A Branch and Bound algorithm for numerical Max-CSP

Constraints

Volumn 15, Issue 2, 2010, Pages 213-237

  Normand, Jean Marie ^a,b   Goldsztejn, Alexandre ^a   Christie, Marc ^a,c   Benhamou, Frédéric ^a  

^a UNIVERSITÉ DE NANTES   (France)

^b UNIVERSITY OF BARCELONA   (Spain)

^c CAMPUS DE BEAULIEU   (France)

Author keywords

Constraint programming; Numerical constraints; Numerical Max CSP

Indexed keywords

BRANCH-AND-BOUND ALGORITHMS; CONSTRAINT PROBLEMS; CONSTRAINT PROGRAMMING; CONSTRAINT SATISFACTION PROBLEMS; FLOATING POINTS; MAX-CSP; OVER-CONSTRAINED; SOLUTION SET;

BRANCH AND BOUND METHOD; COMPUTER PROGRAMMING; CONSTRAINT THEORY; LINEAR PROGRAMMING; REAL VARIABLES;

APPROXIMATION ALGORITHMS;

EID: 77954759125     PISSN: 13837133     EISSN: 15729354     Source Type: Journal    
DOI: 10.1007/s10601-009-9084-1     Document Type: Conference Paper

References (29)

1. Benhamou, F., Goualard, F., Granvilliers, L., & Puget, J.-F. (1999). Revising hull and box consistency. In Proceedings of the 1999 international conference on logic programming, ICLP'99 (pp. 230-244). Cambridge, MA, USA: Massachusetts Institute of Technology.
2. Benhamou, F., Goualard, F., Languenou, E., &Christie, M. (2004). Interval constraint solving for camera control and motion planning. ACM Transactions on Computational Logic, 5(4), 732-767.
3. Benhamou, F., McAllester, D., & van Hentenryck, P. (1994). CLP(intervals) revisited. In International logic programming symposium, ILPS '94 (pp. 124-138). Cambridge: MIT.
4. Benhamou, F., & Older, W. J. (1997). Applying interval arithmetic to real, integer and Boolean constraints. Journal of Logic Programming, 32(1), 1-24.
5. Borning, A., Freeman-Benson, B., & Wilson, M. (1992). Constraint hierarchies. Lisp and Symbolic Computation, 5(3), 223-270.
6. Byrd, R. H., Nocedal, J., & Waltz, R. A. (2006). KNITRO: An integrated package for nonlinear optimization. In Large-scale nonlinear optimization (pp. 35-59). New York: Springer.
7. Christie, M., & Normand, J.-M. (2005). A semantic space partitionning approach to virtual camera control. In Proceedings of the annual eurographics conference (Vol. 24, pp. 247-256).
8. Christie, M., Normand, J.-M., & Truchet, C. (2006). Computing inner approximations of numerical MaxCSP. In Interval analysis, constraint propagation, applications, IntCP 2006.
9. Collavizza, H., Delobel, F., & Rueher, M. (1999). Extending consistent domains of numeric CSP. In IJCAI '99: Proceedings of the sixteenth international joint conference on artificial intelligence (pp. 406-413).
10. de Givry, S., Larrosa, J., Meseguer, P., & Schiex, T. (2003). Solving Max-SAT as weighted CSP. In Principles and practice of constraint programming, CP 2003 (pp. 363-376). New York: Springer.
11. Delanoue, N., Jaulin, L., & Cottenceau, B. (2004). Counting the number of connected components of a set and its application to robotics. In PARA (pp. 93-101).
12. Dongarra, J. (2007). Performance of various computers using standard linear equations software. Technical report CS-89-85, University of Tennessee.
13. Drezner, Z., & Hamacher, H. W. (Eds.) (2002). Facility location. Applications and theory. New York: Springer.
14. Goldberg, D. (1991).What every computer scientist should know about floating-point arithmetic. Computing Surveys, 23(1), 5-48.
15. Hayes, B. (2003). A lucid interval. American Scientist, 91(6), 484-488.
16. Hirsch, M. J., Meneses, C. N., Pardalos, P. M., & Resende, M. G. C. (2007). Global optimization by continuous grasp. Optimization Letters, 1, 201-212.
17. Jaulin, L., &Walter, E. (1993). Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis. Mathematics and Computers in Simulation, 35(2), 123-137.
18. Jaulin, L., & Walter, E. (2002). Guaranteed robust nonlinear minimax estimation. IEEE Transaction on Automatic Control, 47(11), 1857-1864.
19. Jaulin, L., Walter, E., & Didrit, O. (1996). Guaranteed robust nonlinear parameter bounding. In CESA'96, IMACS multiconference (symposium on modelling, analysis and simulation) (pp. 1156-1161).
20. Lhomme, O. (1993). Consistency techniques for numeric CSPs. In IJCAI '93: Proceedings of the thirteenth international joint conference on artificial intelligence (pp. 232-238).
21. Mackworth, A. K. (1977). Consistency in networks of relations. Artificial Intelligence, 8(1), 99-118.
22. Milanese, M., & Vicino, A. (1991). Estimation theory for nonlinear models and set membership uncertainty. Automatica, 27(2), 403-408.
23. Minton, S., Johnston, M. D., Philips, A. B., & Laird, P. (1992). Minimizing conflicts: A heuristic repair method for constraint satisfaction and scheduling problems. Artificial Intelligence, 58(1-3), 161-205.
24. Moore, R. E. (1966). Interval analysis. Englewood Cliffs: Prentice-Hall.
25. Murtagh, B. A., & Saunders, M. A. (1998). Minos 5.5 user's guide. Technical report, Systems Optimization Laboratory, Department of Operations Research, Stanford University.
26. Neumaier, A. (1990). Interval methods for systems of equations. Cambridge: Cambridge University Press.
27. Normand, J.-M. (2008). Placement de caméra en environnements virtuels. PhDthesis, Université de Nantes.
28. Petit, T., Régin, J.-C., & Bessière, C. (2002). Range-based algorithm for Max-CSP. In Principles and practice of constraint programming, CP 2002 (pp. 280-294). New York: Springer.
29. Wallace, R. J. (1996). Analysis of heuristic methods for partial constraint satisfaction problems. In Principles and practice of constraint programming, CP 1996 (pp. 482-496). New York: Springer.