Abstract
We consider the problem of selecting the best variable-value strategy for solving a given problem in constraint programming. We show that the recent Embarrassingly Parallel Search method (EPS) can be used for this purpose. EPS proposes to solve a problem by decomposing it in many subproblems and to give them on-demand to workers which run in parallel. Our method uses a sample of these subproblems for comparing strategies in order to select the most promising one to be used for solving the remaining subproblems. Each subproblem of the sample is solved with all the candidate strategies in parallel using a timeout that is twice the time of the best one. The selection of the strategy is then based on the Wilcoxon signed rank test. This test is able to deal with censored data caused by timeouts and makes no assumption on the solving time distribution. The experiments we performed on a set of classical benchmarks for satisfaction and optimization problems show that our method selects most of the time the best strategy. Our method also outperforms the portfolio approach consisting of running some strategies in parallel and is competitive with the multi armed bandit framework.
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Notes
- 1.
We do not claim that this computation is accurate. We present it only for understanding the intuitive idea.
- 2.
Roughly the activity is defined by the number of times the variables has been introduced in the propagation queue. The activity is increased at most by one for each decision.
- 3.
The weighted degree of a variable is defined by a counter associated with it. Each time a constraint fails, the counter of each variable involved in the constraint is increased by one.
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Acknowledgments
We would like to thank Guillaume Perez for his useful comments and for his help in the multi-armed bandit algorithm, and also the anonymous reviewer who made a lot of comments who helped us to improve this paper.
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Palmieri, A., Régin, JC., Schaus, P. (2016). Parallel Strategies Selection. In: Rueher, M. (eds) Principles and Practice of Constraint Programming. CP 2016. Lecture Notes in Computer Science(), vol 9892. Springer, Cham. https://doi.org/10.1007/978-3-319-44953-1_25
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