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Mathematical Problems in Engineering
Volume 2015, Article ID 580785, 12 pages
Research Article

Top- Based Adaptive Enumeration in Constraint Programming

1Pontificia Universidad Católica de Valparaíso, 2362807 Valparaíso, Chile
2Universidad Autónoma de Chile, 7500138 Santiago, Chile
3Universidad Central de Chile, 8370178 Santiago, Chile
4Universidad Finis Terrae, 7501015 Santiago, Chile
5Facultad de Ingeniería y Tecnología, Universidad San Sebastián, 8420524 Santiago, Chile
6CNRS, LINA, University of Nantes, 44322 Nantes, France
7Universidad de Valparaíso, 2362735 Valparaíso, Chile
8Universidad Técnica Federico Santa María, 2390123 Valparaíso, Chile
9Escuela de Ingeniería Industrial, Universidad Diego Portales, 8370109 Santiago, Chile

Received 23 October 2014; Accepted 3 February 2015

Academic Editor: Youqing Wang

Copyright © 2015 Ricardo Soto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Constraint programming effectively solves constraint satisfaction and optimization problems by basically building, pruning, and exploring a search tree of potential solutions. In this context, a main component is the enumeration strategy, which is responsible for selecting the order in which variables and values are selected to build a possible solution. This process is known to be quite important; indeed a correct selection can reach a solution without failed explorations. However, it is well known that selecting the right strategy is quite challenging as their performance is notably hard to predict. During the last years, adaptive enumeration appeared as a proper solution to this problem. Adaptive enumeration allows the solving algorithm being able to autonomously modifying its strategies in solving time depending on performance information. In this way, the most suitable order for variables and values is employed along the search. In this paper, we present a new and more lightweight approach for performing adaptive enumeration. We incorporate a powerful classification technique named Top- in order to adaptively select strategies along the resolution. We report results on a set of well-known benchmarks where the proposed approach noticeably competes with classical and modern adaptive enumeration methods for constraint satisfaction.