency algorithm. Artif Intell 41:89–95CrossRefGoogle Scholar
  14. 14.
    Cooper PR, Swain MJ (1992) Arc consistency: parallelism and domain dependence. Artif Intell 58:207–235CrossRefGoogle Scholar
  15. 15.
    Davis E (1987) Constraint propagation with interval labels. Artif Intell 32:281–331CrossRefGoogle Scholar
  16. 16.
    Dechter R (1986) Learning while searching in constraint-satisfaction problems. Proc. AAAI-86:178–183Google Scholar
  17. 17.
    Dechter R (1989/90) Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition. Artif Intell 41:273–312CrossRefGoogle Scholar
  18. 18.
    Dechter R (1992) From local to global consistency. Artif Intell 55:87–107CrossRefGoogle Scholar
  19. 19.
    Dechter R, Pearl J (1988) Network-based heuristics for constraint satisfaction problems. Artif Intell 34:1–38CrossRefGoogle Scholar
  20. 20.
    Dincbas M, van Hentenryck P, Simonis H, Aggoun A, Graf T, Berthier F (1988) The constraint logic programming language CHIP. In: Proc Int Conf on Fifth Generation Computer Systems, Tokyo, JapanGoogle Scholar
  21. 21.
    Dincbas M, Simonis H, van Hentenryck P (1990) Solving large combinatorial problems in logic programming. J Logic Program 8:75–93CrossRefGoogle Scholar
  22. 22.
    Domschke W, Drexl A (1990) Logistik: Standorte. 3. Aufl. Oldenbourg München WienGoogle Scholar
  23. 23.
    Domschke W, Drexl A (1991) Einführung in Operations Research. 2. Aufl. Springer, Berlin Heidelberg New YorkCrossRefGoogle Scholar
  24. 24.
    Doyle J (1979) A truth maintenance system. Artif Intell 12:231–272CrossRefGoogle Scholar
  25. 25.
    Drexl A, Pesch E, Salewski F (1993) Zur Bedeutung der Modellbildung für die Entwicklung wissensbasierter Systeme. Z Betriebswirtschaft (in press)Google Scholar
  26. 26.
    Drexl A, Sprecher A (1993) Resource- and time window-constraint production scheduling with alternative process plans: An artificial intelligence approach. In: Fandel G et al (eds) Operations Research in Production Planning and Control. Springer, Berlin Heidelberg New York, pp 307–320CrossRefGoogle Scholar
  27. 27.
    Freuder EC (1982) A sufficient condition of backtrack-free search. J ACM 29:24–32CrossRefGoogle Scholar
  28. 28.
    Freuder EC (1985) A sufficient condition for backtrack-bounded search. J ACM 32:755–761CrossRefGoogle Scholar
  29. 29.
    Freuder EC, Wallace RJ (1992) Partial constraint satisfaction. Artif Intell 58:21–70CrossRefGoogle Scholar
  30. 30.
    Gaschnig J (1974) A constraint satisfaction method for inference making. Proc 12th Annual Allerton Conf Circuit System Theory, Urbana-Champaign, pp 866–874Google Scholar
  31. 31.
    Gaschnig J (1979) Performance Measurement and Analysis of Certain Search Algorithms. PhD thesis, Carnegie-Mellon University, PittsburghGoogle Scholar
  32. 32.
    Günther S (1874) Zur mathematischen Theorie des Schachbretts. Arch Math Phys 56:281–292Google Scholar
  33. 33.
    Güsgen H-W, Hertzberg J (1988) Some fundamental properties of local constraint propagation. Artif Intell 36:237–247CrossRefGoogle Scholar
  34. 34.
    Han CC, Lee CH (1988) Comments on Mohr and Hendersons path consistency algorithm. Artif Intell 36:125–130CrossRefGoogle Scholar
  35. 35.
    Hendry LC (1987) The potential impact of artificial intelligence on the practice of OR. Eur J Oper Res 28:218–225CrossRefGoogle Scholar
  36. 36.
    van Hentenryck P (1989) Constraint Satisfaction in Logic Programming. MIT PressGoogle Scholar
  37. 37.
    van Hentenryck P (1989) A logic language for combinatorial optimization. Ann Oper Res 21:247–274CrossRefGoogle Scholar
  38. 38.
    van Hentenryck P, Deville Y, Teng C-M (1992) A generic arcconsistency algorithm and its specializations. Artif Intell 57:291–321CrossRefGoogle Scholar
  39. 39.
    van Hentenryck P, Simonis H, Dincbas M (1992) Constraint satisfaction using constraint logic programming. Artif Intell 58:113–159CrossRefGoogle Scholar
  40. 40.
    Jordan C, Drexl A (1993) A comparison of logic and mixed-integer programming solvers for batch sequencing with sequence-dependent setups. Arbeitspapier, Universität KielGoogle Scholar
  41. 41.
    Jost T, Skuppin R (1989) Technical Diagnosis based on numerical models using PROLOG III. Conf Proc ESPRIT '89. Kluwer, Dordrecht, pp 513–527Google Scholar
  42. 42.
    Kelly III JJ, Ford KM (1990) Diagnosis using model-based reasoning by constraint propagation: A preleminary report on monitoring NASA Space Shuttle liquid hydrogen loading. Int J Exp Syst 3:87–104Google Scholar
  43. 43.
    de Kleer J (1986) An assumption based truth maintenance system. Artif Intell 28:127–162CrossRefGoogle Scholar
  44. 44.
    Krautter W, Steinert M (1988) A knowledge representation for model-based reasoning using PROLOG III. Conf Proc ESPRIT '88. North-Holland, Amsterdam, pp 814–825Google Scholar
  45. 45.
    Kumar V (1992) Algorithms for constraint-satisfaction problems: a survey. AI Mag 13:32–44Google Scholar
  46. 46.
    Lauriere J (1978) A language and a program for stating and solving combinatorial problems. Artif Intell 10:29–127CrossRefGoogle Scholar
  47. 47.
    Leler W (1988) Constraint Programming Languages: Their Specification and Generation. Addison Wesley, Reading MassGoogle Scholar
  48. 48.
    Lodwick WA (1989) Constraint propagation, relational arithmetic in AI systems and mathematical programs. Ann Oper Res 21:143–148CrossRefGoogle Scholar
  49. 49.
    Luebbe R, Finch B (1992) Theory of constraints and linear programming: a comparison. Int J Prod Res 30:1471–1478CrossRefGoogle Scholar
  50. 50.
    Mackworth AK (1977) Consistency in networks of relations. Artif Intell 8:99–118CrossRefGoogle Scholar
  51. 51.
    Mackworth AK, Freuder EC (1985) The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artif Intell 25:65–74CrossRefGoogle Scholar
  52. 52.
    Meseguer P (1989) Constraint satisfaction problems: an overview. AICOM 2:3–17Google Scholar
  53. 53.
    Minton S, Johnston MD, Philips AB, Laird P (1992) Minimizing conflicts: A heuristic repair method for constraint satisfaction and scheduling problems. Artif Intell 58:161–205CrossRefGoogle Scholar
  54. 54.
    Mitterreiter I, Radermacher FJ (1991) Some notes on experiments on the running time behaviour of some algorithms solving propositional logical problems. Arbeitspapier, FAW UlmGoogle Scholar
  55. 55.
    Mohr R, Henderson TC (1986) Arc and path consistency revisited. Artif Intell 28:225–233CrossRefGoogle Scholar
  56. 56.
    Montanari U (1974) Networks of constraints: fundamental properties and applications to picture processing. Inf Sci 7:95–132CrossRefGoogle Scholar
  57. 57.
    Montanari U, Rossi F (1991) Constraint relaxation may be perfect. Artif Intell 48:143–170CrossRefGoogle Scholar
  58. 58.
    Nadel B (1988) Tree search and arc consistency in constraint satisfaction algorithms. In: Kanal L, Kumar V (eds) Search in Artificial Intelligence. Springer, New York, pp 287–342CrossRefGoogle Scholar
  59. 59.
    Ostroff JS (1991) Constraint logic programming for reasoning about discrete event processes. J Logic Program 11:243–270CrossRefGoogle Scholar
  60. 60.
    Petrie C (1987) Revised dependency-directed backtracking for default reasoning. Proc AAAI-87:167–172Google Scholar
  61. 61.
    Pique J-F (1988) Prolog II, a step on the Prolog road. AICOM 1:4–16Google Scholar
  62. 62.
    Saraswat VA (1993) Concurrent Constraint Programming. MIT Press, CambridgeGoogle Scholar
  63. 63.
    Sussman GJ, Steele GL (1980) CONSTRAINTS — a language for expressing almost hierarchical descriptions. Artif Intell 14:1–39CrossRefGoogle Scholar
  64. 64.
    Tank W (1993) Wissensbasiertes Konfigurieren: Ein Überblick. KI — Künstliche Intelligenz 1/93:7–10Google Scholar
  65. 65.
    Tate A (1985) A review of knowledge-based-planning techniques. Exp Syst 85:89–111Google Scholar
  66. 66.
    Waltz D (1975) Understanding line drawings of scenes with shadows. In: Winston PH (ed) Psychology of Computer Vision. McGraw Hill, Cambridge, pp 19–91Google Scholar
  67. 67.
    Winston PH (1987) Künstliche Intelligenz. Addison-Wesley, Reading MassGoogle Scholar
  68. 68.
    Young RE, Greef A, O'Grady P (1992) An artificial intelligence-based constraint network system for concurrent engineering. Int J Prod Res 30:1715–1735CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Erwin Pesch
    • 1
  • Andreas Drexl
    • 2
  • Antoon Kolen
    • 3
  1. 1.Institut für Gesellschafts- und Wirtschaftswissenschaften, BWL IIIUniversität BonnBonn
  2. 2.Lehrstuhl für Produktion und Logistik, Institut für BetriebswirtschaftslehreUniversität KielKiel
  3. 3.Faculty of Economics and Business Administration, KEUniversity of LimburgMD MaastrichtThe Netherlands

Personalised recommendations