Abstract
In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of “good” methods. These comparisons often led us to consider FC or FC-CBJ associated with a “minimum domain” variable ordering heuristic as the best techniques to solve a wide variety of constraint networks.
In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
F. Bacchus and P. van Run. Dynamic variable ordering in csps. In Proceedings CP '95, pages 258–275, Cassis, France, 1995.
C. Bessière. Systèmes à contraintes évolutifs en intelligence artificielle. Phd thesis, LIRMM, University of Montpellier II, September 1992. (in French).
C. Bessière, E.C. Freuder, and J.C. Régin. Using inference to reduce arc consistency computation. In Proceedings IJCAI'95, pages 592–598, Montréal, Canada, 1995.
R. Dechter. Learning while searching in constraint satisfaction problems. In Proceedings AAAI'86, pages 178–183, Philadelphia PA, 1986.
R. Dechter and I. Meiri. Experimental evaluation of preprocessing algorithms for constraint satisfaction problems. Artificial Intelligence, 68:211–241, 1994.
R. Dechter and I. Pearl. Network-based heuristics for constraint-satisfaction problems. Artificial Intelligence, 34:1–38, 1988.
M.J. Dent and R.E. Mercer. Using local topology to model hard binary constraint satisfaction problems. In Proceedings of the workshop —Studying and Solving Really Hard Problems-CP'95, pages 52–61, Cassis, France, 1995.
O Dubois. Private communication, 1995.
E.C. Freuder. A sufficient condition for backtrack-free search. Journal of the ACM, 29(1):24–32, 1982.
D. Frost and R. Dechter. In search of the best constraint satisfaction search. In Proceedings AAAI'94, pages 301–306, Seattle WA, 1994.
D. Frost and R. Dechter. Look-ahead value ordering for constraint satisfaction problems. In Proceedings IJCAI-95, pages 572–578, Montréal, Canada, 1995.
J. Gaschnig. A general backtrack algorithm that eliminates most redundant tests. In froceedings IJCAI'77, page 457, Cambridge MA, 1977.
J Gaschnig. Performance measurement and analysis of certain search algorithms. Technical Report CMU-CS-79-124, Carnegie-Mellon University, Pittsburgh PA, 1979.
P.A.Geelen. Dual viewpoint heuristics for binary constraint satisfaction problems. In Proceedings ECAI'92, pages 31–35, Vienna, Austria, 1992.
M.L. Ginsberg, M. Frank, M.P. Halpin, and M.C. Torrance. Search lessons learned from crossword puzzles. In Proceedings AAAI'90, pages 210–215, Boston MA, 1990.
R.M. Haralick and G.L. Elliot. Increasing tree seach efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263–313, 1980.
W.D. Harvey and M.L. Ginsberg. Limited discrepancy search. In Proceedings IJCAI'95, pages 607–613, Montréal, Canada, 1995.
P.D. Hubbe and E.C. Freuder. An efficient cross product representation of the constraint satisfaction problem search space. In Proceedings AAAI'92, pages 421–427, San José CA, 1992.
V. Kumar. Algorithms for constraint-satisfaction problems: A survey. AI Magazine, 13(1):32–44, Spring 1992.
B.A. Nadel. Tree search and arc consistency in constraint satisfaction algorithms. In L.Kanal and V.Kumar, editors, Search in Artificial Intelligence, pages 287–342. Springer-Verlag, 1988.
B.A. Nadel. Constraint satisfaction algorithms. Computational Intelligence, 5:188–224, 1989.
P. Prosser. Domain filtering can degrade intelligent backtracking search. In Proceedings IJCAI'93, pages 262–267, Chambéry, France, 1993.
P. Prosser. Hybrid algorithms for the constraint satisfaction problem. Computational Intelligence, 9(3):268–299, August 1993.
P. Prosser. Binary constraint satisfaction problems: some are harder than others. In Proceedings ECAI'94, pages 95–99, Amsterdam, The Netherlands, 1994.
P. Prosser. Mac-cbj: maintaining arc consistency with conflict-directed backjumping. Technical Report 95-177, Department of Computer Science, University of Starthclyde, 1995.
J.F. Puget. Ilog solver. In J. Gensel, editor, Journées Contraintes et Objets, Grenoble, France, November 1992. (in French).
P.W. Purdom. Search rearrangement backtracking and polynomial average time. Artificial Intelligence, 21:117–133, 1983.
D. Sabin and E. Freuder. Contradicting conventional wisdom in constraint satisfaction. In Alan Borning, editor, PPCP'94: Second Workshop on Principles and Practice of Constraint Programming, Seattle WA, May 1994.
B. Smith. The phase transition in constraint satisfaction problems: A closer look at the mushy region. In Proceedings ECAI'94, pages 100–104, Amsterdam, The Netherlands, 1994.
B. Smith and S.A. Grant. Sparse constraint graphs and exceptionally hard problems. In Proceedings IJCAI'95, pages 646–651, Montréal, Canada, 1995.
B. Smith and S.A. Grant. Where the exceptionally hard problems are. In Proceedings of the workshop —Studying and Solving Really Hard Problems-, CP'95, pages 172–182, Cassis, France, 1995.
Pascal Van Hentenryck. Constraint Satisfaction in Logic Programming. MIT Press, Cambridge, MA, 1989.
R. J. Wallace and E.C. Freuder. Conjunctive width heuristics for maximal constraint satisfaction. In Proceedings AAAI'93, pages 762–768, Washington D.C., 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bessière, C., Régin, JC. (1996). MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems. In: Freuder, E.C. (eds) Principles and Practice of Constraint Programming — CP96. CP 1996. Lecture Notes in Computer Science, vol 1118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61551-2_66
Download citation
DOI: https://doi.org/10.1007/3-540-61551-2_66
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61551-4
Online ISBN: 978-3-540-70620-5
eBook Packages: Springer Book Archive