Explanations for identifying and exploiting structures within combinatorial problems

Hadrien Cambazard; Narendra Jussien

RAIRO - Operations Research (2007)

  • Volume: 40, Issue: 4, page 381-401
  • ISSN: 0399-0559

Abstract

top
Identifying structure in a given combinatorial problem is often a key step for designing efficient search heuristics or for understanding the inherent complexity of the problem. Several Operations Research approaches apply decomposition or relaxation strategies upon such a structure identified within a given problem. The next step is to design algorithms that adaptively integrate that kind of information during search. We claim in this paper, inspired by previous work on impact-based search strategies for constraint programming, that using an explanation-based constraint solver may lead to collect invaluable information on the intimate dynamic and static structure of a problem instance.

How to cite

top

Cambazard, Hadrien, and Jussien, Narendra. "Des explications pour reconnaître et exploiter les structures cachées d'un problème combinatoire." RAIRO - Operations Research 40.4 (2007): 381-401. <http://eudml.org/doc/105355>.

@article{Cambazard2007,
abstract = { L'identification de structures propres à un problème est souvent une étape clef pour la conception d'heuristiques de recherche comme pour la compréhension de la complexité du problème. De nombreuses approches en Recherche Opérationnelle emploient des stratégies de relaxation ou de décomposition dès lors que certaines struc- tures idoines ont été identifiées. L'étape suivante est la conception d'algorithmes de résolution qui puissent intégrer à la volée, pendant la résolution, ce type d'information. Cet article propose d'utiliser un solveur de contraintes à base d'explications pour collecter une information pertinente sur les structures dynamiques et statiques inhérentes au problème. },
author = {Cambazard, Hadrien, Jussien, Narendra},
journal = {RAIRO - Operations Research},
keywords = {Programmation par contraintes; explications.; impact-based search strategies; constraint programming},
language = {fre},
month = {2},
number = {4},
pages = {381-401},
publisher = {EDP Sciences},
title = {Des explications pour reconnaître et exploiter les structures cachées d'un problème combinatoire},
url = {http://eudml.org/doc/105355},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Cambazard, Hadrien
AU - Jussien, Narendra
TI - Des explications pour reconnaître et exploiter les structures cachées d'un problème combinatoire
JO - RAIRO - Operations Research
DA - 2007/2//
PB - EDP Sciences
VL - 40
IS - 4
SP - 381
EP - 401
AB - L'identification de structures propres à un problème est souvent une étape clef pour la conception d'heuristiques de recherche comme pour la compréhension de la complexité du problème. De nombreuses approches en Recherche Opérationnelle emploient des stratégies de relaxation ou de décomposition dès lors que certaines struc- tures idoines ont été identifiées. L'étape suivante est la conception d'algorithmes de résolution qui puissent intégrer à la volée, pendant la résolution, ce type d'information. Cet article propose d'utiliser un solveur de contraintes à base d'explications pour collecter une information pertinente sur les structures dynamiques et statiques inhérentes au problème.
LA - fre
KW - Programmation par contraintes; explications.; impact-based search strategies; constraint programming
UR - http://eudml.org/doc/105355
ER -

References

top
  1. D. Achlioptas, L. Kirousis, E. Kranakis, D. Krizanc, M. Molloy and Y. Stamatiou, Random constraint satisfaction: a more accurate picture, in Proceedings CP 1997, Linz, Austria (1997) 121–135.  
  2. J.F. Benders, Partitionning procedures for solving mixed-variables programming problems. Numer. Math.4 (1962) 238–252.  
  3. C. Bessière, A. Chmeiss and L. Saïs, Neighborhood-based variable ordering heuristics for the constraint satisfaction problem, in Proceeding CP'01, Paphos, Cyprus (2001) 565–569. Short paper.  
  4. C. Bessiere and J.C. Regin, MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems, in Proceeding CP'96 (1996) 61–75.  
  5. F. Boussemart, F. Hemery, C. Lecoutre and L. Sais, Boosting systematic search by weighting constraints, in Proceedings ECAI'04 (2004) 482–486.  
  6. B. Cabon, S. de Givry, L. Lobjois, T. Schiex and J.P. Warners, Radio Link Frequency Assignment. Constraints4 (1999) 79–89.  
  7. H. Cambazard, P.-E. Hladik, A.-M. Déplanche, N. Jussien and Y. Trinquet, Decomposition and learning for a real time task allocation problem, in Proceedings CP 2004 (2004) 153–167.  
  8. H. Cambazard and N. Jussien, Integrating Benders decomposition within Constraint Programming, in Proceedings CP 2005 (2005) 752–756. Short paper.  
  9. G. Cleuziou, L. Martin and C. Vrain, Disjunctive learning with a soft-clustering method, in ILP'03:13th International Conference on Inductive Logic Programming, LNCS, September (2003) 75–92.  
  10. A.M. Geoffrion, Generalized Benders Decomposition. J. Optim. Theory Practice10 (1972) 237–260.  
  11. M. Ghoniem, N. Jussien and J.-D. Fekete, VISEXP: visualizing constraint solver dynamics using explanations, in Proceedings FLAIRS'04, Miami, Florida, USA, May (2004) 263–268.  
  12. C.P. Gomes, B.t Selman and N. Crato, Heavy-tailed distributions in combinatorial search, in Proceeding CP 97, Linz, Austria (1997) 121–135.  
  13. R. Haralick and G. Elliot, Increasing tree search efficiency for constraint satisfaction problems. Artificial intelligence14 (1980) 263–313.  
  14. J.N. Hooker and G. Ottosson, Logic-based benders decomposition. Math. Program.96 (2003) 33–60.  
  15. V. Jain and I.E. Grossmann, Algorithms for hybrid MILP/CP models for a class of optimization problems. Informs J. Comput.13 (2001) 258–276.  
  16. N. Jussien, The versatility of using explanations within constraint programming. Habilitation thesis, Université de Nantes, France, also available as RR-03-04 research report at École des Mines de Nantes (2003).  
  17. N. Jussien and V. Barichard, The PaLM system: explanation-based constraint programming, in Proceedings of TRICS: Techniques foR Implementing Constraint programming Systems, a post-conference workshop of CP 2000, Singapore (2000) 118–133.  
  18. N. Jussien, R. Debruyne and P. Boizumault, Maintaining arc-consistency within dynamic backtracking, in Proceedings CP 2000, edited by R. Dechter, Singapore (2000) 249–261.  
  19. N. Jussien and O. Lhomme, Local search with constraint propagation and conflict-based heuristics. Artificial Intelligence139 (2002) 21–45.  
  20. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman and L. Troyanski, Determining computational complexity for characteristic `phase transitions', in Nature400 (1999) 133–137.  
  21. P. Prosser, MAC-CBJ: maintaining arc-consistency with conflict-directed backjumping. Research report 95/177, Department of Computer Science – University of Strathclyde (2005).  
  22. P. Prosser, K. Stergiou and T. Walsh, Singleton consistencies, in Proceedings CP 2000, edited by R. Dechter, Singapore (2000) 353–368.  
  23. P. Refalo, Impact-based search strategies for constraint programming, in Proceedings CP 2004, Toronto, Canada (2004) 556–571.  
  24. J.-C. Régin, A filtering algorithm for constraints of difference in CSPs, in AAAI 94, Twelth National Conference on Artificial Intelligence, Seattle, Washington (1994) 362–367.  
  25. R. Williams, C. Gomes and B. Selman, On the connections between backdoors and heavy-tails on combinatorial search, in the International Conference on Theory and Applications of Satisfiability Testing (SAT) (2003).  
  26. Ryan Williams, Carla P. Gomes, and Bart Selman. Backdoors to typical case complexity, in Proceedings IJCAI 2003 (2003).  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.