Keeping the Routes Open: Optimal Maintenance of Infrastructure Networks.

众所周知，大规模运输基础设施的维护和维修非常昂贵，当这种基础设施的部件受损时，效率和能力的损失也是如此。因此，以最佳方式分配资源以维护这类基础设施是有意义的。具体地说，考虑到基础设施处于某种给定的维修或年久失修状态，某些路线运行良好，而其他路线已损坏且不适合使用，我们希望选择或优先选择某些路线进行维修，以便尽可能有效地分配资源。这些决策也必须按顺序做出：每次已知一条新的路线已损坏，或正在进行的修复已经完成，我们都想对下一步做什么做出新的决定。已有通用算法学习以最优方式控制这些顺序决策问题。对于我们的问题，最优控制意味着我们将正在进行的维修和长期产能损失的平均综合成本降至最低。然而，对于像我们这样的复杂问题，这些算法众所周知非常慢，因此不适合，所以我们必须将注意力转向更接近或启发式(经验法则)的技术。这样的技术可以明确地包含对问题的任何理论理解，允许通过利用任何已知属性来更快地学习最佳方法。这类技术的创建和评估，以及理论性质的发现或证明，是我们研究的重点。我们希望通过找到合适的近似或启发式方法，这些技术可以推广并应用于任何基于网络的基础设施，并产生比任何简单的幼稚方法更好的结果。与海军研究生院合作。

The maintenance and repair of large-scale transportation infrastructure is known to be very costly, as is the loss of efficiency and capacity when components of such infrastructure has been damaged. It is therefore of interest to allocate resources optimally to maintain such infrastructure. Specifically, given that the infrastructure is in some given state of repair or disrepair, with certain routes operating well and other routes damaged and not fit for use, we want to select or prioritise certain routes for repair so as to allocate resources as efficiently as possible. These decisions must also be made sequentially: every time a new route is known to have been damaged, or an ongoing repair has been completed, we want to make a new decision on what to do next.Generic algorithms already exist which learn to control these sequential decision-making problems optimally. For our problem, optimal control would mean that we minimise the average combined cost of ongoing repairs and loss of capacity over a long period of time. However, for complicated problems such as ours, these algorithms are known to be extremely slow and are therefore unsuitable, so we must turn our attention to more approximate or heuristic (rule-of-thumb) techniques. Such techniques can explicitly incorporate any theoretical understanding of the problem, allowing optimal approaches to be learned much faster by exploiting any known properties. It is the creation and evaluation of such techniques, and the discovery or proof of theoretical properties, that is the focus of our research.Our hope is that by finding suitable approximations or heuristics, these could be rolled out and applied to any network-based infrastructure, and yield results that outperform any simple naive approaches. In partnership with Naval Postgraduate School.