混合分支定界学习搜索逼近的研究：SCIP中的节点选择
A Study of Learning Search Approximation in Mixed Integer Branch and Bound: Node Selection in SCIP
摘要：
随着使用机器学习来帮助解决组合优化问题的增长趋势，一个有前途的想法是通过使用学习策略来改进混合整数规划（MIP）分支定界树内的节点选择。先前的工作使用模仿学习表明，通过学习自适应节点搜索顺序获得节点选择策略的可行性。相比之下，我们的模仿学习策略只关注于学习选择节点的哪个子节点。我们提出了一个离线的方法来学习这样的政策在两个设置：一个，包括一个启发式的承诺修剪的节点;一个是准确的，并从叶回溯，以保证找到最佳的整数解。前一个设置对应于在插入期间的子选择器，而后者类似于潜水启发式。我们适用于流行的开源求解器SCIP内的政策，在启发式和精确的设置。五个MIP数据集的实证结果表明，我们的节点选择政策导致解决方案显着更快地比在文献中的国家的最先进的先例。虽然我们在精确解的求解时间方面没有击败高度优化的SCIP实践状态基线节点选择器，但如果预测模型的准确性足够，我们的启发式策略的最优性差距始终优于所有基线。此外，结果还表明，当施加时间限制时，我们的探试法在大多数测试问题中找到比所有基线更好的解决方案。我们解释的结果表明，学习的政策模仿SCIP基线，但没有后者的早期暴跌流产。我们的建议是，尽管在文献中有明显的改进，但这种MIP子选择器在MIP分支定界树决策中使用学习的更广泛方法中更好地被看到。
英文摘要：
In line with the growing trend of using machine learning to help solve combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming (MIP) branch-and-bound tree by using a learned policy. Previous work using imitation learning indicates the feasibility of acquiring a node selection policy, by learning an adaptive node searching order. In contrast, our imitation learning policy is focused solely 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 comprises a heuristic by committing to pruning of nodes; one that is exact and backtracks from a leaf to guarantee finding the optimal integer solution. The former setting corresponds to a child selector during plunging, while the latter is akin to a diving heuristic. We apply the policy within the popular open-source solver SCIP, in both heuristic and exact settings. Empirical results on five MIP datasets indicate that our node selection policy leads to solutions significantly more quickly than the state-of-the-art precedent in the literature. While we do not beat the highly-optimised SCIP state-of-practice baseline node selector in terms of solving time on exact solutions, our heuristic policies have a consistently better optimality gap than all baselines, if the accuracy of the predictive model is sufficient. Further, the results also indicate that, when a time limit is applied, our heuristic method finds better solutions than all baselines in the majority of problems tested. We explain the results by showing that the learned policies have imitated the SCIP baseline, but without the latter's early plunge abort. Our recommendation is that, despite the clear improvements over the literature, this kind of MIP child selector is better seen in a broader approach using learning in MIP branch-and-bound tree decisions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
