Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Using Graph Decomposition for Solving Continuous CSPs
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Efficient and Safe Global Constraints for Handling Numerical Constraint Systems
SIAM Journal on Numerical Analysis
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Algorithms for identifying rigid subsystems in geometric constraint systems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Inter-block backtracking: exploiting the structure in continuous CSPs
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Search heuristics for constraint-aided embodiment design
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Artificial Intelligence
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Constructive interval disjunction
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Filtering numerical CSPs using well-constrained subsystems
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
| Hi-index | 0.00 |
Inter-block backtracking (IBB) computes all the solutions of sparse systems of non-linear equations over the reals. This algorithm, introduced in 1998 by Bliek et al., handles a system of equations previously decomposed into a set of (small) k ×k sub-systems, called blocks. Partial solutions are computed in the different blocks and combined together to obtain the set of global solutions. When solutions inside blocks are computed with interval-based techniques, IBB can be viewed as a new interval-based algorithm for solving decomposed equation systems. Previous implementations used Ilog Solver and its IlcInterval library. The fact that this interval-based solver was more or less a black box implied several strong limitations. The new results described in this paper come from the integration of IBB with the interval-based library developed by the second author. This new library allows IBB to become reliable (no solution is lost) while still gaining several orders of magnitude w.r.t. solving the whole system. We compare several variants of IBB on a sample of benchmarks, which allows us to better understand the behavior of IBB. The main conclusion is that the use of an interval Newton operator inside blocks has the most positive impact on the robustness and performance of IBB. This modifies the influence of other features, such as intelligent backtracking and filtering strategies.