Abstract
In this paper, we improved two classical degree-based variable ordering heuristics, \(\frac{\textit{Dom}}{\textit{Ddeg}}\) and \(\frac{\textit{Dom}}{\textit{Wdeg}}\). We propose a method using the summation of constraint tightness in degree-based heuristics. We also propose two methods to calculate dynamic constraint tightness for binary extensional constraints and non-binary intensional constraints respectively. Our work shows how constraint tightness can be practically used to guide search. We performed a number of experiments on some benchmark instances. The results have shown that, the new heuristics improve the classical ones by both computational time and search tree nodes and they are more efficient than some other successful heuristics on the instances where the classical heuristics work well.
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All these instances are available at http://www.cril.univ-artois.fr/~lecoutre/benchmarks.html.
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Acknowledgments
We would like to thank the anonymous reviewers for their helpful comments and suggestions. Hongbo Li was partially supported by China Scholarship Council. The authors are grateful to the support of the NSFC (61472158, 61272207, 61202306).
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Li, H., Liang, Y., Zhang, N. et al. Improving degree-based variable ordering heuristics for solving constraint satisfaction problems. J Heuristics 22, 125–145 (2016). https://doi.org/10.1007/s10732-015-9305-2
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DOI: https://doi.org/10.1007/s10732-015-9305-2