Enhancing interval constraint propagation by identifying and filtering n-ary subsystems
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When interval branch and bound solvers are used for solving numerical constraint satisfaction problems, constraint propagation algorithms are commonly used for filtering/contracting the variable domains. However, these algorithms suffer from the locality problem which is related to the reduced scope of local consistencies. In this work we propose a preprocessing and a filtering technique to reduce the locality problem and to enhance the contraction power of constraint propagation algorithms. The preprocessing consists in constructing a directed acyclic graph (DAG) by merging equivalent nodes (or common subexpressions) and identifying subsystems of n-ary sums in the DAG. The filtering technique consists in applying iteratively HC4 and an ad-hoc technique for contracting the subsystems until reaching a fixed point. Experiments show that the new approach outperforms state-of-the-art strategies using a well known set of benchmark instances.
KeywordsInterval-based solver Common subexpression elimination Constraint propagation Systems of nonlinear equations
This work is supported by the Fondecyt Project 1160224. Victor Reyes is supported by the Grant Postgrado PUCV 2017.
- 3.Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.-F.: Revising hull and box consistency. In: International Conference on Logic Programming, Citeseer (1999)Google Scholar
- 4.Moore, R.: Interval analysis. Series in automatic computation. Prentice-Hall, Englewood Cliff, N.J. (1966)Google Scholar
- 6.Araya, I., Neveu, B., Trombettoni, G.: Exploiting common subexpressions in numerical CSPs. In: Principles and Practice of Constraint Programming (CP 2008). Springer, pp. 342–357 (2008)Google Scholar
- 8.Ceberio, M., Granvilliers, L.: Solving nonlinear equations by abstraction, Gaussian elimination, and interval methods. In: Frontiers of Combining Systems. Springer, pp. 117–131 (2002)Google Scholar
- 12.Neveu, B., Trombettoni, G., et al.: Adaptive constructive interval disjunction. In: International Conference on Tools with Artificial Intelligence (ICTAI), pp. 900–906 (2013)Google Scholar
- 14.Trombettoni, G., Araya, I., Neveu, B., Chabert, G.: Inner regions and interval linearizations for global optimization. In: AAAI Conference on Artificial Intelligence, pp. 99–104 (2011)Google Scholar
- 15.Ninin, J., Messine, F., Hansen, P.: A reliable affine relaxation method for global optimization. 4OR, vol. 13, no. 3, pp. 247–277 (2015)Google Scholar
- 16.Araya, I., Trombettoni, G., Neveu, B.: A contractor based on convex interval Taylor. In: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. Springer, pp. 1–16 (2012)Google Scholar