arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1809.03359cs.AI
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使用机器学习改进优化边界:决策图满足深度强化学习

Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning

Ecole Polytechnique de Montréal(蒙特利尔综合理工学院);Element AI;Ecole Polytechnique(巴黎综合理工学院);University of Connecticut(康涅狄格大学)

Quentin Cappart, Emmanuel Goutierre, David Bergman, Louis-Martin Rousseau

摘要:

寻找最优解的紧界是离散优化问题的实用求解方法的关键要素。在过去的十年中,决策图(DD)带来了一个新的视角来获得上界和下界,可以显着优于经典的边界机制,如线性松弛。众所周知,通过这种灵活的边界方法实现的边界的质量高度依赖于为构建图而选择的变量的排序,并且找到优化标准度量的排序是NP难问题。在本文中,我们提出了一种基于深度强化学习的创新和通用方法,用于获得用于收紧用放松和限制DD获得的边界的排序。我们将这种方法应用于最大独立集问题和最大割问题。对合成实例的实验结果表明,当实例的分布已知时,通过实现更严格的目标函数界限,深度强化学习方法通常优于文献中常用的排序方法。据作者所知,这是第一篇应用机器学习来直接改进组合优化问题的通用边界机制所获得的松弛边界的论文。

英文摘要:

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bounds achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems.

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。

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