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Learning Efficient Search Approximation in Mixed Integer Branch and Bound
arXiv - CS - Neural and Evolutionary Computing Pub Date : 2020-07-08 , DOI: arxiv-2007.03948
Kaan Yilmaz and Neil Yorke-Smith

In line with the growing trend of using machine learning to improve solving of combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming branch-and-bound tree by using a learned policy. In contrast to previous work using imitation learning, our policy is focused on learning which of a node's children to select. We present an offline method to learn such a policy in two settings: one that is approximate by committing to pruning of nodes; one that is exact and backtracks from a leaf to use a different strategy. We apply the policy within the popular open-source solver SCIP. Empirical results on four MIP datasets indicate that our node selection policy leads to solutions more quickly than the state-of-the-art in the literature, but not as quickly as the state-of-practice SCIP node selector. While we do not beat the highly-optimised SCIP baseline in terms of solving time on exact solutions, our approximation-based policies have a consistently better optimality gap than all baselines if the accuracy of the predictive model adds value to prediction. Further, the results also indicate that, when a time limit is applied, our approximation method finds better solutions than all baselines in the majority of problems tested.

中文翻译:

学习混合整数分支定界中的高效搜索近似

与使用机器学习来改进组合优化问题求解的增长趋势相一致,一个有前景的想法是通过使用学习策略来改进混合整数规划分支定界树中的节点选择。与之前使用模仿学习的工作相比,我们的策略侧重于学习选择节点的哪些子节点。我们提出了一种离线方法来在两种设置中学习这种策略:一种是通过承诺修剪节点来近似的;一个精确的并从叶子回溯以使用不同的策略。我们在流行的开源求解器 SCIP 中应用该策略。四个 MIP 数据集的实证结果表明,我们的节点选择策略比文献中的最新技术更快地得出解决方案,但不如实践状态 SCIP 节点选择器快。虽然我们在精确解的求解时间方面没有超过高度优化的 SCIP 基线,但如果预测模型的准确性为预测增加了价值,我们基于近似的策略具有始终比所有基线更好的最优差距。此外,结果还表明,当应用时间限制时,我们的近似方法在大多数测试问题中找到了比所有基线更好的解决方案。
更新日期:2020-07-09
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